Overview
| Comment: | Created branch optimise-algebraic-equations |
|---|---|
| Downloads: | Tarball | ZIP archive | SQL archive |
| Timelines: | family | ancestors | descendants | both | origin/optimise-algebraic-equations | trunk |
| Files: | files | file ages | folders |
| SHA3-256: |
d7af98a1bae1303a077dacb07cf6fd79 |
| User & Date: | gawthrop@users.sourceforge.net on 2002-07-10 14:55:19 |
| Other Links: | branch diff | manifest | tags |
Context
|
2002-07-10
| ||
| 15:02:33 | Updated from main branch. check-in: 4749685170 user: geraint@users.sourceforge.net tags: origin/optimise-algebraic-equations, trunk | |
| 14:55:19 | Created branch optimise-algebraic-equations check-in: d7af98a1ba user: gawthrop@users.sourceforge.net tags: origin/optimise-algebraic-equations, trunk | |
|
2002-06-21
| ||
| 13:30:59 | Reformat input line for rates and outputs as well as algebraic equations. check-in: a5d8bcd452 user: geraint@users.sourceforge.net tags: origin/optimise-algebraic-equations, trunk | |
Changes
Added mttroot/mtt/doc/mtt.texi version [677998cd3f].
> > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 2059 2060 2061 2062 2063 2064 2065 2066 2067 2068 2069 2070 2071 2072 2073 2074 2075 2076 2077 2078 2079 2080 2081 2082 2083 2084 2085 2086 2087 2088 2089 2090 2091 2092 2093 2094 2095 2096 2097 2098 2099 2100 2101 2102 2103 2104 2105 2106 2107 2108 2109 2110 2111 2112 2113 2114 2115 2116 2117 2118 2119 2120 2121 2122 2123 2124 2125 2126 2127 2128 2129 2130 2131 2132 2133 2134 2135 2136 2137 2138 2139 2140 2141 2142 2143 2144 2145 2146 2147 2148 2149 2150 2151 2152 2153 2154 2155 2156 2157 2158 2159 2160 2161 2162 2163 2164 2165 2166 2167 2168 2169 2170 2171 2172 2173 2174 2175 2176 2177 2178 2179 2180 2181 2182 2183 2184 2185 2186 2187 2188 2189 2190 2191 2192 2193 2194 2195 2196 2197 2198 2199 2200 2201 2202 2203 2204 2205 2206 2207 2208 2209 2210 2211 2212 2213 2214 2215 2216 2217 2218 2219 2220 2221 2222 2223 2224 2225 2226 2227 2228 2229 2230 2231 2232 2233 2234 2235 2236 2237 2238 2239 2240 2241 2242 2243 2244 2245 2246 2247 2248 2249 2250 2251 2252 2253 2254 2255 2256 2257 2258 2259 2260 2261 2262 2263 2264 2265 2266 2267 2268 2269 2270 2271 2272 2273 2274 2275 2276 2277 2278 2279 2280 2281 2282 2283 2284 2285 2286 2287 2288 2289 2290 2291 2292 2293 2294 2295 2296 2297 2298 2299 2300 2301 2302 2303 2304 2305 2306 2307 2308 2309 2310 2311 2312 2313 2314 2315 2316 2317 2318 2319 2320 2321 2322 2323 2324 2325 2326 2327 2328 2329 2330 2331 2332 2333 2334 2335 2336 2337 2338 2339 2340 2341 2342 2343 2344 2345 2346 2347 2348 2349 2350 2351 2352 2353 2354 2355 2356 2357 2358 2359 2360 2361 2362 2363 2364 2365 2366 2367 2368 2369 2370 2371 2372 2373 2374 2375 2376 2377 2378 2379 2380 2381 2382 2383 2384 2385 2386 2387 2388 2389 2390 2391 2392 2393 2394 2395 2396 2397 2398 2399 2400 2401 2402 2403 2404 2405 2406 2407 2408 2409 2410 2411 2412 2413 2414 2415 2416 2417 2418 2419 2420 2421 2422 2423 2424 2425 2426 2427 2428 2429 2430 2431 2432 2433 2434 2435 2436 2437 2438 2439 2440 2441 2442 2443 2444 2445 2446 2447 2448 2449 2450 2451 2452 2453 2454 2455 2456 2457 2458 2459 2460 2461 2462 2463 2464 2465 2466 2467 2468 2469 2470 2471 2472 2473 2474 2475 2476 2477 2478 2479 2480 2481 2482 2483 2484 2485 2486 2487 2488 2489 2490 2491 2492 2493 2494 2495 2496 2497 2498 2499 2500 2501 2502 2503 2504 2505 2506 2507 2508 2509 2510 2511 2512 2513 2514 2515 2516 2517 2518 2519 2520 2521 2522 2523 2524 2525 2526 2527 2528 2529 2530 2531 2532 2533 2534 2535 2536 2537 2538 2539 2540 2541 2542 2543 2544 2545 2546 2547 2548 2549 2550 2551 2552 2553 2554 2555 2556 2557 2558 2559 2560 2561 2562 2563 2564 2565 2566 2567 2568 2569 2570 2571 2572 2573 2574 2575 2576 2577 2578 2579 2580 2581 2582 2583 2584 2585 2586 2587 2588 2589 2590 2591 2592 2593 2594 2595 2596 2597 2598 2599 2600 2601 2602 2603 2604 2605 2606 2607 2608 2609 2610 2611 2612 2613 2614 2615 2616 2617 2618 2619 2620 2621 2622 2623 2624 2625 2626 2627 2628 2629 2630 2631 2632 2633 2634 2635 2636 2637 2638 2639 2640 2641 2642 2643 2644 2645 2646 2647 2648 2649 2650 2651 2652 2653 2654 2655 2656 2657 2658 2659 2660 2661 2662 2663 2664 2665 2666 2667 2668 2669 2670 2671 2672 2673 2674 2675 2676 2677 2678 2679 2680 2681 2682 2683 2684 2685 2686 2687 2688 2689 2690 2691 2692 2693 2694 2695 2696 2697 2698 2699 2700 2701 2702 2703 2704 2705 2706 2707 2708 2709 2710 2711 2712 2713 2714 2715 2716 2717 2718 2719 2720 2721 2722 2723 2724 2725 2726 2727 2728 2729 2730 2731 2732 2733 2734 2735 2736 2737 2738 2739 2740 2741 2742 2743 2744 2745 2746 2747 2748 2749 2750 2751 2752 2753 2754 2755 2756 2757 2758 2759 2760 2761 2762 2763 2764 2765 2766 2767 2768 2769 2770 2771 2772 2773 2774 2775 2776 2777 2778 2779 2780 2781 2782 2783 2784 2785 2786 2787 2788 2789 2790 2791 2792 2793 2794 2795 2796 2797 2798 2799 2800 2801 2802 2803 2804 2805 2806 2807 2808 2809 2810 2811 2812 2813 2814 2815 2816 2817 2818 2819 2820 2821 2822 2823 2824 2825 2826 2827 2828 2829 2830 2831 2832 2833 2834 2835 2836 2837 2838 2839 2840 2841 2842 2843 2844 2845 2846 2847 2848 2849 2850 2851 2852 2853 2854 2855 2856 2857 2858 2859 2860 2861 2862 2863 2864 2865 2866 2867 2868 2869 2870 2871 2872 2873 2874 2875 2876 2877 2878 2879 2880 2881 2882 2883 2884 2885 2886 2887 2888 2889 2890 2891 2892 2893 2894 2895 2896 2897 2898 2899 2900 2901 2902 2903 2904 2905 2906 2907 2908 2909 2910 2911 2912 2913 2914 2915 2916 2917 2918 2919 2920 2921 2922 2923 2924 2925 2926 2927 2928 2929 2930 2931 2932 2933 2934 2935 2936 2937 2938 2939 2940 2941 2942 2943 2944 2945 2946 2947 2948 2949 2950 2951 2952 2953 2954 2955 2956 2957 2958 2959 2960 2961 2962 2963 2964 2965 2966 2967 2968 2969 2970 2971 2972 2973 2974 2975 2976 2977 2978 2979 2980 2981 2982 2983 2984 2985 2986 2987 2988 2989 2990 2991 2992 2993 2994 2995 2996 2997 2998 2999 3000 3001 3002 3003 3004 3005 3006 3007 3008 3009 3010 3011 3012 3013 3014 3015 3016 3017 3018 3019 3020 3021 3022 3023 3024 3025 3026 3027 3028 3029 3030 3031 3032 3033 3034 3035 3036 3037 3038 3039 3040 3041 3042 3043 3044 3045 3046 3047 3048 3049 3050 3051 3052 3053 3054 3055 3056 3057 3058 3059 3060 3061 3062 3063 3064 3065 3066 3067 3068 3069 3070 3071 3072 3073 3074 3075 3076 3077 3078 3079 3080 3081 3082 3083 3084 3085 3086 3087 3088 3089 3090 3091 3092 3093 3094 3095 3096 3097 3098 3099 3100 3101 3102 3103 3104 3105 3106 3107 3108 3109 3110 3111 3112 3113 3114 3115 3116 3117 3118 3119 3120 3121 3122 3123 3124 3125 3126 3127 3128 3129 3130 3131 3132 3133 3134 3135 3136 3137 3138 3139 3140 3141 3142 3143 3144 3145 3146 3147 3148 3149 3150 3151 3152 3153 3154 3155 3156 3157 3158 3159 3160 3161 3162 3163 3164 3165 3166 3167 3168 3169 3170 3171 3172 3173 3174 3175 3176 3177 3178 3179 3180 3181 3182 3183 3184 3185 3186 3187 3188 3189 3190 3191 3192 3193 3194 3195 3196 3197 3198 3199 3200 3201 3202 3203 3204 3205 3206 3207 3208 3209 3210 3211 3212 3213 3214 3215 3216 3217 3218 3219 3220 3221 3222 3223 3224 3225 3226 3227 3228 3229 3230 3231 3232 3233 3234 3235 3236 3237 3238 3239 3240 3241 3242 3243 3244 3245 3246 3247 3248 3249 3250 3251 3252 3253 3254 3255 3256 3257 3258 3259 3260 3261 3262 3263 3264 3265 3266 3267 3268 3269 3270 3271 3272 3273 3274 3275 3276 3277 3278 3279 3280 3281 3282 3283 3284 3285 3286 3287 3288 3289 3290 3291 3292 3293 3294 3295 3296 3297 3298 3299 3300 3301 3302 3303 3304 3305 3306 3307 3308 3309 3310 3311 3312 3313 3314 3315 3316 3317 3318 3319 3320 3321 3322 3323 3324 3325 3326 3327 3328 3329 3330 3331 3332 3333 3334 3335 3336 3337 3338 3339 3340 3341 3342 3343 3344 3345 3346 3347 3348 3349 3350 3351 3352 3353 3354 3355 3356 3357 3358 3359 3360 3361 3362 3363 3364 3365 3366 3367 3368 3369 3370 3371 3372 3373 3374 3375 3376 3377 3378 3379 3380 3381 3382 3383 3384 3385 3386 3387 3388 3389 3390 3391 3392 3393 3394 3395 3396 3397 3398 3399 3400 3401 3402 3403 3404 3405 3406 3407 3408 3409 3410 3411 3412 3413 3414 3415 3416 3417 3418 3419 3420 3421 3422 3423 3424 3425 3426 3427 3428 3429 3430 3431 3432 3433 3434 3435 3436 3437 3438 3439 3440 3441 3442 3443 3444 3445 3446 3447 3448 3449 3450 3451 3452 3453 3454 3455 3456 3457 3458 3459 3460 3461 3462 3463 3464 3465 3466 3467 3468 3469 3470 3471 3472 3473 3474 3475 3476 3477 3478 3479 3480 3481 3482 3483 3484 3485 3486 3487 3488 3489 3490 3491 3492 3493 3494 3495 3496 3497 3498 3499 3500 3501 3502 3503 3504 3505 3506 3507 3508 3509 3510 3511 3512 3513 3514 3515 3516 3517 3518 3519 3520 3521 3522 3523 3524 3525 3526 3527 3528 3529 3530 3531 3532 3533 3534 3535 3536 3537 3538 3539 3540 3541 3542 3543 3544 3545 3546 3547 3548 3549 3550 3551 3552 3553 3554 3555 3556 3557 3558 3559 3560 3561 3562 3563 3564 3565 3566 3567 3568 3569 3570 3571 3572 3573 3574 3575 3576 3577 3578 3579 3580 3581 3582 3583 3584 3585 3586 3587 3588 3589 3590 3591 3592 3593 3594 3595 3596 3597 3598 3599 3600 3601 3602 3603 3604 3605 3606 3607 3608 3609 3610 3611 3612 3613 3614 3615 3616 3617 3618 3619 3620 3621 3622 3623 3624 3625 3626 3627 3628 3629 3630 3631 3632 3633 3634 3635 3636 3637 3638 3639 3640 3641 3642 3643 3644 3645 3646 3647 3648 3649 3650 3651 3652 3653 3654 3655 3656 3657 3658 3659 3660 3661 3662 3663 3664 3665 3666 3667 3668 3669 3670 3671 3672 3673 3674 3675 3676 3677 3678 3679 3680 3681 3682 3683 3684 3685 3686 3687 3688 3689 3690 3691 3692 3693 3694 3695 3696 3697 3698 3699 3700 3701 3702 3703 3704 3705 3706 3707 3708 3709 3710 3711 3712 3713 3714 3715 3716 3717 3718 3719 3720 3721 3722 3723 3724 3725 3726 3727 3728 3729 3730 3731 3732 3733 3734 3735 3736 3737 3738 3739 3740 3741 3742 3743 3744 3745 3746 3747 3748 3749 3750 3751 3752 3753 3754 3755 3756 3757 3758 3759 3760 3761 3762 3763 3764 3765 3766 3767 3768 3769 3770 3771 3772 3773 3774 3775 3776 3777 3778 3779 3780 3781 3782 3783 3784 3785 3786 3787 3788 3789 3790 3791 3792 3793 3794 3795 3796 3797 3798 3799 3800 3801 3802 3803 3804 3805 3806 3807 3808 3809 3810 3811 3812 3813 3814 3815 3816 3817 3818 3819 3820 3821 3822 3823 3824 3825 3826 3827 3828 3829 3830 3831 3832 3833 3834 3835 3836 3837 3838 3839 3840 3841 3842 3843 3844 3845 3846 3847 3848 3849 3850 3851 3852 3853 3854 3855 3856 3857 3858 3859 3860 3861 3862 3863 3864 3865 3866 3867 3868 3869 3870 3871 3872 3873 3874 3875 3876 3877 3878 3879 3880 3881 3882 3883 3884 3885 3886 3887 3888 3889 3890 3891 3892 3893 3894 3895 3896 3897 3898 3899 3900 3901 3902 3903 3904 3905 3906 3907 3908 3909 3910 3911 3912 3913 3914 3915 3916 3917 3918 3919 3920 3921 3922 3923 3924 3925 3926 3927 3928 3929 3930 3931 3932 3933 3934 3935 3936 3937 3938 3939 3940 3941 3942 3943 3944 3945 3946 3947 3948 3949 3950 3951 3952 3953 3954 3955 3956 3957 3958 3959 3960 3961 3962 3963 3964 3965 3966 3967 3968 3969 3970 3971 3972 3973 3974 3975 3976 3977 3978 3979 3980 3981 3982 3983 3984 3985 3986 3987 3988 3989 3990 3991 3992 3993 3994 3995 3996 3997 3998 3999 4000 4001 4002 4003 4004 4005 4006 4007 4008 4009 4010 4011 4012 4013 4014 4015 4016 4017 4018 4019 4020 4021 4022 4023 4024 4025 4026 4027 4028 4029 4030 4031 4032 4033 4034 4035 4036 4037 4038 4039 4040 4041 4042 4043 4044 4045 4046 4047 4048 4049 4050 4051 4052 4053 4054 4055 4056 4057 4058 4059 4060 4061 4062 4063 4064 4065 4066 4067 4068 4069 4070 4071 4072 4073 4074 4075 4076 4077 4078 4079 4080 4081 4082 4083 4084 4085 4086 4087 4088 4089 4090 4091 4092 4093 4094 4095 4096 4097 4098 4099 4100 4101 4102 4103 4104 4105 4106 4107 4108 4109 4110 4111 4112 4113 4114 4115 4116 4117 4118 4119 4120 4121 4122 4123 4124 4125 4126 4127 4128 4129 4130 4131 4132 4133 4134 4135 4136 4137 4138 4139 4140 4141 4142 4143 4144 4145 4146 4147 4148 4149 4150 4151 4152 4153 4154 4155 4156 4157 4158 4159 4160 4161 4162 4163 4164 4165 4166 4167 4168 4169 4170 4171 4172 4173 4174 4175 4176 4177 4178 4179 4180 4181 4182 4183 4184 4185 4186 4187 4188 4189 4190 4191 4192 4193 4194 4195 4196 4197 4198 4199 4200 4201 4202 4203 4204 4205 4206 4207 4208 4209 4210 4211 4212 4213 4214 4215 4216 4217 4218 4219 4220 4221 4222 4223 4224 4225 4226 4227 4228 4229 4230 4231 4232 4233 4234 4235 4236 4237 4238 4239 4240 4241 4242 4243 4244 4245 4246 4247 4248 4249 4250 4251 4252 4253 4254 4255 4256 4257 4258 4259 4260 4261 4262 4263 4264 4265 4266 4267 4268 4269 4270 4271 4272 4273 4274 4275 4276 4277 4278 4279 4280 4281 4282 4283 4284 4285 4286 4287 4288 4289 4290 4291 4292 4293 4294 4295 4296 4297 4298 4299 4300 4301 4302 4303 4304 4305 4306 4307 4308 4309 4310 4311 4312 4313 4314 4315 4316 4317 4318 4319 4320 4321 4322 4323 4324 4325 4326 4327 4328 4329 4330 4331 4332 4333 4334 4335 4336 4337 4338 4339 4340 4341 4342 4343 4344 4345 4346 4347 4348 4349 4350 4351 4352 4353 4354 4355 4356 4357 4358 4359 4360 4361 4362 4363 4364 4365 4366 4367 4368 4369 4370 4371 4372 4373 4374 4375 4376 4377 4378 4379 4380 4381 4382 4383 4384 4385 4386 4387 4388 4389 4390 4391 4392 4393 4394 4395 4396 4397 4398 4399 4400 4401 4402 4403 4404 4405 4406 4407 4408 4409 4410 4411 4412 4413 4414 4415 4416 4417 4418 4419 4420 4421 4422 4423 4424 4425 4426 4427 4428 4429 4430 4431 4432 4433 4434 4435 4436 4437 4438 4439 4440 4441 4442 4443 4444 4445 4446 4447 4448 4449 4450 4451 4452 4453 4454 4455 4456 4457 4458 4459 4460 4461 4462 4463 4464 4465 4466 4467 4468 4469 4470 4471 4472 4473 4474 4475 4476 4477 4478 4479 4480 4481 4482 4483 4484 4485 4486 4487 4488 4489 4490 4491 4492 4493 4494 4495 4496 4497 4498 4499 4500 4501 4502 4503 4504 4505 4506 4507 4508 4509 4510 4511 4512 4513 4514 4515 4516 4517 4518 4519 4520 4521 4522 4523 4524 4525 4526 4527 4528 4529 4530 4531 4532 4533 4534 4535 4536 4537 4538 4539 4540 4541 4542 4543 4544 4545 4546 4547 4548 4549 4550 4551 4552 4553 4554 4555 4556 4557 4558 4559 4560 4561 4562 4563 4564 4565 4566 4567 4568 4569 4570 4571 4572 4573 4574 4575 4576 4577 4578 4579 4580 4581 4582 4583 4584 4585 4586 4587 4588 4589 4590 4591 4592 4593 4594 4595 4596 4597 4598 4599 4600 4601 4602 4603 4604 4605 4606 4607 4608 4609 4610 4611 4612 4613 4614 4615 4616 4617 4618 4619 4620 4621 4622 4623 4624 4625 4626 4627 4628 4629 4630 4631 4632 4633 4634 4635 4636 4637 4638 4639 4640 4641 4642 4643 4644 4645 4646 4647 4648 4649 4650 4651 4652 4653 4654 4655 4656 4657 4658 4659 4660 4661 4662 4663 4664 4665 4666 4667 4668 4669 4670 4671 4672 4673 4674 4675 4676 4677 4678 4679 4680 4681 4682 4683 4684 4685 4686 4687 4688 4689 4690 4691 4692 4693 4694 4695 4696 4697 4698 4699 4700 4701 4702 4703 4704 4705 4706 4707 4708 4709 4710 4711 4712 4713 4714 4715 4716 4717 4718 4719 4720 4721 4722 4723 4724 4725 4726 4727 4728 4729 4730 4731 4732 4733 4734 4735 4736 4737 4738 4739 4740 4741 4742 4743 4744 4745 4746 4747 4748 4749 4750 4751 4752 4753 4754 4755 4756 4757 4758 4759 4760 4761 4762 4763 4764 4765 4766 4767 4768 4769 4770 4771 4772 4773 4774 4775 4776 4777 4778 4779 4780 4781 4782 4783 4784 4785 4786 4787 4788 4789 4790 4791 4792 4793 4794 4795 4796 4797 4798 4799 4800 4801 4802 4803 4804 4805 4806 4807 4808 4809 4810 4811 4812 4813 4814 4815 4816 4817 4818 4819 4820 4821 4822 4823 4824 4825 4826 4827 4828 4829 4830 4831 4832 4833 4834 4835 4836 4837 4838 4839 4840 4841 4842 4843 4844 4845 4846 4847 4848 4849 4850 4851 4852 4853 4854 4855 4856 4857 4858 4859 4860 4861 4862 4863 4864 4865 4866 4867 4868 4869 4870 4871 4872 4873 4874 4875 4876 4877 4878 4879 4880 4881 4882 4883 4884 4885 4886 4887 4888 4889 4890 4891 4892 4893 4894 4895 4896 4897 4898 4899 4900 4901 4902 4903 4904 4905 4906 4907 4908 4909 4910 4911 4912 4913 4914 4915 4916 4917 4918 4919 4920 4921 4922 4923 4924 4925 4926 4927 4928 4929 4930 4931 4932 4933 4934 4935 4936 4937 4938 4939 4940 4941 4942 4943 4944 4945 4946 4947 4948 4949 4950 4951 4952 4953 4954 4955 4956 4957 4958 4959 4960 4961 4962 4963 4964 4965 4966 4967 4968 4969 4970 4971 4972 4973 4974 4975 4976 4977 4978 4979 4980 4981 4982 4983 4984 4985 4986 4987 4988 4989 4990 4991 4992 4993 4994 4995 4996 4997 4998 4999 5000 5001 5002 5003 5004 5005 5006 5007 5008 5009 5010 5011 5012 5013 5014 5015 5016 5017 5018 5019 5020 5021 5022 5023 5024 5025 5026 5027 5028 5029 5030 5031 5032 5033 5034 5035 5036 5037 5038 5039 5040 5041 5042 5043 5044 5045 5046 5047 5048 5049 5050 5051 5052 5053 5054 5055 5056 5057 5058 5059 5060 5061 5062 5063 5064 5065 5066 5067 5068 5069 5070 5071 5072 5073 5074 5075 5076 5077 5078 5079 5080 5081 5082 5083 5084 5085 5086 5087 5088 5089 5090 5091 5092 5093 5094 5095 5096 5097 5098 5099 5100 5101 5102 5103 5104 5105 5106 5107 5108 5109 5110 5111 5112 5113 5114 5115 5116 5117 5118 5119 5120 5121 5122 5123 5124 5125 5126 5127 5128 5129 5130 5131 5132 5133 5134 5135 5136 5137 5138 5139 5140 5141 5142 5143 5144 5145 5146 5147 5148 5149 5150 5151 5152 5153 5154 5155 5156 5157 5158 5159 5160 5161 5162 5163 5164 5165 5166 5167 5168 5169 5170 5171 5172 5173 5174 5175 5176 5177 5178 5179 5180 5181 5182 5183 5184 5185 5186 5187 5188 5189 5190 5191 5192 5193 5194 5195 5196 5197 5198 5199 5200 5201 5202 5203 5204 5205 5206 5207 5208 5209 5210 5211 5212 5213 5214 5215 5216 5217 5218 5219 5220 5221 5222 5223 5224 5225 5226 5227 5228 5229 5230 5231 5232 5233 5234 5235 5236 5237 5238 5239 5240 5241 5242 5243 5244 5245 5246 5247 5248 5249 5250 5251 5252 5253 5254 5255 5256 5257 5258 5259 5260 5261 5262 5263 5264 5265 5266 5267 5268 5269 5270 5271 5272 5273 5274 5275 5276 5277 5278 5279 5280 5281 5282 5283 5284 5285 5286 5287 5288 5289 5290 5291 5292 5293 5294 5295 5296 5297 5298 5299 5300 5301 5302 5303 5304 5305 5306 5307 5308 5309 5310 5311 5312 5313 5314 5315 5316 5317 5318 5319 5320 5321 5322 5323 5324 5325 5326 5327 5328 5329 5330 5331 5332 5333 5334 5335 5336 5337 5338 5339 5340 5341 5342 5343 5344 5345 5346 5347 5348 5349 5350 5351 5352 5353 5354 5355 5356 5357 5358 5359 5360 5361 5362 5363 5364 5365 5366 5367 5368 5369 5370 5371 5372 5373 5374 5375 5376 5377 5378 5379 5380 5381 5382 5383 5384 5385 5386 5387 5388 5389 5390 5391 5392 5393 5394 5395 5396 5397 5398 5399 5400 5401 5402 5403 5404 5405 5406 5407 5408 5409 5410 5411 5412 5413 5414 5415 5416 5417 5418 5419 5420 5421 5422 5423 5424 5425 5426 5427 5428 5429 5430 5431 5432 5433 5434 5435 5436 5437 5438 5439 5440 5441 5442 5443 5444 5445 5446 5447 5448 5449 5450 5451 5452 5453 5454 5455 5456 5457 5458 5459 5460 5461 5462 5463 5464 5465 5466 5467 5468 5469 5470 5471 5472 5473 5474 5475 5476 5477 5478 5479 5480 5481 5482 5483 5484 5485 5486 5487 5488 5489 5490 5491 5492 5493 5494 5495 5496 5497 5498 5499 5500 5501 5502 5503 5504 5505 5506 5507 5508 5509 5510 5511 5512 5513 5514 5515 5516 5517 5518 5519 5520 5521 5522 5523 5524 5525 5526 5527 5528 5529 5530 5531 5532 5533 5534 5535 5536 5537 5538 5539 5540 5541 5542 5543 5544 5545 5546 5547 5548 5549 5550 5551 5552 5553 5554 5555 5556 5557 5558 5559 5560 5561 5562 5563 5564 5565 5566 5567 5568 5569 5570 5571 5572 5573 5574 5575 5576 5577 5578 5579 5580 5581 5582 5583 5584 5585 5586 5587 5588 5589 5590 5591 5592 5593 5594 5595 5596 5597 5598 5599 5600 5601 5602 5603 5604 5605 5606 5607 5608 5609 5610 5611 5612 5613 5614 5615 5616 5617 5618 5619 5620 5621 5622 5623 5624 5625 5626 5627 5628 5629 5630 5631 5632 5633 5634 5635 5636 5637 5638 5639 5640 5641 5642 5643 5644 5645 5646 5647 5648 5649 5650 5651 5652 5653 5654 5655 5656 5657 5658 5659 5660 5661 5662 5663 5664 5665 5666 5667 5668 5669 5670 5671 5672 5673 5674 5675 5676 5677 5678 5679 5680 5681 5682 5683 5684 5685 5686 5687 5688 5689 5690 5691 5692 5693 5694 5695 5696 5697 5698 5699 5700 5701 5702 5703 5704 5705 5706 5707 5708 5709 5710 5711 5712 5713 5714 5715 5716 5717 5718 5719 5720 5721 5722 5723 5724 5725 5726 5727 5728 5729 5730 5731 5732 5733 5734 5735 5736 5737 5738 5739 5740 5741 5742 5743 5744 5745 5746 5747 5748 5749 5750 5751 5752 5753 5754 5755 5756 5757 5758 5759 5760 5761 5762 5763 5764 5765 5766 5767 5768 5769 5770 5771 5772 5773 5774 5775 5776 5777 5778 5779 5780 5781 5782 5783 5784 5785 5786 5787 5788 5789 5790 5791 5792 5793 5794 5795 5796 5797 5798 5799 5800 5801 5802 5803 5804 5805 5806 5807 5808 5809 5810 5811 5812 5813 5814 5815 5816 5817 5818 5819 5820 5821 5822 5823 5824 5825 5826 5827 5828 5829 5830 5831 5832 5833 5834 5835 5836 5837 5838 5839 5840 5841 5842 5843 5844 5845 5846 5847 5848 5849 5850 5851 5852 5853 5854 5855 5856 5857 5858 5859 5860 5861 5862 5863 5864 5865 5866 5867 5868 5869 5870 5871 5872 5873 5874 5875 5876 5877 5878 5879 5880 5881 5882 5883 5884 5885 5886 5887 5888 5889 5890 5891 5892 5893 5894 5895 5896 5897 5898 5899 5900 5901 5902 5903 5904 5905 5906 5907 5908 5909 5910 5911 5912 5913 5914 5915 5916 5917 5918 5919 5920 5921 5922 5923 5924 5925 5926 5927 5928 5929 5930 5931 5932 5933 5934 5935 5936 5937 5938 5939 5940 5941 5942 5943 5944 5945 5946 5947 5948 5949 5950 5951 5952 5953 5954 5955 5956 5957 5958 5959 5960 5961 5962 5963 5964 5965 5966 5967 5968 5969 5970 5971 5972 5973 5974 5975 5976 5977 5978 5979 5980 5981 5982 5983 5984 5985 5986 5987 5988 5989 5990 5991 5992 5993 5994 5995 5996 5997 5998 5999 6000 6001 6002 6003 6004 6005 6006 6007 6008 6009 6010 6011 6012 6013 6014 6015 6016 6017 6018 6019 6020 6021 6022 6023 6024 6025 6026 6027 6028 6029 6030 6031 6032 6033 6034 6035 6036 6037 6038 6039 6040 6041 6042 6043 6044 6045 6046 6047 6048 6049 6050 6051 6052 6053 6054 6055 6056 6057 6058 6059 6060 6061 6062 6063 6064 6065 6066 6067 6068 6069 6070 6071 6072 6073 6074 6075 6076 6077 6078 6079 6080 6081 6082 6083 6084 6085 6086 6087 6088 6089 6090 6091 6092 6093 6094 6095 6096 6097 6098 6099 6100 6101 6102 6103 6104 6105 6106 6107 6108 6109 6110 6111 6112 6113 6114 6115 6116 6117 6118 6119 6120 6121 6122 6123 6124 6125 6126 6127 6128 6129 6130 6131 6132 6133 6134 6135 6136 6137 6138 6139 6140 6141 6142 6143 6144 6145 6146 6147 6148 6149 6150 6151 6152 6153 6154 6155 6156 6157 6158 6159 6160 6161 6162 6163 6164 6165 6166 6167 6168 6169 6170 6171 6172 6173 6174 6175 6176 6177 6178 6179 6180 6181 6182 6183 6184 6185 6186 6187 6188 6189 6190 6191 6192 6193 6194 6195 6196 6197 6198 6199 6200 6201 6202 6203 6204 6205 6206 6207 6208 6209 6210 6211 6212 6213 6214 6215 6216 6217 6218 6219 6220 6221 6222 6223 6224 6225 6226 6227 6228 6229 6230 6231 6232 6233 6234 6235 6236 6237 6238 6239 6240 6241 6242 6243 6244 6245 6246 6247 6248 6249 6250 6251 6252 6253 6254 6255 6256 6257 6258 6259 6260 6261 6262 6263 6264 6265 6266 6267 6268 6269 6270 6271 6272 6273 6274 6275 6276 6277 6278 6279 6280 6281 6282 6283 6284 6285 6286 6287 6288 6289 6290 6291 6292 6293 6294 6295 6296 6297 6298 6299 6300 6301 6302 6303 6304 6305 6306 6307 6308 6309 6310 6311 6312 6313 6314 6315 6316 6317 6318 6319 6320 6321 6322 6323 6324 6325 6326 6327 6328 6329 6330 6331 6332 6333 6334 6335 6336 6337 6338 6339 6340 6341 6342 6343 |
\input texinfo
@c %**start of header
@setfilename mtt.info
@settitle MTT: Model Transformation Tools
@c %**end of header
@finalout
@c Here is what I use in the Info `dir' file:
@c * Mtt: (mtt). Model transformation tools.
@comment %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@comment Version control history
@comment %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@comment $Id$
@comment $Log$
@comment Revision 1.9 2002/07/05 13:29:34 geraint
@comment Added notes about generating dynamically linked functions for Octave and Matlab.
@comment
@comment Revision 1.8 2002/07/04 21:34:12 geraint
@comment Updated gnuplot view description to describe Tcl/Tk interface instead of obsolete txt method.
@comment
@comment Revision 1.7 2002/04/23 09:51:54 gawthrop
@comment Changed incorrect statement about searching for components.
@comment
@comment Revision 1.6 2001/10/15 14:29:50 gawthrop
@comment Added documentaton on [1:N] style port labels
@comment
@comment Revision 1.5 2001/07/23 03:35:29 geraint
@comment Updated file structure (mtt/bin).
@comment
@comment Revision 1.4 2001/07/23 03:25:02 geraint
@comment Added notes on -ae hybrd, rk4, ode2odes.cc, .oct dependencies.
@comment
@comment Revision 1.3 2001/07/13 03:02:38 geraint
@comment Added notes on #ICD, gnuplot.txt and odes.sg rep.
@comment
@comment Revision 1.2 2001/07/03 22:59:10 gawthrop
@comment Fixed problems with argument passing for CRs
@comment
@comment Revision 1.1 2001/06/04 08:18:52 gawthrop
@comment Putting documentation under CVS
@comment
@comment Revision 1.66 2000/12/05 14:20:55 peterg
@comment Added the c++ anf m CR info.
@comment
@comment Revision 1.65 2000/11/27 15:36:15 peterg
@comment NOPAR --> NOTPAR
@comment
@comment Revision 1.64 2000/11/16 14:22:48 peterg
@comment added UNITS declaration
@comment
@comment Revision 1.63 2000/11/03 14:41:08 peterg
@comment Added PAR and NOPAR stuff
@comment
@comment Revision 1.62 2000/10/17 17:53:34 peterg
@comment Added some simulation details
@comment
@comment Revision 1.61 2000/09/14 17:13:06 peterg
@comment New options table
@comment
@comment Revision 1.60 2000/09/14 17:09:20 peterg
@comment Tidied up valid name sections
@comment Tidied up defining represnetations table
@comment Verion 4.6
@comment
@comment Revision 1.59 2000/08/30 13:09:00 peterg
@comment Updated option table
@comment
@comment Revision 1.58 2000/08/01 13:30:19 peterg
@comment Version 4.4
@comment updated STEPFACTOR info
@comment describes octave and OCST interfaces
@comment
@comment Revision 1.57 2000/07/20 07:55:44 peterg
@comment Version 4.3
@comment
@comment Revision 1.56 2000/05/19 17:49:17 peterg
@comment Extended the user defined representation section -- new nppp rep.
@comment
@comment Revision 1.55 2000/03/16 13:53:31 peterg
@comment Correct date
@comment
@comment Revision 1.54 2000/03/15 21:22:57 peterg
@comment Updated to 4.1 -- old style SS no longer supported
@comment
@comment Revision 1.53 1999/12/22 05:33:10 peterg
@comment Updated for 4.0
@comment
@comment Revision 1.52 1999/11/23 00:25:11 peterg
@comment Added the sensitivity reps
@comment
@comment Revision 1.51 1999/11/16 04:43:47 peterg
@comment Added start of sensitivity section
@comment
@comment Revision 1.50 1999/11/16 00:30:35 peterg
@comment Updated simulation section
@comment Added vector components
@comment
@comment Revision 1.49 1999/07/20 23:44:58 peterg
@comment V 3.8
@comment
@comment Revision 1.48 1999/07/19 03:08:33 peterg
@comment Added documentation for (new) SS lbl fields
@comment
@comment Revision 1.47 1999/03/09 01:42:22 peterg
@comment Rearranged the User interface section
@comment
@comment Revision 1.46 1999/03/09 01:18:01 peterg
@comment Updated for 3.5 including xmtt
@comment
@comment Revision 1.45 1999/03/03 02:39:26 peterg
@comment Minor updates
@comment
@comment Revision 1.44 1999/02/17 06:52:14 peterg
@comment New level formula dor artwork
@comment
@comment Revision 1.43 1998/11/25 16:49:24 peterg
@comment Put in subs.r documentation (was called params.r)
@comment
@comment Revision 1.42 1998/11/24 12:24:59 peterg
@comment Added section on simulation output
@comment Version 3.4
@comment
@comment Revision 1.41 1998/09/02 12:04:15 peterg
@comment Version 3.2
@comment
@comment Revision 1.40 1998/08/27 08:36:39 peterg
@comment Removed in. methods except Euler anf implicit
@comment
@comment Revision 1.39 1998/08/18 10:44:28 peterg
@comment Typo
@comment
@comment Revision 1.38 1998/08/18 09:16:38 peterg
@comment Version 3.1
@comment
@comment Revision 1.37 1998/08/17 16:14:30 peterg
@comment Version 3.1 - includes documentation on METHOD=IMPLICIT
@comment
@comment Revision 1.36 1998/07/30 17:33:15 peterg
@comment VERSION 3.0
@comment
@comment Revision 1.35 1998/07/22 11:00:53 peterg
@comment Correct date!
@comment
@comment Revision 1.34 1998/07/22 11:00:13 peterg
@comment Version to BAe
@comment
@comment Revision 1.33 1998/07/17 19:32:19 peterg
@comment Added more about aliases
@comment
@comment Revision 1.32 1998/07/05 14:21:56 peterg
@comment Further additions (Carlisle-Glasgow)
@comment
@comment Revision 1.31 1998/07/04 11:35:57 peterg
@comment Strarted new lbl description
@comment
@comment Revision 1.30 1998/07/02 18:39:20 peterg
@comment Started 3.0
@comment Added alias and default sections.
@comment
@comment Revision 1.29 1998/05/19 19:46:58 peterg
@comment Added the odess description
@comment
@comment Revision 1.28 1998/05/14 09:17:22 peterg
@comment Added METHOD variable to the simpar file
@comment
@comment Revision 1.27 1998/05/13 10:03:09 peterg
@comment Added unknown/zero SS label documentation.
@comment
@comment Revision 1.26 1998/04/29 15:12:46 peterg
@comment Version 2.9.
@comment
@comment Revision 1.25 1998/04/12 17:00:26 peterg
@comment Added new port features: coerced direction and top-level behaviour.
@comment
@comment Revision 1.24 1998/04/05 18:27:20 peterg
@comment This was the 2.6 version
@comment
@comment Revision 1.23 1997/08/24 11:17:51 peterg
@comment This is the released version 2.5
@comment
@comment Revision 1.22 1997/08/23 19:38:53 peterg
@comment Added simulation chapter.
@comment
@comment Revision 1.21 1997/08/23 16:50:10 peterg
@comment Added desc section.
@comment Included named and vector ports
@comment Completed list of representations.
@comment
@comment Revision 1.20 1997/06/16 15:39:24 peterg
@comment THis is the released 2.4 document.
@comment
@comment Revision 1.19 1997/06/16 09:48:23 peterg
@comment Back under revision control (elm)
@comment
@comment Revision 1.18 1997/06/14 20:27:41 peterg
@comment Added complex example section.
@comment
@comment Revision 1.18 1997/06/13 14:51:07 peterg
@comment Added report section
@comment
@comment Revision 1.17 1997/05/09 15:06:02 peterg
@comment Changed to version 2.4.
@comment
@comment Revision 1.16 1996/12/05 10:06:25 peterg
@comment Modified .octaverc : 'true' --> 1
@comment
@comment Revision 1.15 1996/11/20 19:02:28 peterg
@comment Added some system admin stuff.
@comment Added section on simple models.
@comment
@comment Revision 1.14 1996/11/12 13:19:04 peterg
@comment Put paths as section, not subsection.
@comment
@comment Revision 1.13 1996/11/11 16:53:14 peterg
@comment Added params documentation
@comment Sorted out table bug.
@comment
@comment Revision 1.12 1996/11/10 20:29:31 peterg
@comment Added section on help -- needs more
@comment
@comment Revision 1.11 1996/11/09 21:15:28 peterg
@comment Rewrite of quick start.
@comment Update of file structure.
@comment
@comment Revision 1.10 1996/11/09 20:25:54 peterg
@comment Final v2.0.
@comment
@comment Revision 1.9 1996/10/01 10:33:02 peter
@comment Cleaned up cross references.
@comment
@comment Revision 1.8 1996/10/01 09:31:00 peter
@comment Added sections written in Hong Kong.
@comment
@comment Revision 1.7 1996/09/16 09:49:47 peter
@comment Added ese section
@comment
@comment Revision 1.6 1996/09/16 08:33:53 peter
@comment Added constitutive relationship section etc.
@comment
@comment Revision 1.5 1996/09/15 20:20:56 peter
@comment Added abg and rbg stuff
@comment
@comment Revision 1.4 1996/08/30 19:07:40 peter
@comment Added some admin stuff.
@comment
@comment Revision 1.3 1996/08/30 07:50:16 peter
@comment Added file structure section.
@comment
@comment Revision 1.2 1996/08/22 14:28:50 peter
@comment Added stuff about labels.
@comment
@comment Revision 1.1 1996/08/22 11:52:59 peter
@comment Initial revision
@comment %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@ifinfo
This file documents MTT a set of Model Transformation Tools.
Copyright (C) Peter J. Gawthrop 1996, 1997, 1998, 1999
Permission is granted to make and distribute verbatim copies of this
manual provided the copyright notice and this permission notice are
preserved on all copies.
@ignore
Permission is granted to process this file through TeX and print the
results, provided the printed document carries copying permission
notice identical to this one except for the removal of this paragraph
(this paragraph not being relevant to the printed manual).
@end ignore
Permission is granted to copy and distribute modified versions of this
manual under the conditions for verbatim copying, provided also that the
section entitled ``GNU General Public License'' is included exactly as
in the original, and provided that the entire resulting derived work is
distributed under the terms of a permission notice identical to this one.
Permission is granted to copy and distribute translations of this manual
into another language, under the above conditions for modified versions,
except that the section entitled ``GNU General Public License'' may be
included in a translation approved by the author instead of in the
original English.
@end ifinfo
@titlepage
@title MTT: Model Transformation Tools
@subtitle December 2000
@subtitle For version 4.9.
@author Peter Gawthrop
@page
@vskip 0pt plus 1filll
Copyright @copyright{} 1996,1997,1998,1999,2000 Peter J. Gawthrop
Permission is granted to make and distribute verbatim copies of
this manual provided the copyright notice and this permission notice
are preserved on all copies.
Permission is granted to copy and distribute modified versions of this
manual under the conditions for verbatim copying, provided also that the
section entitled ``GNU General Public License'' is included exactly in
the original, and provided that the entire resulting derived work is
distributed under the terms of a permission notice identical to this
one.
Permission is granted to copy and distribute translations of this manual
into another language, under the above conditions for modified versions,
except that the section entitled ``GNU General Public License'' may be
included in a translation approved by the author instead of in the
original English.
General information about MTT is available at URL
@example
http://mtt.sourceforge.net
@end example
@ifhtml
<A
HREF="http://mtt.sourceforge.net"> here</A>.
@end ifhtml
@end titlepage
@ifinfo
@node Top, Introduction, (dir), (dir)
@top MTT
@strong{MTT} is a set of Model Transformation Tools based on bond graphs.
@strong{MTT} implements the theory to be found in the book ``Metamodelling: Bond
Graphs and Dynamic Systems'' by Peter Gawthrop and Lorcan Smith
published by Prentice Hall in 1996 (ISBN 0-13-489824-9).
It implements two features not discussed in that book:
@itemize @bullet
@item
bicausal bond graphs and
@item
hierarchical bond graphs.
@end itemize
@contents
@end ifinfo
@c @include intro.texi
@c Copyright (C) 1996 Peter J. Gawthrop
@c This is part of the MTT manual.
@c For copying conditions, see the file MTT.texi.
@menu
* Introduction::
* User interface::
* Creating Models::
* Simulation::
* Sensitivity models::
* Representations::
* Extending MTT::
* Languages::
* Language tools::
* Administration::
* Glossary::
* Index::
@detailmenu
--- The Detailed Node Listing ---
Introduction
* What is a Representation?::
* What is a Transformation?::
* Bond graphs:: What is a bond graph?
* Variables::
* Bonds::
* Components::
* Algebraic loops::
* Switched systems::
Components
* Ports::
* Constitutive relationship::
* Symbolic parameters::
* Numeric parameters::
User interface
* Menu-driven interface::
* Command line interface::
* Options::
* Utilities::
Utilities
* Help::
* Copy::
* Clean::
* Version control::
Help
* help representations::
* help components::
* help examples::
* help crs::
* help <name>::
Creating Models
* Quick start::
* Creating simple models::
* Creating complex models::
Creating complex models
* Top level::
Simulation
* Steady-state solutions::
* Simulation parameters::
* Simulation input::
* Simulation logic::
* Simulation initial state::
* Simulation code::
* Simulation output::
Steady-state solutions
* Steady-state solutions - numerical(odess)::
* Steady-state solutions - symbolic (ss)::
Simulation parameters
* Euler integration::
* Implicit integration::
* Runge Kutta IV integration::
* Hybrd algebraic solver::
Simulation code
* Dynamically linked functions::
Simulation output
* Viewing results with gnuplot::
* Exporting results to SciGraphica::
Representations
* Representation summary::
* Defining representations::
* Verbal description (desc)::
* Acausal bond graph (abg)::
* Stripped acausal bond graph (sabg)::
* Labels (lbl)::
* Description (desc)::
* Structure (struc)::
* Constitutive Relationship (cr)::
* Parameters::
* Causal bond graph (cbg)::
* Elementary system equations::
* Differential-Algebraic Equations::
* Constrained-state Equations::
* Ordinary Differential Equations::
* Descriptor matrices::
* Report::
Acausal bond graph (abg)
* Language fig (abg.fig)::
* Language m (rbg.m)::
* Language m (abg.m)::
* Language tex (abg.tex)::
Language fig (abg.fig)
* icon library::
* bonds::
* strokes::
* components::
* Simple components::
* SS components::
* Simple components - implementation::
* Compound components::
* Named SS components::
* Coerced bond direction::
* Port labels::
* Vector port labels::
* Port label defaults::
* Vector components::
* artwork::
* Valid names::
Simple components
* SS components::
* Simple components - implementation::
Compound components
* Named SS components::
Language m (rbg.m)
* Transformation abg2rbg_fig2m::
Language m (abg.m)
* Arrow-orientated causality::
* Component-orientated causality::
* Transformation rbg2abg_m::
Stripped acausal bond graph (sabg)
* Language fig (sabg.fig)::
* Stripped acausal bond graph (view)::
Labels (lbl)
* SS component labels ::
* Other component labels ::
* Component names::
* Component constitutive relationship::
* Component arguments::
* Parameter declarations::
* Units declarations::
* Interface Control Definition::
* Aliases::
* Parameter passing::
* Old-style labels (lbl)::
Other component labels
* Component names::
* Component constitutive relationship::
* Component arguments::
* Aliases::
* Parameter passing::
* Old-style labels (lbl)::
Aliases
* Port aliases::
* Parameter aliases::
* CR aliases::
* Component aliases::
Old-style labels (lbl)
* SS component labels (old-style)::
* Other component labels (old-style)::
* Parameter passing (old-style)::
Description (desc)
* Language tex (desc.tex)::
Structure (struc)
* Language txt (struc.txt)::
* Language tex (struc.tex)::
* Structure (view)::
Constitutive relationship (cr)
* Predefined constitutive relationships::
* DIY constitutive relationships::
* Unresolved constitutive relationships::
* Unresolved constitutive relationships - Octave::
* Unresolved constitutive relationships - c++::
Predefined constitutive relationships
* lin::
* exotherm::
Parameters
* Symbolic parameters (subs.r)::
* Symbolic parameters for simplification (simp.r)::
* Numeric parameters (numpar)::
Numeric parameters (numpar)
* Text form (numpar.txt)::
Causal bond graph (cbg)
* Language fig (cbg.fig)::
* Language m (cbg.m)::
Language m (cbg.m)
* Transformation abg2cbg_m::
Elementary system equations (ese)
* Transformation cbg2ese_m2r::
Differential-Algebraic Equations (dae)
* Differential-Algebraic Equations (reduce)::
* Differential-Algebraic Equations (m)::
Language reduce (dae.r)
* Transformation ese2dae_r::
Language m (dae.m)
* Transformation dae_r2m::
Constrained-state Equations (cse)
* Constrained-state Equations (reduce)::
* Constrained-state Equations (view)::
Language reduce (cse.r)
* Transformation dae2cse_r::
Ordinary Differential Equations
* Ordinary Differential Equations (reduce)::
* Ordinary Differential Equations (m)::
* Ordinary Differential Equations (view)::
Language reduce (ode.r)
* Transformation cse2ode_r::
Language m (ode.m)
* Transformation ode_r2m::
Descriptor matrices (dm)
* Descriptor matrices (reduce)::
* Descriptor matrices (m)::
Report (rep)
* Report (text)::
* Report (view)::
Extending MTT
* Makefiles::
* New representations::
* Component library ::
Languages
* Fig:: r
* m::
* Reduce::
* c::
Language tools
* Views::
* Xfig::
* Text editors::
* Octave::
* LaTeX::
Octave
* Octave control system toolbox (OCST)::
* Creating GNU Octave .oct files::
* Creating Matlab .mex files::
* Embedding MTT models in Simulink::
Administration
* Software components::
* REDUCE setup::
* Octave setup::
* Paths::
* File structure::
Octave setup
* .octaverc::
* .oct file dependencies::
Paths
* $MTTPATH::
* $MTT_COMPONENTS::
* $MTT_CRS::
* $MTT_EXAMPLES::
* $OCTAVE_PATH::
@end detailmenu
@end menu
@node Introduction, User interface, Top, Top
@chapter Introduction
@cindex MTT, purpose of
@pindex MTT
@strong{MTT} is a set of Model Transformation Tools based on bond
graphs. @strong{MTT} implements the theory to be found in the book
``Metamodelling: Bond Graphs and Dynamic Systems'' by Peter Gawthrop and
Lorcan Smith published by Prentice Hall in 1996 (ISBN 0-13-489824-9).
It implements two features not discussed in that book:
@itemize @bullet
@item
bicausal bond graphs and
@item
hierarchical bond graphs.
@end itemize
In the context of software, it has been said that one good tool is worth many
packages. UNIX is a good example of this philosophy: the user can put together
applications from a range of ready made tools.
This manual describes the application of this philosophy to dynamic
system modeling embodied in @strong{MTT} - a set of Model Transformation Tools
each of which implements a single transformation between system
representations.
System representations have two attributes.
@itemize @bullet
@item
A Form: e.g. acausal bond graph, differential algebraic, linear
state-space etc.
@item
A Language: e.g. Fig, Matlab, LaTeX, Reduce, postscript etc.
@end itemize
Transformations in @strong{MTT} are accomplished using appropriate software (e.g.
Octave/Matlab, Reduce) encapsulated in UNIX Bourne shell scripts. The
relationships between the tools are encoded in a Make File; thus the
user can specify a final representation and all the necessary
intermediate transformations are automatically generated.
@menu
* What is a Representation?::
* What is a Transformation?::
* Bond graphs:: What is a bond graph?
* Variables::
* Bonds::
* Components::
* Algebraic loops::
* Switched systems::
@end menu
@node What is a Representation?, What is a Transformation?, Introduction, Introduction
@section What is a representation?
@cindex Representations, what are they?
@pindex Representations
Physical systems have many representations. These include
@itemize @bullet
@item
a schematic diagram,
@item
a block diagram,
@item
a bunch of equations,
@item
a single differential(-algebraic) equation,
@item
simulation code,
@item
linearised state-space (or descriptor) equations,
@item
transfer function (of the linearised system),
@item
frequency response (of the linearised system),
@item
etc...
@end itemize
Each of these representations is related to other representations by an
appropriate transformation (@pxref{What is a Transformation?}. In many cases, a
modeler is presented with a physical system and needs to make a
model. In particular, a model, in this context, is a representation of
the system appropriate to a particular use, for example:
@itemize @bullet
@item
simulation,
@item
control system design,
@item
optimisation
@item
etc.
@end itemize
Indeed, for a given physical system, the modeler would need to derive
a number of models. This process can be viewed as a series of steps;
each involving a transformation between representations (@pxref{What is a Transformation?}.
In this context, the following considerations are relevant.
@itemize @bullet
@item
There is a unique `core' representation of any system.
There are many routes from this core representation, each leading to
an appropriate model.
There are many possible routes to this core representation
from the physical system: the route chosen is a matter of convenience.
@item
Because the core representation is unique, it is easy to expand the
tool-box to include additional transformations from the physical system
to the core representation and additional transformations from the core
representation to the mode.
@item
Transformation_1 probably cannot, and certainly should not, be
completely automated. Engineering insight, knowledge and experience is
essential to capture the essence (with respect to the particular use) of
the physical system whilst discarding irrelevant form.
@item
Representation_1 should be `close' in some sense to the Physical system.
@item
The core representation, and hence the representations leading to it,
must contain enough information to generate all of the required models.
@item
Representations must be easily extensible: it must be possible to add
extra components or attributes without restructuring the representation.
@end itemize
I happen to believe that Bond graphs (@pxref{Bond graphs}) provide the
most convenient and powerful basis for the core representation.
@node What is a Transformation?, Bond graphs, What is a Representation?, Introduction
@comment node-name, next, previous, up
@section What is a transformation?
@cindex Transformations
Each system representation (@pxref{What is a Representation?} is related to other representations by an
appropriate transformation as follows:
@itemize @bullet
@item
Physical system
@item
Transformation_1 ---> Representation_1
@item
Transformation_2 ---> Representation_2
@item
...
@item
Transformation_N ---> Core representation
@item
Transformation_N+1 ---> Representation_N+1
@item
Transformation_N+2 ---> Representation_N+2
@item
...
@item
Transformation_N+M ---> Model
@end itemize
Thus modeling is seen as a sequence of transformations between
representations.
@node Bond graphs, Variables, What is a Transformation?, Introduction
@section What is a bond graph?
@cindex Bond graphs, what are they?
@pindex Bond graphs
Bond graphs provide a graphical high-level language for describing
dynamic systems in a precise and unambiguous fashion.
They make a clear distinction between structure (how components are
connected together), and behavior (the particular constitutive
relationships, or physical laws, describing each component.
They can describe a range of physical systems including:
@itemize @bullet
@item
Electrical systems
@item
Mechanical systems
@item
Hydraulic systems
@item
Chemical process systems
@end itemize
More importantly, they can describe systems which contain subsystems
drawn from all of these domains in a uniform manner.
Bond graphs are made up of components (@pxref{Components}) connected by
bonds (@pxref{Bonds}) which define the relationship between
variables (@pxref{Variables}).
@node Variables, Bonds, Bond graphs, Introduction
@comment node-name, next, previous, up
@section Variables
@cindex Variables
In bond graph terminology there are four sorts of variables:
@itemize @bullet
@item @emph{effort} variables
@item @emph{flow} variables
@item @emph{integrated effort} variables
@item @emph{integrated flow} variables
@end itemize
Examples of @emph{effort} variables are
@itemize @bullet
@item
voltage
@item
pressure
@item
force
@item
torque
@item
temperature
@end itemize
Examples of @emph{flow} variables are
@itemize @bullet
@item
current
@item
volumetric flow rate
@item
velocity
@item
angular velocity
@item
heat flow
@end itemize
Examples of integrated @emph{flow} variables are
@itemize @bullet
@item
charge
@item
volume
@item
momentum
@item
angular momentum
@item
heat
@end itemize
@node Bonds, Components, Variables, Introduction
@comment node-name, next, previous, up
@section Bonds
@cindex Bonds
Bonds connect components (@pxref{Components}) together. Each bond
carries two variables:
@itemize @bullet
@item an effort (@pxref{Variables}) variable and
@item a flow (@pxref{Variables}) variable.
@end itemize
Each bond has three notations associated with it:
@itemize @bullet
@item a half-arrow,
@item a causal stroke and
@item a causal half-stroke.
@end itemize
The half-arrow indicates two things:
@itemize @bullet
@item the direction of power (or pseudo power) flow and
@item the side of the bond associated with the flow variable.
@end itemize
The causal stroke indicates two things:
@itemize @bullet
@item the effort variable is imposed at the same end as the stroke and
@item the flow variable is imposed at the opposite end to the stroke.
@end itemize
The causal half-stoke indicates one thing:
@itemize @bullet
@item if it is on the effort side of the bond, the effort variable is
imposed at the same end as the stroke or
@item if it is on the flow side of the bond, the flow variable is
imposed at the opposite end to the stroke.
@end itemize
@node Components, Algebraic loops, Bonds, Introduction
@comment node-name, next, previous, up
@section Components
@cindex Components
Components provide the building blocks of a dynamic system when
connected by bonds (@pxref{bonds}).
Components have the following attributes:
@vtable @code
@item ports
provide the connections to other components (@pxref{Ports})
@item constitutive relationships
define how the port-variables are related (@pxref{Constitutive
relationship})
@end vtable
@menu
* Ports::
* Constitutive relationship::
* Symbolic parameters::
* Numeric parameters::
@end menu
@node Ports, Constitutive relationship, Components, Components
@comment node-name, next, previous, up
@subsection Ports
@cindex ports
Components have one or more ports. Each port carries two variables,
and effort and a flow variable (@pxref{Variables}). Any pair of ports
can be connected by a bond (@pxref{Bonds}); this connection is
equivalent to saying that the effort variables at each port are
identical and that the flow variables at each port are
identical.
Ports are implemented in @strong{MTT} using named SS components.
(@pxref{Named SS components}).
The direction of the named SS components.
(@pxref{Named SS components})
is coerced (@pxref{Coerced bond direction}) to have the same direction
as the bons connected to the corresponding port. Thus the direction of
the direction of the named SS components has no significance unless the
component is at the top level.
@node Constitutive relationship, Symbolic parameters, Ports, Components
@comment node-name, next, previous, up
@subsection Constitutive relationship
@cindex Constitutive Relationship
The constitutive relationship of a component defines how the port
variables are related. This relationship may be linear
or non-linear. This typically contains symbolic parameters
(@pxref{Symbolic parameters}) which may be replaced, for the purposes
of numerical analysis by numeric parameters
(@pxref{Numeric parameters}).
@node Symbolic parameters, Numeric parameters, Constitutive relationship, Components
@comment node-name, next, previous, up
@subsection Symbolic parameters
@cindex Symbolic parameters
The constitutive relationship of a system component (@pxref{Components})
typically contains symbolic parameters. For example a resistor may have
a symbolic resistance r. It is convenient to leave such parameters as
symbols when viewing equations or when performing symbolic analysis such
as differentiation.
However, @strong{MTT} allows replacement of symbolic parameters by
numeric parameters (@pxref{Numeric parameters}) when appropriate.
@node Numeric parameters, , Symbolic parameters, Components
@comment node-name, next, previous, up
@subsection Numeric parameters
@cindex Numeric parameters
Numerical parameters are needed to give specific values to symbolic
parameters (@pxref{Symbolic parameters}) for the purposes of numeric
analysis;
for example: simulation, graph plotting or use within a numerical
package such as Octave (@pxref{Octave}).
@node Algebraic loops, Switched systems, Components, Introduction
@section Algebraic loops
@cindex Algebraic loops
Following Chapter 3 of the book, algebraic loops appear as under-causal
components in the bond graph. It is up to the modeler to indicate how these loops
are to be resolved by adding appropriate SS elements.
For more information, refer to:
``Metamodelling: Bond Graphs and Dynamic Systems'' by Peter Gawthrop and
Lorcan Smith published by Prentice Hall in 1996 (ISBN 0-13-489824-9).
@node Switched systems, , Algebraic loops, Introduction
@comment node-name, next, previous, up
@section Switched systems
@cindex Switched systems
@cindex Hybrid systems
@cindex logic
Some systems contain switch-like components. For example an electrical
system may contain on-off switches and diodes and a hydraulic system may
shut-off valves and non-return valves.
Such systems are sometimes called hybrid systems. The modelling an
simulation of such systems is the subject of current research.
@strong{MTT} implements a simple pragmatic approach to the modelling and
simulation of such systems via two new Bond Graph components:
@vtable @code
@item ISW
a switched @code{I} component
@item CSW
a switched @code{C} component
@end vtable
These switches are user controlled through the logic representation
(@pxref{Simulation logic}).
@node User interface, Creating Models, Introduction, Top
@comment node-name, next, previous, up
@chapter User interface
@cindex User interface
@pindex User interface
There are two user interfaces to @strong{MTT}: a command line interface
(@pxref{Command line interface}) and a menu-driven interface
(@pxref{Menu-driven interface}).
@menu
* Menu-driven interface::
* Command line interface::
* Options::
* Utilities::
@end menu
@node Menu-driven interface, Command line interface, User interface, User interface
@comment node-name, next, previous, up
@section Menu-driven interface
@cindex Menu-driven interface
@pindex Menu-driven interface
The Menu-driven interface for @strong{MTT} is invoked as:
@example
xmtt
@end example
This will bring up a menu which should be self explanatory :-).
Various messages will be echoed in the window from whence @strong{xMTT}
was invoked.
@node Command line interface, Options, Menu-driven interface, User interface
@comment node-name, next, previous, up
@section Command line interface
@cindex Command line interface
@pindex Command line interface
The command line interface for @strong{MTT} is of the form:
@example
mtt [options] <system_name> <representation> <language>
@end example
@vtable @code
@item [options]
the (optional) option switches (@pxref{Options})
@item <system_name>
the name of the system being transformed
@item <representation>
the mnemonic for the system representation (@pxref{Representation summary})
@item <language>
the mnemonic for language for the representation (@pxref{Languages})
@end vtable
for example
@example
mtt rc rep view
@end example
creates a view of the report describing system rc and
@example
mtt rc sm m
@end example
creates an m file (suitlable for Octave or Matlab) containing state
matrices describing the system rc.
@node Options, Utilities, Command line interface, User interface
@comment node-name, next, previous, up
@section Options
@cindex Options
@strong{MTT} has a number of optional switches to control its
operation. These are invoked immediately after `mtt' on the command
line; for example:
@example
mtt -o -s -c syst cbg view
@end example
invokes the @code{-o}, @code{-s}, and @code{-c} options.
The available options are:
@vtable @code
@item -q
quiet mode -- suppress MTT banner
@item -A
solve algebraic equations symbolically
@item -ae
<hybrd> solve algebraic equations numerically
(this option requires -cc or -oct)
@item -D
debug -- leave log files etc
@item -I
prints more information
@item -abg
start at abg.m representation
@item -c
c-code generation
@item -cc
C++ code generation
@item -d
<dir> use directory <dir>
@item -dc
Maximise derivative (not integral) causality
@item -dc
Maximise derivative (not integral) causality
@item -i
<implicit|euler|rk4> Use implicit, euler or Runge Kutta IVintegration
@item -o
ode is same as dae
@item -oct
use oct files in place of m files where appropriate
@item -opt
optimise code generation
@item -p
print environment variables
@item -partition
partition hierachical system
@item -r
reset time stamp on representation
@item -s
try to generate sensitivity BG (experimental)
@item -ss
use steady-state info to initialise simulations
@item -stdin
read input data from standard input for simulations
@item -sub
<subsystem> operate on this subsystem
@item -t
tidy mode (default)
@item -u
untidy mode (leaves files in current dir)
@item -v
verbose mode (multiple uses increase the verbosity)
@item -viewlevel
<N> View N levels of hierachy
@item --version
print version and exit
@item --versions
print version of mtt and components and exit
@end vtable
@node Utilities, , Options, User interface
@comment node-name, next, previous, up
@section Utilities
@cindex Utilities
@pindex Utilities
@strong{MTT} provides some utilities to help you keep track of model
building and to keep things clean and tidy. The commands, and there
purpose are:
@ftable @code
@item mtt help
Lists the help/browser commands
@item mtt copy <system>
Copies the system (ie directory and enclosed files) to the
current working directory.
@item mtt rename <old_name> <new_name>
Renames all of the defining representations (@pxref{Defining
representations}) and textually changes each file appropriately.
@item mtt <system> clean
Remove all files generated by @strong{MTT} associated with
system `system'.
@item mtt clean
Remove all files generated by @strong{MTT} associated with
all systems within the current directory.
@item mtt system representation vc
Apply version control to representation `representation' of
system `system'.
@item mtt system vc
Apply version control to all representations (under version control)
system `system'.
@end ftable
These are described in more detail in the following sections.
@menu
* Help::
* Copy::
* Clean::
* Version control::
@end menu
@node Help, Copy, Utilities, Utilities
@comment node-name, next, previous, up
@subsection Help
@cindex Help
@cindex browser
@strong{MTT} implements a browser to keep track of all the systems,
subsystems and constitutive relationships that you, and others may
write. It is invoked in the following ways:
@example
mtt help representations
mtt help components
mtt help examples
mtt help crs
mtt help representations <match_string>
mtt help components <match_string>
mtt help examples <match_string>
mtt help crs <match_string>
mtt help <component_or_example_or_CR_name>
@end example
@menu
* help representations::
* help components::
* help examples::
* help crs::
* help <name>::
@end menu
@node help representations, help components, Help, Help
@comment node-name, next, previous, up
@subsubsection help representations
@cindex help
@cindex representations
The command
@example
mtt help representations
@end example
lists all of the representations (@pxref{Representations}) available in
@strong{MTT}. These may change as the version number of @strong{MTT}
increases.
The command
@example
mtt help representations <match_string>
@end example
lists those representation which contain the string @code{match_string}.
This string can be any regular expression (see standard Linux
documentation under @code{awk}).
For example
@example
mtt help representations descriptor
@end example
gives all representations containing the word @code{descriptor}.
@node help components, help examples, help representations, Help
@comment node-name, next, previous, up
@subsubsection help components
@cindex help
@cindex components
The command
@example
mtt help components
@end example
lists all of the components (@pxref{Components}) available in
@strong{MTT}. These may change as the version number of @strong{MTT}
increases.
The command
@example
mtt help components <match_string>
@end example
lists those component which contain the string @code{match_string}.
This string can be any regular expression (see standard Linux
documentation under @code{awk}).
For example
@example
mtt help components source
@end example
gives all components containing the word @code{component}.
@node help examples, help crs, help components, Help
@comment node-name, next, previous, up
@subsubsection help examples
@cindex help
@cindex examples
This command provides a good way to get started in @strong{MTT}. having
found an interesting example, copy it to your working directory using
@example
mtt copy <example_name>
@end example
(@pxref{Copy})
@example
mtt help examples
@end example
lists all of the examples available in
@strong{MTT}.
This list will change as more examples are added.
The command
@example
mtt help examples <match_string>
@end example
lists those component which contain the string @code{match_string}.
This string can be any regular expression (see standard Linux
documentation under @code{awk}).
For example
@example
mtt help examples pharmokinetic
@end example
gives all examples containing the word @code{pharmokinetic}.
@node help crs, help <name>, help examples, Help
@comment node-name, next, previous, up
@subsubsection help crs
@cindex help
@cindex crs
The command
@example
mtt help crs
@end example
lists all of the constitutive relationships (@pxref{Constitutive
relationship}) available in
@strong{MTT}. These may change as the version number of @strong{MTT}
increases.
The command
@example
mtt help crs <match_string>
@end example
lists those constitutive relationships which contain the string @code{match_string}.
This string can be any regular expression (see standard Linux
documentation under @code{awk}).
For example
@example
mtt help crs sin
@end example
gives all crs containing the word @code{sin}.
@node help <name>, , help crs, Help
@comment node-name, next, previous, up
@subsubsection help <name>
@cindex help
@cindex <name>
The command
@example
mtt help <name>
@end example
gives a detailed description of the entity called @code{name}.
@node Copy, Clean, Help, Utilities
@comment node-name, next, previous, up
@subsection Copy
@cindex Copy
@strong{MTT} provides a way of copying examples to your working directory:
@example
mtt copy <example_name>
@end example
Use the command
@example
mtt help examples
@end example
(@pxref{help examples}) to find something of interest.
Note that components and constitutive relationships are automatically
copied when required.
@node Clean, Version control, Copy, Utilities
@comment node-name, next, previous, up
@subsection Clean
@cindex Clean
@strong{MTT} generates a lot of representations in a number of
languages.
Some of these you will edit yourself; others can always be recreated by
@strong{MTT}. It makes sense, therefore to have a utility that removes
all of these other files when you have finished actively working with a
particular system. These are two versions:
@enumerate
@item
@code{mtt system clean}
@item
@code{mtt clean}
@end enumerate
The first removes all files that can be regenerated with @strong{MTT}
associated with system `system'; the second removes all such files
associated with all systems in the current working directory.
The files which remain after such a clean are the Defining
representations (@pxref{Defining representations}).
@node Version control, , Clean, Utilities
@comment node-name, next, previous, up
@subsection Version control
@cindex Version control
When you are working on a modeling project, it is easy to forget what
changes you made to a system and why you made them. Sometimes, you may
regret some changes and wish to revert to an earlier version: even if
you use .old files this may be difficult to achieve safely.
These are very similar problems to those faced by software developers
and can be solved in the same way: using version control.@strong{MTT}
provides version control using the standard GNU Revision Control System
(RCS). This is hidden from the user, but is fully complementary to
direct use of RCS (e.g. via emacs vc commands) to the more experienced
user who wishes to do so.
The only files that you should ever change (i.e. the ones never
overwritten by @strong{MTT}) are the Defining representations
(@pxref{Defining representations}).
All of the files, with the exception of @code{system_abg.fig},
are initially created by @strong{MTT} and contain the RCS header for
version control.
The @strong{MTT} version control will automatically expand this part of
the text to include all change comments that you give it -- so will
direct use of RCS (e.g. via emacs vc commands)
The @strong{MTT} version commands are as follows:
@ftable @code
@item mtt system representation vc
Apply version control to representation `representation' of
system `system'.
@item mtt system vc
Apply version control to all representations (under version control)
system `system'.
@end ftable
The first is appropriate after you have made a revision to a single
file. It will prompt you for a change comment; this will be
automatically included in the file header. In addition, enough
information will be saved to enable any version to be retrieved via
RCS.
The second is appropriate to record the state of the entire model. This
assumes that all relevant files have been recorded by the first version
of the command. Once again, old versions of the entire model can be
retrieved using the relevant RCS commands.
A subdirectory `RCS' is created to hold this information. You need not
bother about the contents, except that you must not delete any files
within `RCS'.
@node Creating Models, Simulation, User interface, Top
@comment node-name, next, previous, up
@chapter Creating Models
@cindex Creating Models
@strong{MTT} helps you to analyse and transform system models --
ultimately the process of capturing the real world in a model is up to
you. This chapter discusses the @strong{MTT} aspects of creating a
model. For convenience, this is divided into creating simple models and
creating complex models.
@menu
* Quick start::
* Creating simple models::
* Creating complex models::
@end menu
@node Quick start, Creating simple models, Creating Models, Creating Models
@section Quick start
@cindex Quick start
@pindex Quick start
It is probably worth a quick skim though @strong{MTT} to get a flavour of
what it can do before plunging into the detail of the rest of this
document. Here is a series of commands to do this.
Copy an initial set of files describing the bond graph.
@example
mtt copy rc
@end example
@noindent
Move to it.
@example
cd rc
@end example
@noindent
@noindent
View the acausal bond graph (the system is called ``rc'').
@example
mtt rc abg view
@end example
@noindent
View the causal bond graph of the system.
@example
mtt rc cbg view
@end example
@noindent
View the corresponding ordinary differential equations (ode).
@example
mtt rc ode view
@end example
@noindent
View the system (output) step response
@example
mtt rc sro view
@end example
@noindent
An alternative (but more general) way of achieving the same result is
@example
mtt -c rc odeso view
@end example
@noindent
View the system transfer function
@example
mtt rc tf view
@end example
@noindent
View the log modulus frequency response of the system.
@example
mtt rc lmfr view
@end example
@noindent
View the log modulus frequency response of the system for 100
logarithmically spaced frequencies in the range 0.1 to 10
radians per second.
@example
mtt rc lmfr view 'W=logspace(-1,1,100);'
@end example
@strong{MTT} has a report generation ((@pxref{Report}) facility which
can generate a hypertext description of the system.
@example
mtt rc rep hview
@end example
The report contents are specified by the rep representation
(@pxref{Report}), in this case the corresponding file is:
@example
% %% Outline report file for system rc (rc_rep.txt)
mtt rc abg tex
mtt rc struc tex
mtt rc cbg ps
mtt rc ode tex
mtt rc ode dvi
mtt rc sm tex
mtt rc tf tex
mtt rc tf dvi
mtt rc sro ps
mtt rc lmfr ps
mtt rc odes h
mtt rc numpar txt
mtt rc input txt
mtt -c rc odeso ps
mtt rc rep txt
@end example
A non-hypertext version can be viewed using:
@example
mtt rc rep view
@end example
Now have a go at modifying the bond graph.
@example
mtt rc abg fig
@end example
This brings up the bond graph in Xfig (@pxref{Xfig}). Try creating a
system with two rs and 2 cs.
More examples can be found using
@example
mtt help examples
@end example
Details of an example can be found using
@example
mtt help <example_name>
@end example
and copied using
@example
mtt copy <example_name>
@end example
Lots of examples are available.
@example
mtt help examples
@end example
lists them and
@example
mtt copy <name>
@end example
gets you an example.
@ifhtml
A number of examples are to be found
<A
HREF="http://www.mech.gla.ac.uk/~peterg/software/MTT/examples/Examples/Examples.html"> here</A>.
@end ifhtml
@node Creating simple models, Creating complex models, Quick start, Creating Models
@comment node-name, next, previous, up
@section Creating simple models
@cindex Creating simple models
For then purposes of this section, simple models are those which are
built up from bond graphs involving predefined components. In contrast,
more complex systems (@pxref{Creating complex models}) need to be built
up hierarchically.
The recommended sequence of steps to create a simple model is:
@enumerate
@item Decide on a name for the system; let us call it `syst' for the
purposes of this discussion.
@item Invoke the Bond Graph editor to draw the acausal Bond Graph.
@example
mtt syst abg fig
@end example
@item Draw the Bond Graph (@pxref{Language fig (abg.fig)}), including
the bonds (@pxref{Bonds}), the components (@pxref{Components}) and any
artwork (@pxref{artwork}) to make the Bond Graph more readable. The
graphical editor xfig is (@pxref{Xfig}) is self-explanatory.
The icon library is helpful here (see @pxref{icon library}).
@item Add causal strokes (@pxref{strokes}) where needed to define
causality. As a general rule, use the minimum number of strokes needed
to define the problem; this will often be only on the @code{SS} components.
(@pxref{SS components}).
Save the bond graph.
@item View the corresponding causal bond graph.
@example
mtt syst cbg view
@end example
@enumerate
@item
At this stage, @strong{MTT} will warn you that the labeled components do
not appear in the label file - this can safely be ignored.
@item
@strong{MTT} will indicate the percentage of components which are
causally complete -- ideally this will be 100\%. Components which are
not causally complete will be listed.
@item
A view of the causal bond graph will be created. The added causal
strokes are indicated in blue, undercausal components in green and
overcausal components in red.
@item
If the bond graph is causally complete, proceed to the next step,
otherwise think hard and return to the first step.
@end enumerate
@item
At this stage, no constitutive relationships have been
defined. Nevertheless, @strong{MTT} will proceed in a semi-qualitative
fashion by assuming that all constitutive relationships are unity (and
therefore linear). It may be useful at this stage to view various
derived representations to check the overall model properties before
proceeding further. For example:
@enumerate
@item
View the system Differential-algebraic equations
@example
mtt syst dae view
@end example
@item
View the system state matrices
@example
mtt syst sm view
@end example
@item
View the system transfer function
@example
mtt syst tf view
@end example
@item
View the system step response
@example
mtt syst sro view
@end example
@end enumerate
@item
As well as creating the causal bond graph, @strong{MTT} has also
generated templates for other text files
(@pxref{Defining representations})
used to further specify the
system.
These can now be edited using your favorite text editor (@pxref{Text
editors}).
@item @strong{MTT} will now generate the representations
(@pxref{Representation summary})that you desire.
For example the system can be simulated by
@example
mtt syst odeso view
@end example
@strong{MTT} will complain if a component is named in the bond graph but
not in the label file and vice versa. This mainly to catch typing errors.
@end enumerate
@node Creating complex models, , Creating simple models, Creating Models
@comment node-name, next, previous, up
@section Creating complex models
@cindex Creating complex models
Complex models -- in distinction to simple models (@pxref{Creating
simple models}) -- have a hierarchical structure. In particular, bond
graph components can be created by specifying their bond
graph. Typically, such components will have more than one port
(@pxref{Ports}); within each component, ports are represented by
named SS components (@pxref{Named SS components}); outwith
each component, ports are unambiguously identified by
labels (@pxref{Port labels}) and vector labels (@pxref{Vector port labels}).
Complex models are thus created by conceptually decomposing the system
into simple subsystems, and then creating the corresponding bond graphs.
The procedure for simple systems (@pxref{Creating simple models}) is
then followed using the top level system (@pxref{Top level}); @strong{MTT} then recursively
operates on the lower level systems.
The report representation (@pxref{Report}) provides a convenient way of
viewing a complex system.
An example of such a system can be created as follows:
@example
mtt copy twolink
mtt twolink rep hview
@end example
@ifhtml
The result is <A
HREF="./examples/twolink/twolink_rep/twolink_rep.html"> here</A>.
@end ifhtml
@menu
* Top level::
@end menu
@node Top level, , Creating complex models, Creating complex models
@comment node-name, next, previous, up
@subsection Top level
@cindex Top level
The top level of a complex model contains subsystems but is not, itself,
contained by other systems.
It has the following special features:
@itemize @bullet
@item
its name is used in the mtt command as the system name.
@item
all named SS componenents (@pxref{Named SS components}) are treated as
ordinary SS components (@pxref{SS components}).
@end itemize
@c node next prev up
@node Simulation, Sensitivity models, Creating Models, Top
@chapter Simulation
@cindex Simulation
@pindex Simulation
One purpose of modelling is to simulate the modeled dynamic
system. Although this is just another transformation (@pxref{What is a
Transformation?}) and therefore is covered in the appropriate chapter
(@pxref{Representations}), it is important enough to be given its own
chapter.
Simulation is typically performed using an appropriate simulation
language (which is often inappropriately conflated with modelling
tools). @strong{MTT} provides a number of alternative routes to
simulation based on the following representations (@pxref{Representations}):
@ftable @code
@item cse
constrained-state differential equation form
@item ode
ordinary differential (or state-space) equations
@c @item dae
@c differential-algebraic (or generalised state-space) equations --
@c these may be linear or nonlinear.
@end ftable
in each case these equations may be
linear or nonlinear.
Special cases of numerical simulation, appropriate to @emph{linear}
systems, are:
@ftable @code
@item ir
impulse response - state
@item iro
impulse response - output
@item sr
impulse response - state
@item sro
impulse response - output
@end ftable
There are a number of languages (@pxref{Languages}) which can be used to describe these
representations for the purposes of numerical simulation:
@ftable @code
@item m
@code{octave} a high-level interactive language for numerical
computation.
@item c
@code{gcc} a c compiler.
@item cc
@code{g++} a C++ front-end to gcc.
@end ftable
There are a number solution algorithms available:
@itemize @bullet
@item
explicit solution via the matrix exponential
@item
backward Euler integration (explicit)
@item
forward Euler integration (implicit)
@item
Runge Kutta IV integration (explicit, fixed step)
@item
Hybrd algebraic solver (MINPACK, Octave fsolve)
@c @item
@c LSODE (Hindmarsh's ODE solver as implemented in Octave)
@c @item
@c DASSL (Petzold's DAE solver as implemented in Octave) (Unavailable just now)
@end itemize
However, all combinations of representation, language and solution
method are not supported by @strong{MTT} at the moment. Given a system
`system', some recommended commands are:
@ftable @code
@item mtt system iro view
creates the impulse response of a @emph{linear} system via the
system_sm.m representation using explicit solution via the matrix exponential.
@item mtt system sro view
creates the step response of a @emph{linear} system via the system_sm.m
representation using explicit solution via the matrix exponential.
@c @item mtt system odeso view
@c creates the step response of a @emph{nonlinear} system via the
@c system_ode.m representation using either METHOD=Euler or
@c METHOD=LSODE in the parameter file (@pxref{Simulation parameters}).
@item mtt -c system odeso view
creates the response of a @emph{nonlinear} system via the
system_ode.c representation using implicit integration.
@item mtt -c -i euler system odeso view
creates the response of a @emph{nonlinear} system via the
system_ode.c representation using euler integration.
@end ftable
Simulation parameters are described in the system_simpar.txt file
(@pxref{Simulation parameters}).
The steady-state solution of a system can also be
``simulated''(@pxref{Steady-state solutions}).
@menu
* Steady-state solutions::
* Simulation parameters::
* Simulation input::
* Simulation logic::
* Simulation initial state::
* Simulation code::
* Simulation output::
@end menu
@node Steady-state solutions, Simulation parameters, Simulation, Simulation
@comment node-name, next, previous, up
@section Steady-state solutions
@cindex Steady-state solutions
@menu
* Steady-state solutions - numerical(odess)::
* Steady-state solutions - symbolic (ss)::
@end menu
@node Steady-state solutions - numerical(odess), Steady-state solutions - symbolic (ss), Steady-state solutions, Steady-state solutions
@comment node-name, next, previous, up
@subsection Steady-state solutions (odess)
@cindex Steady-state solutions - numerical
@strong{MTT} can compute the steady-state solutions of an ordinary
differential equation; this used the octave function `fsolve'. The
solution is computed as a function of time using the input specified in
the input file. The simulation parameter file (@pxref{Simulation
parameters}) is used to provide the time scales.
For example
@example
mtt copy rc
cd rc
mtt rc odess view
@end example
@node Steady-state solutions - symbolic (ss), , Steady-state solutions - numerical(odess), Steady-state solutions
@comment node-name, next, previous, up
@subsection Steady-state solutions (ss)
@cindex Steady-state solutions - symbolic
A rudimentary form of steady-state solution exists in mtt.
The steady states and inouts are supplied by the user in the file
system_simpar.r and the corresponding output and sate derivative
computed by @strong{MTT} using
@example
mtt system ss view
@end example
For example
@example
mtt copy rc
cd rc
mtt rc sspar view
mtt rc ss view
@end example
@node Simulation parameters, Simulation input, Steady-state solutions, Simulation
@comment node-name, next, previous, up
@section Simulation parameters
@cindex Simulation parameters
Simulation parameters are set in the system_simpar.txt file. At the
moment this sets the following variables:
@itemize @bullet
@item LAST
the last simulation time
@item DT
the incremental time (for plotting)
@item STEPFACTOR
the number of integration steps per DT -- thus the integration
interval is DT/STEPFACTOR
@c ; for sparse implicit integration (@pxref{Sparse
@c implicit integration}) the number of conjugate-gradient minimisation
@c steps.
@c @item METHOD
@c The integration methods available appear in the following table
@item WMIN
Minimum frequency = 10^WMIN
@item WMAX
Maximum frequency = 10^WMAX
@item WSTEPS
Number of Frequency steps.
@item INPUT
The input index for frequency response
@end itemize
There are a number of solution algorithms
@itemize @bullet
@item Euler
basic Euler integration (@pxref{Euler integration}). This method
is simple, but not recommended for stiff systems.
@item Implicit
semi-implicit integration (@pxref{Implicit integration}) - uses the smx representation to give
stability.
@item Runge Kutta IV
fixed step Runge Kutta fourth order integration (@pxref{Runge Kutta IV integration}).
@item Hybrd
numerical algebraic equation solver
@c @item ImplicitS
@c Sparse semi-implicit integration (@pxref{Sparse implicit integration})
@c -- takes advantage of the sparsity of the A matrix.
@c @item LSODE
@c the variable step-size method that comes with Octave (@pxref{Octave}).
@end itemize
@menu
* Euler integration::
* Implicit integration::
* Runge Kutta IV integration::
* Hybrd algebraic solver::
@end menu
@node Euler integration, Implicit integration, Simulation parameters, Simulation parameters
@comment node-name, next, previous, up
@subsection Euler integration
@cindex Euler integration
Euler integration approximates the solution of the Ordinary Differential Equation
@example
dx/dt = f(x,u)
@end example
by
@example
x := x + f(x,u)*DDT
@end example
where
@example
DDT = DT/STEPFACTOR
@end example
If the system is linear, stability is ensured if the integer STEPFACTOR
is chosen to be greater than the real number
@example
(maximum eigenvalue of -A)*DT/2
@end example
where A is the nxn matrix appearing in
@example
f(x,u) = Ax + Bu
@end example
If the system is non linear, the linearised system matrix A should act
as a guide to the choice of STEPFACTOR.
@node Implicit integration, Runge Kutta IV integration, Euler integration, Simulation parameters
@comment node-name, next, previous, up
@subsection Implicit integration
@cindex Implicit integration
Implicit integration approximates the solution of the Ordinary Differential Equation
@example
dx/dt = f(x,u)
@end example
by
@example
(I-A*DT)x := (I-A*DT)x + f(x,u)DT
@end example
where A is the linearised system matrix. This implies the solution of N
(=number of states) linear equations at each sample interval. The OCTAVE
version used the `\' operator to solve the set of linear equations, the
C version uses LU decomposition.
If the system is linear, stability is ensured unconditionaly. If the
system is non-linear, then the method still works well.
This method is nice in that choice of DT trades of accuracy against
computation time without compromising stability. In addition, the
correct stready-state values are achieved.
This approach can also be used for constrained state equations of the
form:
@example
E(x) dx/dt = f(x,u)
@end example
where E(x) is a state-dependent matrix. The approximate solution is then
given by:
@example
(E(x)-A*DT)x := (E(x)-A*DT)x + f(x,u)DT
@end example
which reduces to the ordinary differential equation case when E(x)=I.
The _smx representation includes the E matrix.
@node Runge Kutta IV integration, Hybrd algebraic solver, Implicit integration, Simulation parameters
@comment node-name, next, previous, up
@subsection Runge Kutta IV integration
Runge Kutta IV approximates the solution of the Ordinary Differential Equation
@example
dx/dt = f(x,t)
@end example
by
@example
x := x + (DT/6)*(k1 + 2*k2 + 2*k3 + k4)
@end example
where
@example
k1 := f(x,t)
k2 := f(x+(1/2)*k1,t+(1/2)*DT)
k3 := f(x+(1/2)*k2,t+(1/2)*DT)
k4 := f(x+k3,t+DT)
@end example
The @strong{MTT} implementation of Runge-Kutta integration
is a fourth order, fixed-step, explicit integration method.
For some systems of equations, the increased accuracy of using a fourth order
method can allow larger step-lengths to be used than would allowed by the
lower order Euler integration method.
It should be noted that during the interemediate calculations (k1...k4),
the input vector @code{u} is not advanced w.r.t. time; the system inputs are
assumed to be constant over the period of the integration step-length.
@node Hybrd algebraic solver, , Runge Kutta IV integration, Simulation parameters
@comment node-name, next, previous, up
@subsection Hybrd algebraic solver
The hybrd algebraic solver of @uref{http://www.netlib.org/minpack/hybrd.f,MINPACK},
which is used by Octave in the @code{fsolve} routine, may be used in conjunction
with one of the other integration methods to solve semi-explicit, index 1, differential
algebraic equations; these may be generated in @strong{MTT} models by use of
@code{unknown} SS Components @pxref{SS component labels}.
This method requires that compiled simulation code is used; either -cc or -oct.
To perform a simulation based on a model @code{sys},
@example
mtt -cc -ae hybrd -i euler sys odeso view
@c XXX: should be daeso view?
@end example
@strong{MTT} will attempt to minimise the residual error at each integration time-step
using the hybrd routine.
This method of simulation is particularly well suited to stiff systems where very fast
dynamics are of little interest. Care must be taken to ensure that an acceptable level
of convergence is achieved by the solver for the system under investigation.
@c XXX: tolerance option
@c @node Sparse implicit integration, , Implicit integration, Simulation parameters
@c @comment node-name, next, previous, up
@c @subsection Sparse implicit integration
@c @cindex Sparse implicit integration
@c This is an experimental approach for large (N>50) systems.
@c Implicit integration (@pxref{Implicit integration}) requires the
@c solution of N linear equations at each step. This is an O(N^3) operation
@c which can be time consuming for large (N>50) systems. However, the A
@c matrix (and hence the (I-A*DT) matrix) is often sparse - most elements
@c are zero.
@c This method uses a conjugate-gradient optimisation method to solve the
@c linear equations
@c @example
@c (I-A*DT)x := (I-A*DT)x + f(x,u)DT
@c @end example
@c by recasting them as the minimisation of the quadratic function
@c @example
@c [(I-A*DT)x_new - (I-A*DT)x_old + f(x,u)DT]^2
@c @end example
@c with respect to x_new. This is solved by the conjugate gradient method.
@c MTT generates two representations _smxx.m and _smxtx to compute
@c (I-A*DT)x and (I-A*DT)'x respectively making full use of the sparsity of
@c the (I-A*DT) matrices to speed up the minimisation procedure.
@c A fixed number of iterations (STEPFACTOR) are used in each optimisation
@c to give a fixed simulation time. This must be chosen by the user, but
@c between 5N and 10N seems ok. Note that the initial value of the
@c optimisation is x_old.
@node Simulation input, Simulation logic, Simulation parameters, Simulation
@comment node-name, next, previous, up
@section Simulation input
@cindex Simulation input
This is defined in the system_input.txt file. A default file is created
automatically by @strong{MTT}. This is done explicitly by
@example
mtt system input txt
@end example
If the file already exists, the same command checks that all inputs are
defined and that all defined inputs exist in the system and promts the
user to correct discrepancies.
Inputs are defined by the full system name appearing in the structure
file (@pxref{Structure (struc)}). They can depend on states (again defined by
name), time (defined by t) and parameters
For example:
@example
system_pump_l_1_u = 4e5*atm;
system_pump_r_1_u = 4e5*(t<10)*atm;
system_ss_i = 0*kg;
system_ss_o = 3e-3*kg;
system_v_1_u = (t>10);
system_v_ll_1_u = 1;
system_v_lr_1_u = (t<10);
system_v_ul_1_u = 0;
system_v_ur_1_u = (t>10);
@end example
@node Simulation logic, Simulation initial state, Simulation input, Simulation
@comment node-name, next, previous, up
@section Simulation logic
@cindex Simulation logic
This is defined in the system_logic.txt file. A default file is created
automatically by @strong{MTT}. This is done explicitly by
@example
mtt system logic txt
@end example
If the file already exists, the same command checks that the logic
corresponding to all switch states (@pxref{Switched systems}) are
defined and that all defined logic exists in the system and promts the
user to correct discrepancies.
Logical inputs are defined by the full system name corresponding to
MTT_switch components appearing in the structure file (@pxref{Structure
(struc)}) @emph{with `_logic' appended}. They can depend on states (again defined by name), time
(defined by t) and parameters
For example:
@example
bounce_ground_1_mtt_switch_logic = bounce_intf_1_mtt3<0;
@end example
@node Simulation initial state, Simulation code, Simulation logic, Simulation
@comment node-name, next, previous, up
@section Simulation initial state
@cindex Simulation initial state
This is defined in the system_state.txt file. A default file is created
automatically by @strong{MTT}. This is done explicitly by
@example
mtt system state txt
@end example
If the file already exists, the same command checks that all states are
defined and that all defined states exist in the system and prompts the
user to correct discrepancies.
States are defined by the full system name appearing in the structure
file (@pxref{Structure (struc)}). They can depend on parameters.
For example
@example
system_c_l = (1e4/k_l)/kg;
system_c_ll = (1e4/k_s)/kg;
system_c_lr = (1e4/k_s)/kg;
system_c_u = (1e4/k_l)/kg;
@end example
@c The initial state of a simulation of is set in the @code{state}
@c representation with the language @code{txt}.
@c As usual, @strong{MTT} defaults this for you. There are two
@c possibilities
@c @itemize @bullet
@c @item
@c The -ss switch is not present: the states default to zero
@c @item
@c The -ss switch is present: the states default to those set in the
@c sspar.r file.
@c @end itemize
@node Simulation code, Simulation output, Simulation initial state, Simulation
@comment node-name, next, previous, up
@section Simulation code
simulation code can be generated by @strong{MTT} in the form
of the @code{ode2odes} transformation. This can be produced in a number
of languages, including .m, .oct, C and C++ @pxref{Languages}.
To generate simulation code in C:
@example
mtt -c [options] sys ode2odes c
@end example
Similarly, to generate C++ code:
@example
mtt -cc [options] sys ode2odes cc
@end example
To generate an executable based on the C++ representation:
@example
mtt -cc [options] sys ode2odes exe
@end example
@menu
* Dynamically linked functions::
@end menu
@node Dynamically linked functions, , Simulation code, Simulation code
@comment node-name, next, previous, up
@subsection Dynamically linked functions
Some model representations can be compiled into dynamically loaded
code (shared objects) which are compiled prior to use in other
modelling and simulation environments; in particular, .oct files can
be generated for use in GNU Octave (@pxref{Creating GNU Octave .oct
files}) and .mex files can be generated for use in Matlab
(@pxref{Creating Matlab .mex files}) or Simulink (@pxref{Embedding MTT
models in Simulink}). The use of compiled (and possibly
compiler-optimised) code can offer significant processing speed
advantages over equivalent interpreted functions (e.g. .m files) for
computationally intensive procedures.
The C++ code generated by @strong{MTT} allows the same code to be
generated as standalone code, Octave .oct files or Matlab .mexglx
files. Although @strong{MTT} usually takes care of the compilation
options, if it is necessary to compile the code on a machine on which
@strong{MTT} is not installed, the appropriate flag should be passed
to the compiler pre-processor:
@itemize @bullet
@item
@code{-DCODEGENTARGET=STANDALONE}
@item
@code{-DCODEGENTARGET=OCTAVEDLD}
@item
@code{-DCODEGENTARGET=MATLABMEX}
@end itemize
@node Simulation output, , Simulation code, Simulation
@comment node-name, next, previous, up
@section Simulation output
@cindex Simulation output
The view (@pxref{Views}) representation provides a graphical
representation of the results of a simulation; the postscript language
provides the same thing in a form that can be included in a document.
These are two simulation output representations
@ftable @code
@item odes
ordinary differential equation solution (states)
@item odeso
ordinary differential equation solution (output)
@end ftable
Particular output variables can be selected by adding a fourth argument
in one of 2 forms
@ftable @code
@item 'name1;name2;..;namen'
plot the variables with names na1 .. namen against time
@item 'name1:name2'
plot the variable with name2 against that with name 1
@end ftable
An example of plotting a single variable against time is:
@example
mtt -o -c -ss OttoCycle odeso ps 'OttoCycle_cycle_V'
@end example
An example of plotting one variable against another is:
@example
mtt -o -c -ss OttoCycle odeso ps 'OttoCycle_cycle_V:OttoCycle_cycle_P'
@end example
@menu
* Viewing results with gnuplot::
* Exporting results to SciGraphica::
@end menu
@node Viewing results with gnuplot, Exporting results to SciGraphica, Simulation output, Simulation output
@comment node-name, next, previous, up@subsection
@subsection Viewing results with gnuplot
@cindex gnuplot
Simulation plots may be conveniently selected, viewed with
@uref{http://www.gnuplot.org,gnuplot}
and saved to file (in PostScript format) using the command
@example
mtt [options] rc gnuplot view
@end example
This will cause a menu to be displayed, from which states and outputs may be selected for viewing. Clicking on a @emph{parameter name} will cause a new window to be opened displaying the time history of the selected parameter. Selecting the @emph{print} option in the main window provides the option of saving to file a plot of the last selected parameter. Clicking on the @emph{title bar} of the main window (``Outputs'' or ``States'') will alter the order in which the parameter names are displayed.
It should be noted that unlike other representations, if a simulation has been previously run in a directory, this command will @emph{not} cause @strong{MTT} to re-run a simulation, even if any of the input files have been changed.
If it is desired to re-run a simulation, it is advisable to run the command
@example
mtt [options] rc odeso view ; mtt [options] rc gnuplot view
@end example
As with @strong{xMTT} (@pxref{Menu-driven interface}), the Wish Tcl/Tk interpreter must be installed to make use of this feature.
@node Exporting results to SciGraphica, , Viewing results with gnuplot, Simulation output
@comment node-name, next, previous, up
@subsection Exporting results to SciGraphica
@cindex SciGraphica
Simulation results can be converted into an XML-format
@uref{http://scigraphica.sourceforge.net,SciGraphica} (version 0.61)
@emph{.sg} file with the command
@example
mtt [options] sys odes sg
@end example
The SciGraphica file will contain two worksheets, X_sys and Y_sys, containing
the state and output time-histories from the simulation.
@c node next prev up
@node Sensitivity models, Representations, Simulation, Top
@chapter Sensitivity models
@cindex Sensitivity models
@pindex Sensitivity models
The sensitivity model of a system is a set of equations giving the
sensitivity of the system outputs with respect to system parameters.
@strong{MTT} has built in methods for assisting with the development of
such models.
This feature is experimental at the moment, but the following example
gives an idea of what can be achieved.
@example
mtt copy rc
cd rc
mtt -s src ode view
mtt -s src odeso view
@end example
The sensitivity system src is automatically created from the system rc
using the predefined sR and sC components together with vector junctions
(@pxref{Vector components}). The four outputs are the two system
outputs plus the two sensitivity functions.
An alternative route is to create the sensitivity functions by symbolic
differentiation.
The following sensitivity representations are available:
@ftable @code
@item scse
sensitivity constrained-state equations
@item sm
sensitivity state matrices
@item scsm
sensitivity constrained-state matrices
@end ftable
@c node next prev up
@node Representations, Extending MTT, Sensitivity models, Top
@chapter Representations
@cindex Representations
@pindex Representations
@cindex Defining representations
@cindex Representations, defining
As discussed in @ref{What is a Representation?}, a system has many
representations. The purpose of @strong{MTT} is to provide an easy way to
generate such representation by applying the appropriate sequence of
transformations. The representations supported by @strong{MTT} are
summarised in @ref{Representation summary}.
There is a two-fold division of representations into those with which the user
defines the system and its various attributes, and those which are
derived from these. The @emph{defining representations} are listed in
@ref{Defining representations}.
Each representation is implemented in one or more languages depending on
its use. These languages are discussed in @ref{Languages} and are
associated with appropriate tools for modifying or viewing the
representations.
@menu
* Representation summary::
* Defining representations::
* Verbal description (desc)::
* Acausal bond graph (abg)::
* Stripped acausal bond graph (sabg)::
* Labels (lbl)::
* Description (desc)::
* Structure (struc)::
* Constitutive Relationship (cr)::
* Parameters::
* Causal bond graph (cbg)::
* Elementary system equations::
* Differential-Algebraic Equations::
* Constrained-state Equations::
* Ordinary Differential Equations::
* Descriptor matrices::
* Report::
@end menu
@node Representation summary, Defining representations, Representations, Representations
@comment node-name, next, previous, up
@section Representation summary
@cindex Representation summary
Some of the the representations
available in @strong{MTT} are (in alphabetical order):
@ftable @code
@item abg
acausal bond graph
@item cbg
causal bond graph
@item cr
constitutive relationship for each subsystem
@item cse
constrained-state equations
@item csm
constrained-state matrices
@item dae
differential-algebraic equations
@item daes
dae solution - state
@item daeso
dae solution - output
@item def
definitions - system orders etc.
@item desc
Verbal description of system
@item dm
descriptor matrices
@item ese
elementary system equations
@item fr
frequency response
@item input
numerical input declaration
@item ir
impulse response - state
@item iro
impulse response - output
@item lbl
label file
@item lmfr
loglog modulus frequency response
@item lpfr
semilog phase frequency response
@item nifr
Nichols style frequency response
@item numpar
numerical parameter declaration
@item nyfr
Nyquist style frequency response
@item obs
observer equations for CGPC
@item ode
ordinary differential equations
@item odes
ode solution - state
@item odes
ODE simulation header file
@item odeso
ode solution - output
@item odess
ode numerical steady-states - states
@item odesso
ode numerical steady-states - outputs
@item rbg
raw bond graph
@item rep
report
@item rfe
robot-form equations
@item sabg
stripped acausal bond graph
@item simp
simplification information
@item sm
state matrices
@item smx
state matrices containing explicit states and inputs
@item sms
ode
@item smss
SM simulation header file
@item sr
step response - state
@item sro
step response - output
@item ss
steady-state equations
@item sspar
steady-state definition
@item struc
structure - list of inputs, outputs and states
@item sub
Executable subsystem list
@item sub
LaTeX subsystem list
@item sympar
symbolic parameters
@item tf
transfer function
@end ftable
A complete list can be found via the @code{help representations} command
(@pxref{help representations}).
Many of these representations have more than one language (@pxref{Representations}) associated
with them.
Some of these representations define the system (@pxref{Defining
representations}).
@node Defining representations, Verbal description (desc), Representation summary, Representations
@comment node-name, next, previous, up
@section Defining representations
@cindex Defining representations
The following representations define the system and therefore must,
ultimately, be defined by the user. However, all of these are assigned
default values by @strong{MTT} and may then be subsequently edited
(@pxref{Text editors}) viewed or operated on by the appropriate tools
(@pxref{Language tools}).
@vtable @code
@item system_abg.fig
the acausal bond graph (@pxref{Acausal bond graph (abg)})
@item system_lbl.txt
the label file (@pxref{Labels (lbl)})
@item system_desc.tex
the description file (@pxref{Description (desc)})
@item system_simp.r
algebraic simplifications to make output more readable
(@pxref{Symbolic parameters for simplification (simp.r)})
@item system_subs.r
algebraic substitutions to resolve, eq trig. identities
(@pxref{Symbolic parameters (subs.r)})
@item system_simpar.txt
simulation parameters (@pxref{Simulation parameters})
@item system_numpar.txt
numerical parameters (@pxref{Numeric parameters (numpar)})
@item system_input.txt
the system input for simulations (@pxref{Simulation input})
@item system_logic.txt
the switching logic for simulations (@pxref{Simulation logic})
@item system_sspar.r
defines the system steady-state (@pxref{Steady-state solutions - symbolic (ss)})
@end vtable
@node Verbal description (desc), Acausal bond graph (abg), Defining representations, Representations
@comment node-name, next, previous, up
@section Verbal description (desc)
@cindex Verbal description (desc)
Systems can be documented in LaTeX using the _desc.tex file. This file
is included in the report (@pxref{Report}) if the abg tex option
is included in the rep.txt file. As usual, @strong{MTT} provides a
default text file to be edited by the user (@pxref{Text editors}).
@c node next prev up
@node Acausal bond graph (abg), Stripped acausal bond graph (sabg), Verbal description (desc), Representations
@section Acausal bond graph (abg)
@cindex Acausal bond graph (abg)
@pindex Acausal bond graph (abg)
The acausal bond graph is the main input to @strong{MTT}. It is up to you, as a
system modeler, to distill the essential aspects of the system that you
wish to model and capture this information in the form of a bond graph.
The inexperienced modeler may wish to look in one of the standard
textbooks and copy some bond graphs of systems to get going.
To create the acausal bond graph of system `sys' in language fig type:
@example
mtt sys abg fig
@end example
To create the acausal bond graph of system `sys' in language m type:
@example
mtt sys abg m
@end example
To view the acausal bond graph of system `sys' type:
@example
mtt sys abg view
@end example
@menu
* Language fig (abg.fig)::
* Language m (rbg.m)::
* Language m (abg.m)::
* Language tex (abg.tex)::
@end menu
@node Language fig (abg.fig), Language m (rbg.m), Acausal bond graph (abg), Acausal bond graph (abg)
@subsection Language fig (abg.fig)
@cindex Language fig (abg.fig)
@pindex Language fig (abg.fig)
A bond graph is made up of:
@ftable @code
@item bonds
To connect components together.
@item strokes
To indicate causality.
@item components
Either simple or compound.
@item artwork
Irrelevant to the system but useful to the user.
@end ftable
An icon library of bonds, components and other symbols is available
within xfig (@pxref{icon library}).
@menu
* icon library::
* bonds::
* strokes::
* components::
* Simple components::
* SS components::
* Simple components - implementation::
* Compound components::
* Named SS components::
* Coerced bond direction::
* Port labels::
* Vector port labels::
* Port label defaults::
* Vector components::
* artwork::
* Valid names::
@end menu
@node icon library, bonds, Language fig (abg.fig), Language fig (abg.fig)
@subsubsection Icon library
@cindex Icon
@cindex library
A number of predefined iconic symbols are available within xfig.
@example
Click onto the library icon
Click onto the library pull-down menu and select BondGraph
Select iconic symbols from the presented list
@end example
@node bonds, strokes, icon library, Language fig (abg.fig)
@subsubsection Bonds
@cindex bonds
@pindex bonds
Bonds are represented by polylines with two segments. They must be the
default style (i.e. plain not dashed or dotted). The shortest segment is
taken to be the half-arrow. its positioning is significant because:
@itemize @bullet
@item
It points in the direction of power flow; thus a bond normally points
towards C, I and R components.
@item
the corresponding side of the bond indicates flow causality; the other
side represents effort causality. This is significant when using casual
half-strokes (@pxref{strokes}). Please adopt the convention of having
the half-arrows below horizontal bonds and to the right of vertical bonds.
@end itemize
@c node next prev up
@node strokes, components, bonds, Language fig (abg.fig)
@subsubsection Strokes
@cindex strokes
@pindex strokes
Causal strokes are represented by single-segment polylines.
There are two sorts of strokes:
@itemize @bullet
@item
@emph{Full} strokes: these are the usual bond-graph strokes and determine
both the effort and flow causality in the usual way. The @emph{centre} of the
stroke should be at about one end of the bond and be at right angles to
it.
@item
@emph{Half} strokes: these are an innovation in @strong{MTT} and allow you to
specify the effort and flow causality independently. The @emph{end} of the
stroke should be at about one end of the bond and be at right angles to
it. If the causal half-stroke is on the @emph{same} side as the half-arrow
(@pxref{bonds}) then it determines @emph{flow} causality; if, on the other
hand, it is on the @emph{opposite} side to the half-arrow
(@pxref{bonds}) then it determines @emph{effort} causality.
Two half strokes on the @emph{same}, but on @emph{opposite} sides of the
bond are equivalent to a a full stroke at the same end of the bond.
@end itemize
@strong{MTT} is reasonably forgiving; but a neat diagram will be less ambiguous to
you as well as to @strong{MTT}.
Causality is indicated as follows:
@itemize @bullet
@item
@emph{Effort} is imposed at the @emph{same} end as the stroke.
@item
@emph{Flow} is imposed at the @emph{opposite} end as the stroke.
@end itemize
@c node next prev up
@node components, Simple components, strokes, Language fig (abg.fig)
@subsubsection Components
@cindex components
@pindex components
Components are represented by a text string in fig. The recommended
style is: 20pt, Times-Roman and centre justified.
The component text string can be of the following forms:
@ftable @code
@item type
Just the type of the component is indicated. Components may be either
Simple components (@pxref{Simple components}) or Compound components
(@pxref{Compound components}). For example:
@example
R
@end example
@item type:label
Both the type and the label of the component are given. The type must be
a valid name (@pxref{Valid names}.The name provides a link to more
information to be found in @xref{Labels (lbl)}. For example:
@example
R:r
@end example
@item type:label:cr
Not only are the type and the label of the component given, but also the
component cr argument. The type must be
a valid name (@pxref{Valid names}.The name provides a link to more
information to be found in @xref{Labels (lbl)}. For example:
@example
R:r:flow,r
@end example
@item type:label:expression
Expression is a mathematical expression relating the effort (called
mtt_e) to the flow (called mtt_f).
For example the following three forms are equivalent
@example
R:r:mtt_e=r*mtt_f
R:r:mtt_e-r*mtt_f=0
R:r:mtt_f=mtt_e/r
@end example
A non-linear example is:
@example
R:r:mtt_e = sin(mtt_f)
@end example
@item type*n
The name, together with the number @samp{n} of repetitions of the
component, are given. This repetition only makes sense if the component
has an even number of ports (@pxref{Port labels}); n copies of the component
are concatenated with odd Named ports (@pxref{Port labels}) of the
component being connected to the even Named ports of the previous
component in the chain in numerical order. This feature is particularly
useful if the component is compound and can be used for, example to give
a lumped approximation of a distributed system. For example:
@example
MySystem*25
@end example
@item type:label*n
This complete form and is a combination of the simpler forms. For
example:
@example
MySystem:MyLabel*25
@end example
@end ftable
@node Simple components, SS components, components, Language fig (abg.fig)
@comment node-name, next, previous, up
@subsubsection Simple components
@cindex Simple components
The following simple components are defined in MTT.
@ftable @code
@item R
Standard one-port R
@item C
Standard one-port I
@item I
Standard one-port I
@item SS
Source-sensor
@item TF
Transformer
@item GY
Gyrator
@item AE
Effort amplifier
@item AF
Flow amplifier
@item CSW
Switched one-port I
@item ISW
Switched one-port I
@end ftable
@menu
* SS components::
* Simple components - implementation::
@end menu
@node SS components, Simple components - implementation, Simple components, Language fig (abg.fig)
@comment node-name, next, previous, up
@subsubsection SS components
@cindex SS components
@iftex
$$
@end iftex
@code{SS} components provide input and output variables for a system;
Named SS components (@pxref{Named SS components}) provide this for
subsystems.
@node Simple components - implementation, Compound components, SS components, Language fig (abg.fig)
@comment node-name, next, previous, up
@subsubsection Simple components - implementation
@cindex Simple components - implementation
Each simple component, with name NAME, is defined by two m files:
@ftable @code
@item NAME_cause.m
defines the possible causal patterns for the component
@item NAME_eqn.m
defines the equations generated
@end ftable
Only the experienced user would normally define simple components -
Compound components (@pxref{Compound components}) are recommended for
DIY components.
@node Compound components, Named SS components, Simple components - implementation, Language fig (abg.fig)
@comment node-name, next, previous, up
@subsubsection Compound components
@cindex Compound components
@cindex Named SS
Compound components are systems described by bond graphs and implemented
by MTT. They have special SS components, Named SS components
(@pxref{Named SS components}), to indicate connections to the
encapsulating system.
Like any other system, they are described by a graphical Bond Graph description
(@pxref{Language fig (abg.fig) }), and a label file (@pxref{Labels (lbl)}).
By convention, all of the files describing a component live in a
directory with the same name as the component.
@menu
* Named SS components::
@end menu
@node Named SS components, Coerced bond direction, Compound components, Language fig (abg.fig)
@comment node-name, next, previous, up
@subsubsection Named SS components
@cindex Named SS components
Named SS components provide the link from the system which @emph{defines}
compound component to the system which @emph{uses} a compound
component @pxref{Compound components}.
A named SS components is of the form
@code{SS:[name]};
Where `name' is a name consisting of alphanumeric characters and
underscore; for example:
@example
SS:[Mechanical_1]
@end example
Each such named SS provides one of the ports
(@pxref{Ports}).
The direction of the named SS components.
(@pxref{Named SS components})
is coerced (@pxref{Coerced bond direction}) to have the same direction
as the bond connected to the corresponding port. Thus the direction of
the direction of the named SS components has no significance unless the
component is at the top level of a system.
If a named SS component exists at the top level (@pxref{Top level})
and is treated as an
ordinary SS component with the given direction and with the attributes
specified in the label file (@pxref{Labels (lbl)}).
@node Coerced bond direction, Port labels, Named SS components, Language fig (abg.fig)
@comment node-name, next, previous, up
@subsubsection Coerced bond direction
@cindex Coerced bond direction
@pindex Coerced bond direction
Named SS components (@pxref{Named SS components}) provide the mechanism
for declaring the ports (@pxref{Ports}) of a component. The
corresponding bond has a direction. However, under some circumstances,
it may be useful to reverse this direction. @strong{MTT} provides a
coercion mechanism for this: the the direction of the bond attached to
the named SS component (@pxref{Named SS components}) is replaced by the
direction of the bond attached to the component port.
@node Port labels, Vector port labels, Coerced bond direction, Language fig (abg.fig)
@comment node-name, next, previous, up
@subsubsection Port labels
@cindex ports
@pindex ports
Most multi-port components have ports
@pxref{Ports})which display different
behaviors; the exception to this is the junction (@code{0} and @code{1})
components. For this reason, @strong{MTT} provides a method for unambiguously
identifying the ports of a multi-port component by port labels.
A port label is indicated by a name within parentheses of the form
@code{[name]}, where `name' is a name consisting of alphanumeric
characters and underscore; for example:
@example
[Mechanical_1]
@end example
This provides a label for corresponding to the component to which the
nearest bond-end is attached.
The following rules must be be obeyed:
@itemize @bullet
@item
If a component has any port labels at all, there must be one for each
port of the component.
@c @item
@c If a component is to be used repetitively (see @ref{components}), it
@c must have an even number of ports and the odd ports are connected to the
@c even points within the chain of components.
@end itemize
Port labels may be grouped into vector port labels (@pxref{Vector port
labels}). Components with compatible (ie containing the same number of ports)
vector ports may be connected by a @emph{single} bond
(@pxref{Bonds}); such a bond implies the corresponding number of bonds
(one for each element of the vector port label). All such bonds inherit
the same direction and any @emph{explicit} causal strokes (@pxref{strokes})
@node Vector port labels, Port label defaults, Port labels, Language fig (abg.fig)
@comment node-name, next, previous, up
@subsubsection Vector port labels
@cindex vector port labels
@cindex port labels
Port labels (@pxref{Port labels}) may be grouped into vector port
labels of the form @code{[name1,name2,name3]}.
@example
[Mechanical_1,Electrical,Hydraulic_5]
@end example
@node Port label defaults, Vector components, Vector port labels, Language fig (abg.fig)
@comment node-name, next, previous, up
@subsubsection Port label defaults
@cindex Port label defaults
@pindex Port label defaults
Whether impicitly or explicity, all ports of components (with the
exception of 0 and 1 junctions) must have lables (@pxref{Port
labels}). However, these can be omitted from the bond graph in the
following circumstances and default labels are supplied by @strong{MTT}.
@enumerate
@item A single unlabled inport defaults to [in]
@item A single unlabled outport defaults to [out]
@end enumerate
These defaults may, in turn be aliases (@pxref{Aliases}) for port labels
(@pxref{Port labels}) or vector port labels (@pxref{Vector port
labels}). Combining the default and alias mechanism is a powerful tool
for creating uncluttered, yet complex, bond graph models.
@node Vector components, artwork, Port label defaults, Language fig (abg.fig)
@subsubsection Vector Components
@cindex Vector components
@pindex Vector components
Vectors of components can be created in four cases:
@code{0} junctions,
@code{1} junctions,
@code{SS} components and
@code{SS} port components.
In each case, the presence of a vector component is indicated by a
single port label (@pxref{Port labels}) of one of two forms:
@enumerate
@item containing numerals from 1 to
the order of the vector. Thus a vector of 3 components is indicated by a
port label of the form [1,2,3].
@item 1: followed by
the order of the vector. Thus a vector of 3 components is indicated by a
port label of the form [1:3].
@end enumerate
Within the corresponding label file (@pxref{Labels (lbl)}), the
components of a vector port can be accessed using _i where i is the
corresponding index. Thus a port SS:[Electrical] appearing near the port
label [1,2,3] could contain the port alias (@pxref{Port aliases})
@example
%ALIAS in Electrical_1,Electrical_2,Electrical_3
@end example
@node artwork, Valid names, Vector components, Language fig (abg.fig)
@subsubsection Artwork
@cindex artwork
@pindex artwork
You are encouraged to annotate your bond graphs extensively - this makes
them an immediately readable document whilst retaining the precise and
unambiguous expressive power of the bond graph.
You may add any Fig (@pxref{Fig}) object to the bond graph as long as it
will not be interpreted as part of the bond graph.
The reccommended way to acheive this is to put the Bond Graph at depth
0,10,20 etc (ie depth modulo 10 is zero) and artwork at any other depth.
@c The recommended way to do this is to @emph{put all artwork at or below
@c Depth 1} in the figure. @strong{MTT} ignores all objects not at depth 0.
For compatibility with earlier versions of @strong{MTT}, the following
objects are ignored even at level 0. However, their use is strongly
discouraged.
@itemize @bullet
@item
Adding text is OK as long as it cannot be confused with components
(@pxref{components}). In particular, you can include invalid component
characters such as white space, @code{"}, @code{'}, @code{!} etc.
@item
Adding boxes, arcs etc is always OK.
@item
Adding dotted or dashes lines is always OK.
@end itemize
The stripped abg file (sabg) (@pxref{Stripped acausal bond graph
(sabg)})
shows only those parts of the diagram recognised by @strong{MTT} and is
therefore useful for distinguishing artwork.
@node Valid names, , artwork, Language fig (abg.fig)
@subsubsection Valid Names
@cindex valid name
@pindex valid name
A valid name is a text string containing alphanumeric characters. It
must @strong{NOT} contain underscore @samp{_}, hyphen @samp{-}, @samp{:}
or @samp{*}.
The following reserved words in reduce should also be avoided (with any case)
@example
Commands ALGEBRAIC ANTISYMMETRIC ARRAY BYE CLEAR CLEARRULES COMMENT
CONT DECOMPOSE DEFINE DEPEND DISPLAY ED EDITDEF END EVEN FACTOR FOR
FORALL FOREACH GO GOTO IF IN INDEX INFIX INPUT INTEGER KORDER LET
LINEAR LISP LISTARGP LOAD LOAD PACKAGE MASS MATCH MATRIX MSHELL
NODEPEND NONCOM NONZERO NOSPUR ODD OFF ON OPERATOR ORDER OUT PAUSE
PRECEDENCE PRINT PRECISION PROCEDURE QUIT REAL REMFAC REMIND RETRY
RETURN SAVEAS SCALAR SETMOD SHARE SHOWTIME SHUT SPUR SYMBOLIC
SYMMETRIC VECDIM VECTOR WEIGHT WRITE WTLEVEL
Boolean Operators EVENP FIXP FREEOF NUMBERP ORDP PRIMEP
Infix Operators := = >= > <= < => + * / ^ ** . WHERE SETQ OR AND
MEMBER MEMQ EQUAL NEQ EQ GEQ GREATERP LEQ LESSP PLUS DIFFERENCE MINUS
TIMES QUOTIENT EXPT CONS Numerical Operators ABS ACOS ACOSH ACOT ACOTH
ACSC ACSCH ASEC ASECH ASIN ASINH ATAN ATANH ATAN2 COS COSH COT COTH
CSC CSCH EXP FACTORIAL FIX FLOOR HYPOT LN LOG LOGB LOG10 NEXTPRIME
ROUND SEC SECH SIN SINH SQRT TAN TANH
Prefix Operators APPEND ARGLENGTH CEILING COEFF COEFFN COFACTOR CONJ
DEG DEN DET DF DILOG EI EPS ERF FACTORIZE FIRST GCD G IMPART INT
INTERPOL LCM LCOF LENGTH LHS LINELENGTH LTERM MAINVAR MAT MATEIGEN MAX
MIN MKID NULLSPACE NUM PART PF PRECISION RANDOM RANDOM NEW SEED RANK
REDERR REDUCT REMAINDER REPART REST RESULTANT REVERSE RHS SECOND SET
SHOWRULES SIGN SOLVE STRUCTR SUB SUM THIRD TP TRACE VARNAME
Reserved Variables CARD NO E EVAL MODE FORT WIDTH HIGH POW I INFINITY
K!* LOW POW NIL PI ROOT MULTIPLICITY T
Switches ADJPREC ALGINT ALLBRANCH ALLFAC BFSPACE COMBINEEXPT
COMBINELOGS COMP COMPLEX CRAMER CREF DEFN DEMO DIV ECHO ERRCONT
EVALLHSEQP EXP EXPANDLOGS EZGCD FACTOR FORT FULLROOTS GCD IFACTOR INT
INTSTR LCM LIST LISTARGS MCD MODULAR MSG MULTIPLICITIES NAT NERO
NOSPLIT OUTPUT PERIOD PRECISE PRET PRI RAT RATARG RATIONAL RATIONALIZE
RATPRI REVPRI RLISP88 ROUNDALL ROUNDBF ROUNDED SAVESTRUCTR
SOLVESINGULAR TIME TRA TRFAC TRIGFORM TRINT
Other Reserved Ids BEGIN DO EXPR FEXPR INPUT LAMBDA LISP MACRO PRODUCT
REPEAT SMACRO SUM UNTIL WHEN WHILE WS
@end example
@node Language m (rbg.m), Language m (abg.m), Language fig (abg.fig), Acausal bond graph (abg)
@comment node-name, next, previous, up
@subsection Language m (rbg.m)
The raw bond graph of system `sys' is represented as
an m file with heading:
@example
function [rbonds, rstrokes,rcomponents,rports,n_ports] = sys_rbg
@end example
This representation is a half-way house between the fig
(@pxref{Language fig (abg.fig)}) and m
(@pxref{Language m (abg.m)}) representations. It contains the
geometric information from the fig file in a form digestible by Octave
(@pxref{Octave}).
The five outputs of this function are:
@itemize @bullet
@item
rbonds
@item
rstrokes
@item
rcomponents
@item
rports
@item
n_ports
@end itemize
@emph{rbonds} is a matrix with
@itemize @bullet
@item
one row for each bond (@pxref{bonds})
@item
columns 1 and 2 containing the x,y coordinates for one end of the bond
@item
columns 3 and 4 containing the x,y coordinates for the corner of the bond
@item
columns 5 and 6 containing the x,y coordinates for the other end of the bond
@end itemize
@emph{rstrokes} is a matrix with (@pxref{strokes})
@itemize @bullet
@item
one row for each stroke or half-stroke
@item
columns 1 and 2 containing the x,y coordinates for one end of the stroke
@item
columns 3 and 4 containing the x,y coordinates for the other end of the stroke
@end itemize
@emph{rcomponents} is a matrix with (@pxref{components})
@itemize @bullet
@item
one row for each component
@item
columns 1 and 2 containing the x,y coordinates of the component
@item
the remaining columns containing fig file information
@end itemize
@emph{rports} is a matrix with (@pxref{Port labels})
@itemize @bullet
@item
one row for each component port that is explicitly labeled
@item
columns 1 and 2 containing the x,y coordinates of the port label
@item
column 3 contains the port number.
@end itemize
@emph{n_ports} is the number of ports associated with the system -- i.e. the
number of Named SS components (@pxref{Named SS components}).
@menu
* Transformation abg2rbg_fig2m::
@end menu
@node Transformation abg2rbg_fig2m, , Language m (rbg.m), Language m (rbg.m)
@comment node-name, next, previous, up
@subsubsection Transformation abg2rbg_fig2m
@cindex Transformation abg2rbg_fig2m
This transformation takes the acausal bond graph as a fig file
(@pxref{Language fig (abg.fig)}) and transforms it into a raw bond graph in
m-file format (@pxref{Language m (rbg.m)}).
This transformation is implemented in GNU awk (gawk).
It scans both the fig file (@pxref{Language fig (abg.fig)})
and the label file (@pxref{Labels (lbl)}) and generates the rbg
(@pxref{Language m (rbg.m)}) with components sorted according to the
label file.
It also generates a file sys_fig.fig containing details of the bond
graph with the components removed.
@node Language m (abg.m), Language tex (abg.tex), Language m (rbg.m), Acausal bond graph (abg)
@comment node-name, next, previous, up
@subsection Language m (abg.m)
@cindex Language m (abg.m)
@cindex bonds
@cindex components
@cindex n_ports
The acausal bond graph of system `sys' is represented as
an m file with heading:
@example
function [bonds,components,n_ports] = sys_abg
@end example
The three outputs of this function are:
@itemize @bullet
@item
bonds
@item
components
@item
n_ports
@end itemize
@emph{bonds} is a matrix with
@itemize @bullet
@item
one row for each bond
@item
the first column contains the arrow-orientated
(@pxref{Arrow-orientated causality})
causality of the @emph{effort} variable.
@item
the second column contains the arrow-orientated
(@pxref{Arrow-orientated causality})
causality of the @emph{flow} variable.
@end itemize
@emph{components} is a matrix with
@itemize @bullet
@item
one row for each component
@item
one column for each bond impinging on the component. The
@emph{magnitude} of each entry corresponds to the bond number (the
appropriate row index of` bonds'); the sign is positive if the bond
arrow points into the component and negative otherwise.
@end itemize
@emph{n_ports} is the number of ports associated with the system -- i.e. the
number of Named SS components (@pxref{Named SS components}).
@menu
* Arrow-orientated causality::
* Component-orientated causality::
* Transformation rbg2abg_m::
@end menu
@node Arrow-orientated causality, Component-orientated causality, Language m (abg.m), Language m (abg.m)
@comment node-name, next, previous, up
@subsubsection Arrow-orientated causality
@cindex Arrow-orientated causality
The arrow-orientated causality convention assigns -1, 0 or 1
to both the effort and flow (@pxref{Variables}) sides of a bond
to represent the causal stroke (@pxref{strokes})
as follows:
@vtable @code
@item 0
if there is no causality set.
@item 1
if the causal stroke is at the arrow end of the bond.
@item -1
if the causal stroke is at the other end of the bond.
@end vtable
@pxref{Component-orientated causality}.
@node Component-orientated causality, Transformation rbg2abg_m, Arrow-orientated causality, Language m (abg.m)
@comment node-name, next, previous, up
@subsubsection Component-orientated causality
@cindex Component-orientated causality
The component-orientated causality convention assigns -1, 0 or 1
to both the effort and flow (@pxref{Variables}) sides of a bond
to represent the causal stroke (@pxref{strokes})
as follows:
@vtable @code
@item 0
if there is no causality set.
@item 1
if the causal stroke is at the component end of the bond.
@item -1
if the causal stroke is at the other end of the bond.
@end vtable
@pxref{Arrow-orientated causality}.
@node Transformation rbg2abg_m, , Component-orientated causality, Language m (abg.m)
@comment node-name, next, previous, up
@subsubsection Transformation rbg2abg_m
@cindex Transformation rbg2abg_m
This transformation takes the raw bond graph and, by doing some
geometrical computation, determines the topology of the bond graph -- ie
what is close to what.
@node Language tex (abg.tex), , Language m (abg.m), Acausal bond graph (abg)
@comment node-name, next, previous, up
@subsection Language tex (abg.tex)
@cindex Language tex (abg.tex)
For the purpose of producing a report (@pxref{Report}), @strong{MTT}
generates a LaTeX (@pxref{LaTeX}) file describing the bond graph and its
subsystems. Additional information may be supplied using the description
representation (@pxref{Description (desc)}).
@c node next prev up
@node Stripped acausal bond graph (sabg), Labels (lbl), Acausal bond graph (abg), Representations
@section Stripped acausal bond graph (sabg)
@cindex Stripped acausal bond graph (sabg)
@pindex Stripped acausal bond graph (sabg)
The stripped acausal bond graph is the acausal bond graph representation
(@pxref{Acausal bond graph (abg)}) without the artwork
(@pxref{artwork}). It is useful to check for mistakes by showing
precisely what is recognised by @strong{MTT}.
@menu
* Language fig (sabg.fig)::
* Stripped acausal bond graph (view)::
@end menu
@node Language fig (sabg.fig), Stripped acausal bond graph (view), Stripped acausal bond graph (sabg), Stripped acausal bond graph (sabg)
@subsection Language fig (sabg.fig)
@cindex Language fig (sabg.fig)
@pindex Language fig (sabg.fig)
The stripped acausal bond graph can be generated as a fig (@pxref{Fig})
file using
@example
mtt syst sabg fig
@end example
@node Stripped acausal bond graph (view), , Language fig (sabg.fig), Stripped acausal bond graph (sabg)
@subsection Stripped acausal bond graph (view)
@cindex Language m (view)
@cindex view Constrained-state Equations
This representation has the standard text view
(@pxref{Views}).
@node Labels (lbl), Description (desc), Stripped acausal bond graph (sabg), Representations
@comment node-name, next, previous, up
@section Labels (lbl)
@cindex Labels
@cindex lbl
Bond graph components have optional labels. These provide pointers to
further information relating to the component; this avoids clutter on
the bond graph.
The label file contains the following non-blank lines (blank lines are ignored)
@itemize @bullet
@item Summary - lines beginning with %SUMMARY
@item Description - lines beginning with %DESCRIPTION
@item Alias - lines beginning with %ALIAS
@item Comments - lines beginning with %
@item Labels - other non-blank lines
@end itemize
Each lable contains three fields (in the following order) separated by
white space and on one line:
@enumerate
@item The component name @pxref{Component names}. This must be a valid
name (@pxref{Valid names}.
@item The component constitutive relationship @pxref{Component constitutive relationship}
@item The component arguments @pxref{Component arguments}
@end enumerate
Not each component @pxref{components} needs a label, only those which are explicitly
labeled on the Bond Graph @pxref{Acausal bond graph (abg)}.
@strong{MTT} checks whether all components labelled on the bond graph
have labels and vice versa.
If no lbl file exists, @strong{MTT} will create a valid one for you;
including a default set of arguments and crs for both simplae and
compound components.
If wish to create one to edit yourself, type
@example
mtt system_name lbl txt
@end example
An example lbl file (for the RC system is):
@example
%% Label file for system RC (RC_lbl.txt)
%SUMMARY RC
%DESCRIPTION <Detailed description here>
% Port aliases
%ALIAS in in
%ALIAS out out
% Argument aliases
%ALIAS $1 c
%ALIAS $2 r
%% Each line should be of one of the following forms:
% a comment (ie starting with %)
% component-name cr_name arg1,arg2,..argn
% blank
% ---- Component labels ----
% Component type C
c lin effort,c
% Component type R
r lin flow,r
% Component type SS
[in] SS external,external
[out] SS external,external
@end example
The old-style lbl files (@pxref{Old-style labels (lbl)}) are NO LONGER
supported -- you are encouraged to convert them ASAP.
@menu
* SS component labels ::
* Other component labels ::
* Component names::
* Component constitutive relationship::
* Component arguments::
* Parameter declarations::
* Units declarations::
* Interface Control Definition::
* Aliases::
* Parameter passing::
* Old-style labels (lbl)::
@end menu
@node SS component labels , Other component labels , Labels (lbl), Labels (lbl)
@comment node-name, next, previous, up
@subsection SS component labels
@cindex SS component labels
In addition to the label there are two information fields, @pxref{Labels
(lbl)}. The first must be `SS', the second contains two information
fields of the form info_field_1,info_field_2.
These two information
fields correspond to the effort and flow variables of the of the SS components as follows
@vtable @code
@item info_field_1
effort
@item info_field_2
flow
@end vtable
Each of these two fields contains one of the following @emph{attributes}:
@vtable @code
@item external
indicates that the corresponding variable is a system input or
output
@item internal
indicates that the variable does not appear as a system output;
it is an error to label an input in this way.
@item a number
the value of the input; or the value of the (imposed) output
@item a symbol
the symbolic value of the input; or the value of the (imposed) output
@item unknown
used for the SS method of solving algebraic loops. This
indicates that the corresponding system input (SS output) is to
be chosen to set the corresponding system output (SS input) to zero.
@item zero
used for the SS method of solving algebraic loops. This
indicates that the corresponding system output (SS input) is to
be set to zero using the variable indicted by the corresponding
`unknown' label.
@end vtable
Some examples are:
@example
%% ss1 is both a source and sensor
ss1 SS external,external
%% ss1 acts as a flow sensor - it imposes zero effort.
ss2 SS 0,external
@end example
@node Other component labels, Component names, SS component labels , Labels (lbl)
@comment node-name, next, previous, up
@subsection Other component labels
@cindex Other component labels
In addition to the label there are two information fields,
@pxref{Labels (lbl)}.
They correspond to the constitutive relationship
(see @pxref{Constitutive relationship} and arguments of the
component as follows
@vtable @code
@item info_field_1
constitutive relationship
@item info_field_2
parameters
@end vtable
Some examples are:
@example
%Armature resistance
r_a lin effort,r_a
%Gearbox ratio
n lin effort,n
@end example
@strong{MTT} supports parameter-passing to (@pxref{Parameter passing })
subsystems.
@menu
* Component names::
* Component constitutive relationship::
* Component arguments::
* Aliases::
* Parameter passing::
* Old-style labels (lbl)::
@end menu
@node Component names, Component constitutive relationship, Other component labels , Labels (lbl)
@comment node-name, next, previous, up
@subsection Component names
@cindex Component names
The component name field must contain a valid name (@pxref{Valid names} corresponding to the
name (the bit after the :) of each named component (@pxref{components})
on the bond graph (@pxref{Acausal bond graph (abg)}).
@node Component constitutive relationship, Component arguments, Component names, Labels (lbl)
@comment node-name, next, previous, up
@subsection Component constitutive relationship
@cindex Component constitutive relationship
The constitutive relationship field contains the name of a constitutive
relationship for the component. There are three sorts of constitutive
relationship recognised by @strong{MTT}:
@enumerate
@item A generic constitutive relationship such as @var{lin} (the generic
linear constitutive relationship.
@item A local constitutive relationship with the same name as the
component type
@item The @var{SS} constitutive relationship reserved for @var{SS}
components.
All labels for @var{SS} components must contain SS in this field.
@end enumerate
@node Component arguments, Parameter declarations, Component constitutive relationship, Labels (lbl)
@comment node-name, next, previous, up
@subsection Component arguments
@cindex Component arguments
@node Parameter declarations, Units declarations, Component arguments, Labels (lbl)
@comment node-name, next, previous, up
@subsection Parameter declarations
@cindex parameter declarations
@pindex parameter declarations
@pindex PAR
@pindex NOTPAR
@pindex VAR
@pindex NOTVAR
It is sometimes useful to use parameters (in addition to those implied by
the Component arguments @pxref{Component arguments}) to compute values
in, for example the numpar file. These can be declared in the label
file;
for examples , the two parameters par1 and par 2 can be declared as:
@example
#PAR par1
#PAR par2
@end example
On the other hand, some CR arguments (eg foo and bar) may not correspond to
parameters. These can be excluded from the sympar list using
the NOTPAR declaration
@example
#NOTPAR foo
#NOTPAR bar
@end example
For comapability with old code, VAR may be used in place of PAR, but
this usage is deprecated.
@node Units declarations, Interface Control Definition, Parameter declarations, Labels (lbl)
@comment node-name, next, previous, up
@subsection Units declarations
@cindex units declarations
@pindex units declarations
@pindex UNITS
The units and domains of ports (@pxref{Ports}) are declared as:
@example
#UNITS Port_name domain effort_units flow_units
@end example
where "Port_name" is the name of the port, domain is one of:
@vtable @code
@item electrical
the electrical domain
@item translational
the translational mechanical domain
@item rotational
the rotational mechanical domain
@item fluid
the fluid domain
@item thermal
the thermal domain
@end vtable
and effort_units and flow_units are corresponding units for the effort
and the flow.
Allowed units are those defined in the @strong{units} package.
@strong{MTT} checks that units are
@itemize @bullet
@item defined consistently with the domain
@item the same for connected ports when both ports have defined units.
@end itemize
No checks are done if one or both ends of a bond are not connected to a
port with defined units.
@node Interface Control Definition, Aliases, Units declarations, Labels (lbl)
@comment node-name, next, previous, up
@subsection Interface Control Definition
@cindex ICD (label file directive)
It is sometimes useful to be able to automatically generate a set of
assignments mapping @strong{MTT} inputs and outputs to an external interface
definition. This can be achieved with use of the @emph{#ICD} directive.
@example
#ICD PressureSensor PUMP1_PRESSURE_SENSOR,Pa;null,none
#ICD Electrical PUMP1_VOLTAGE,volt;PUMP1_CURRENT,amp
% Component type De
PressureSensor SS external
% Component type SS
Electrical SS external,external
@end example
The ICD directive consists of 3 whitespace delimited fields:
@enumerate
@item [%|#]ICD
@item component name
@item Four comma (,) or semi-colon (;) delimited fields:
@enumerate
@item name of effort parameter
@item unit of effort parameter
@item name of flow parameter
@item unit of flow parameter
@end enumerate
@end enumerate
If no parameter name is required, a value of "null" should be used.
If the parameter does not have any units, a value of "none" should be used.
ICD parameters may be aliased @pxref{Aliases} in the same way as normal
parameters, thus it is possible to define some or all of the ICD in higher
level components.
The command
@example
mtt sys ICD txt
@end example
will generate a text file containing a list of mappings:
@example
## Interface Control Definition for System sys
## sys_ICD.txt: Generated by MTT Thu Jul 12 21:21:21 CDT 2001
Input: PUMP1_VOLTAGE sys_P1_1_Electrical Causality: Effort Units: volt
Output: PUMP1_CURRENT sys_P1_1_Electrical Causality: Flow Units: amp
Output: PUMP1_PRESSURE_SENSOR sys_P1_1_PressureSensor Causality: Effort Units: Pa
@end example
A set of assignments can be generated with the command
@example
mtt sys ICD m
@end example
resulting in:
@example
# Interface Control Definition mappings for system sys
# sys_ICD.m: Generated by MTT Thu Jul 12 21:26:56 CDT 2001
# Inputs
mttu(1) = PUMP1_VOLTAGE;
# Outputs
PUMP1_CURRENT = mtty(1);
PUMP1_PRESSURE_SENSOR = mtty(2);
@end example
A similar file will be generated by the command
@example
mtt sys ICD cc
@end example
@node Aliases, Parameter passing, Interface Control Definition, Labels (lbl)
@comment node-name, next, previous, up
@subsection Aliases
@cindex aliases
@pindex aliases
Aliases provide a convenient mechanism for relabelling words appearing
in the label file (@pxref{Labels (lbl)}). There are three contexts in
which the alias mechanism is used:
@enumerate
@item renaming ports (@pxref{Port aliases}),
@item renaming parameters (@pxref{Parameter aliases}) and
@item renaming components (@pxref{Component aliases}).
@end enumerate
All three mechanisms use the same form of statement within the label
file
@example
%ALIAS short_label real_label
@end example
@strong{MTT} distinguishes between the three forms as follows:
@itemize @bullet
@item Parameter aliases: `short_label' starts with a `$'
@item Component aliases: `real_label' contains the directory separator
`/'
@item Port aliases: neither of the above
@end itemize
@menu
* Port aliases::
* Parameter aliases::
* CR aliases::
* Component aliases::
@end menu
@node Port aliases, Parameter aliases, Aliases, Aliases
@comment node-name, next, previous, up
@subsubsection Port aliases
@cindex port aliases
@pindex port aliases
Aliases provide a way of refering to (@pxref{Port labels}) or vector port labels (@pxref{Vector
port labels}) on the bond graph using a short-hand notation. With in a
component label file (@pxref{Labels (lbl)}) statements of the following
forms can occur
@example
%ALIAS short_label real_label
@end example
When the component is used within another component, the short_lable may
be used in place of the real_label.
More than one alias per label can be used, for example
@example
%ALIAS short_label_1 real_label
%ALIAS short_label_2 real_label
%ALIAS short_label_3 real_label
@end example
The port can then be refered to in four ways: as real_label,
short_label_1, short_label_2 or short_label_3.
An alternative notation for the ALIAS statement in this case is
@example
%ALIAS short_label_1|short_label_2|short_label_3 real_label
@end example
The alias feature is particularly powerful in conjunction with vector
port labels (@pxref{Vector port labels}) and the port label default
(@pxref{Port label defaults}) mechanisms. For example, a component with
5 ports appearing in the lbl file as:
@example
[Hydraulic_in] external external
[Hydraulic_out] external external
[Power_Shaft] external external
[Thermal_in] external external
[Thermal_out] external external
@end example
together with the following statements in the label file:
@example
%ALIAS in Thermal_in,Hyydraulic_in
%ALIAS out Thermal_out,Hydraulic_out
%ALIAS shaft|power Power_Shaft
@end example
can appear in the bond graph containing that component with one bond
labeled either [shaft] or [power] or [Power_Shaft], one unlabeled vector
bond pointing in and one unlabeled vector bond pointing out.
@node Parameter aliases, CR aliases, Port aliases, Aliases
@comment node-name, next, previous, up
@subsubsection Parameter aliases
@cindex parameter aliases
@pindex parameter aliases
Parameter aliases are of the form
@example
%ALIAS $n actual parameter
@end example
where n is an integer (unique within the label file).
For example
@example
%ALIAS $1 c_v
%ALIAS $2 density,ideal_gas,r
%ALIAS $3 alpha
%ALIAS $4 flow,k_p
@end example
Assigns four symbolic parameters to the corresponding strings These four
parameters (@code{$1}--@code{$4}) can then be used for parameter
passing(@pxref{Parameter passing}).
@node CR aliases, Component aliases, Parameter aliases, Aliases
@comment node-name, next, previous, up
@subsubsection CR aliases
@cindex CR aliases
@pindex CR aliases
CR aliases are of the form
@example
%ALIAS $an actual parameter
@end example
where n is an integer (unique within the label file).
For example
@example
%ALIAS $a1 lin
@end example
assigns the symbolic parameter to be lin. This parameter @code{$1} can
then be used for passing a diofferent cr to the
component (@pxref{Parameter passing}).
@node Component aliases, , CR aliases, Aliases
@comment node-name, next, previous, up
@subsubsection Component aliases
@cindex component aliases
@pindex component aliases
Component aliases are of the form
@example
%ALIAS Component_name Component_location
@end example
An example appears in the following label file fragment
@example
...
%ALIAS wPipe CompressibleFlow/wPipe
%ALIAS Poly CompressibleFlow/Poly
....
@end example
The two components `wPipe' and `Poly' are both to be found within the
library `Compressible flow' and the respective subdirectories. This
follows the @strong{MTT} convention that compound components
(@pxref{Compound components}) live within a directory of the same name.
@node Parameter passing, Old-style labels (lbl), Aliases, Labels (lbl)
@comment node-name, next, previous, up
@subsection Parameter passing
@cindex Parameter passing
@strong{MTT} supports parameter-passing to subsystems within label files
(@pxref{Labels (lbl)}). Within a subsystem, explicit constitutive
relationships and parameters (or groups thereof) can be replaced by
postitional parameters such as @code{$1}, @code{$2} etc. Although this
can be done directly, it is recommended that this is done via the alias
mechanism (@pxref{Parameter aliases}).
In a subsystem
@code{$i}, is replaced by the ith field of a colon @code{;} separated
field in the calling label file. This field may include commas @code{,}
and the four arithmetic operators @code{+}, @code{-}, @code{*} and
@code{/}.
For example, consider the following example label file fragment (associated with a
component called Pump:
@example
...
%ALIAS $1 c_v
%ALIAS $2 density,ideal_gas,r
%ALIAS $3 alpha
%ALIAS $4 flow,k_p
%ALIAS wPipe CompressibleFlow/wPipe
%ALIAS Poly CompressibleFlow/Poly
% Component type wPipe
pipe none c_v;density,ideal_gas,r
% Component type Poly
poly Poly alpha
@end example
The 4 parameters @code{$1}, @code{$2}, @code{$3}, and @code{$4} can be
passed from a higher level component as in the following label file
fragment:
@example
% Component type Pump
comp none c_v;rho,ideal_gas,r;alpha;effort,k_c
turb none c_v;rho,ideal_gas,r;alpha;effort,k_t
@end example
Thus in component `comp':
@itemize @bullet
@item @code{$1} is replaced by c_v
@item @code{$2} is replaced by rho,ideal_gas
@item @code{$3} is replaced by alpha
@item @code{$4} is replaced by effort,k_c
@end itemize
whereas in component `turb' the first three parameters are the same but
@itemize @bullet
@item @code{$4} is replaced by effort,k_t
@end itemize
@node Old-style labels (lbl), , Parameter passing, Labels (lbl)
@comment node-name, next, previous, up
@subsection Old-style labels (lbl)
@cindex Old-style labels
@cindex lbl
Old syle labels (mtt version 2.x) are supported by mtt version
3.x. However, you are advised to use the new form (@pxref{Labels
(lbl)}).
Each line of the @code{_label.txt} file is of one of three forms:
@enumerate
@item
Contains three fields (separated by white space) of the form
@example
label field_1 field_2
@end example
@item
Blank
@item
Preceded by %
@end enumerate
Only the first is noticed by @strong{MTT}; the second and third are for
providing helpful commenting.
The role of the two information fields depends on the component with the
corresponding label. In particular the classes of components are:
@itemize @bullet
@item
SS components, @pxref{SS components}.
@item
Other components, @pxref{components}.
@end itemize
Named SS component, @pxref{Named SS components} never have labels.
@menu
* SS component labels (old-style)::
* Other component labels (old-style)::
* Parameter passing (old-style)::
@end menu
@node SS component labels (old-style), Other component labels (old-style), Old-style labels (lbl), Old-style labels (lbl)
@comment node-name, next, previous, up
@subsubsection SS component labels (old-style)
@cindex SS component labels (old-style)
In addition to the label there are two information fields,
@pxref{Labels (lbl)}.
They correspond to the effort and flow of the components as follows
@vtable @code
@item info_field_1
effort
@item info_field_2
flow
@end vtable
Each of these two fields contains one of the following @emph{attributes}:
@vtable @code
@item
external
indicates that the corresponding variable is a system input or
output
@item internal
indicates that the variable does not appear as a system output;
it is an error to label an input in this way.
@item a number
the value of the input; or the value of the (imposed) output
@item a symbol
the symbolic value of the input; or the value of the (imposed) output
@item unknown
used for the SS method of solving algebraic loops. This
indicates that the corresponding system input (SS output) is to
be chosen to set the corresponding system output (SS input) to zero.
@item zero
used for the SS method of solving algebraic loops. This
indicates that the corresponding system output (SS input) is to
be set to zero using the variable indicted by the corresponding
`unknown' label.
@end vtable
Some examples are:
@example
%Label field1 field2
ss1 external external
ss2 0 external
@end example
@node Other component labels (old-style), Parameter passing (old-style), SS component labels (old-style), Old-style labels (lbl)
@comment node-name, next, previous, up
@subsubsection Other component labels (old-style)
@cindex Other component labels (old-style)
In addition to the label there are two information fields,
@pxref{Labels (lbl)}.
They correspond to the constitutive relationship
(see @pxref{Constitutive relationship} and arguments of the
component as follows
@vtable @code
@item info_field_1
constitutive relationship
@item info_field_2
parameters
@end vtable
Some examples are:
@example
%Armature resistance
r_a lin effort,r_a
%Gearbox ratio
n lin effort,n
@end example
@strong{MTT} supports parameter-passing to (@pxref{Parameter passing (old-style)})
subsystems.
@node Parameter passing (old-style), , Other component labels (old-style), Old-style labels (lbl)
@comment node-name, next, previous, up
@subsubsection Parameter passing (old-style)
@cindex Parameter passing (old-style)
@strong{MTT} supports parameter-passing to (@pxref{Parameter passing (old-style)})
subsystems within label files (@pxref{Labels (lbl)}). Within a subsystem,
explicit constitutive relationships and parameters (or groups thereof)
can be replaced by
@code{$1}, @code{$2}, etc.
In a subsystem
@code{$i}, is replaced by the ith field of a colon @code{;} separated
field in the calling label file. This field may include commas @code{,}.
For example subsystem ROD contains the following lines in the label
file:
@example
%DESCRIPTION Parameter 1: length from end 1 to mass centre
%DESCRIPTION Parameter 2: length from end 2 to mass centre
%DESCRIPTION Parameter 3: inertia about mass centre
%DESCRIPTION Parameter 4: mass
%DESCRIPTION See Section 10.2 of "Metamodelling"
%Inertias
J lin flow,$3
m_x lin flow,$4
m_y lin flow,$4
%Integrate angular velocity to get angle
th
%Modulated transformers
s1 lsin flow,$1
s2 lsin flow,$2
c1 lcos flow,$1
c2 lcos flow,$2
@end example
This can be used in a higher-level lbl (@pxref{Labels (lbl)}) file as:
@example
%SUMMARY Pendulum example from Section 10.3 of "Metamodelling"
%Rod parameters
rod none l;l;j;m
@end example
@node Description (desc), Structure (struc), Labels (lbl), Representations
@comment node-name, next, previous, up
@section Description (desc)
@cindex Description
@cindex desc
The bond graph can be described textually in LaTeX (.tex) description
file; this is the only language for this representation. This
representation is used by the LaTeX language version (@pxref{Language tex
(abg.tex)}) of the acausal bond graph representation (@pxref{Acausal
bond graph (abg)}).
@menu
* Language tex (desc.tex)::
@end menu
@node Language tex (desc.tex), , Description (desc), Description (desc)
@comment node-name, next, previous, up
@subsection Language tex (desc.tex)
@cindex Language tex (desc.tex)
This file may contain any LaTeX compatible commands. Any mathematics
should conform to the AMSmath package.
@node Structure (struc), Constitutive Relationship (cr), Description (desc), Representations
@comment node-name, next, previous, up
@section Structure (struc)
@cindex Structure
@cindex struc
The causal bond graph implies a set of equations describing the
system. The Structure (struc) representation describes the structure of
these equations in terms of the input, outputs, states and non-states of
the system.
@menu
* Language txt (struc.txt)::
* Language tex (struc.tex)::
* Structure (view)::
@end menu
@node Language txt (struc.txt), Language tex (struc.tex), Structure (struc), Structure (struc)
@comment node-name, next, previous, up
@subsection Language txt (struc.txt)
@cindex Language txt (struc.txt)
This text tile contains a description of the system structure
(@pxref{Structure (struc)} with 5 tab-separated columns containing the
following information:
@vtable @code
@item type
input, output state or nonstate
@item
index
an integer corresponding to the array index
@item
component name
the name of the component corresponding to the variable
@item system name
the name of the system containing the component
@item repetition
an integer corresponding to the repetition of a repeated subsystem.
@end vtable
An example of such a file (corresponding to rc) (@pxref{Quick start}) is:
@example
input 1 e1 rc 1
output 1 e2 rc 1
state 1 c rc 1
@end example
@node Language tex (struc.tex), Structure (view), Language txt (struc.txt), Structure (struc)
@comment node-name, next, previous, up
@subsection Language tex (struc.tex)
@cindex Language tex (struc.tex)
This LaTeX (@pxref{LaTeX}) file contains a description of the system structure
(@pxref{Structure (struc)} in @code{longtable} format. It is a useful
item to include in a report(@pxref{Report}).
@node Structure (view), , Language tex (struc.tex), Structure (struc)
@subsection Language tex (view)
@cindex Structure (view)
@cindex view Structure
This representation has the standard text view
(@pxref{Views}).
@node Constitutive Relationship (cr), Parameters, Structure (struc), Representations
@comment node-name, next, previous, up
@section Constitutive relationship (cr)
@cindex Constitutive relationship
The constitutive relationship (@pxref{Constitutive relationship})
of a simple component (@pxref{Simple components} is
defined in the symbolic algebra language Reduce (@pxref{Reduce}).
The constitutive relationship of a compound components
(@pxref{Compound components})
is implied by the constitutive relationships of its constituent components.
@menu
* Predefined constitutive relationships::
* DIY constitutive relationships::
* Unresolved constitutive relationships::
* Unresolved constitutive relationships - Octave::
* Unresolved constitutive relationships - c++::
@end menu
@node Predefined constitutive relationships, DIY constitutive relationships, Constitutive Relationship (cr), Constitutive Relationship (cr)
@comment node-name, next, previous, up
@subsection Predefined constitutive relationships
@cindex Predefined constitutive relationships
Some common cr's are predefined by MTT; these are:
@vtable @code
@item lin
a linear constitutive relationship
@item exotherm
an exothermic reaction
@end vtable
@menu
* lin::
* exotherm::
@end menu
@node lin, exotherm, Predefined constitutive relationships, Predefined constitutive relationships
@comment node-name, next, previous, up
@subsubsection lin
@findex lin
The constitutive relationship @code{lin} is predefined for the following
components.
@vtable @code
@item R
(one-port) R component
@item TF
transformer
@item GY
gyrator
@item MTF
modulated transformer
@item MGY
modulated gyrator
@item FMR
flow-modulated resistor
@end vtable
Lin takes two arguments in the form causality,gain
@vtable @code
@item causality
the causality (effort or flow) of the @emph{input} to the
constitutive relationship
@item gain
the gain of the component when the input causality is as
specified in the first argument.
@end vtable
For example the arguments
@example
flow,r
@end example
given to an R component corresponds to
@example
e = rf
@end example
if if the input causality is flow
or
@example
f = e/r
@end example
if if the input causality is effort.
@node exotherm, , lin, Predefined constitutive relationships
@comment node-name, next, previous, up
@subsubsection exotherm
@findex exotherm
@node DIY constitutive relationships, Unresolved constitutive relationships, Predefined constitutive relationships, Constitutive Relationship (cr)
@comment node-name, next, previous, up
@subsection DIY constitutive relationships
@cindex DIY constitutive relationships
You can write your own constitutive relationships using Reduce
(@pxref{Reduce}). This requires some understanding as to how
@strong{MTT} represent the elementary system equations
(@pxref{Elementary system equations}). Looking at the predefined
constitutive relationships is a good way to get started
(@pxref{File structure}).
@node Unresolved constitutive relationships, Unresolved constitutive relationships - Octave, DIY constitutive relationships, Constitutive Relationship (cr)
@subsection Unresolved constitutive relationships
@cindex Unresolved constitutive relationships
Consider the following CR file.
@example
FOR ALL rho,g,vol,h,topt,bott,flowin,press
LET tktf2(rho,g,vol,h,topt,bott,effort,2,press,effort,1)
= tank(rho,g,vol,h,topt,bott,press);
@end example
Assuming that `tank' is not defined in a
reduce file, MTT will leave it unresolved when generating m or c code.
The resulting function can then be expressed as octave
(@pxref{Unresolved constitutive relationships - Octave}) or c++ code as
(@pxref{Unresolved constitutive relationships - c++}) appropriate.
@node Unresolved constitutive relationships - Octave, Unresolved constitutive relationships - c++, Unresolved constitutive relationships, Constitutive Relationship (cr)
@subsection Unresolved constitutive relationships - Octave
@cindex Unresolved constitutive relationships - Octave
Following the example of the previous section, the unresolved CR `tank'
can be expressed as an Octave m-file. For example:
@example
function p = tank (rho,g,vol,h,topt,bott,press)
## usage: p = tank (vol,h,topt,bott,press)
##
##
val = press; zt = topt; zb = bott;
zval = 0.5*(abs(zb+(zt-zb)*val-h)+(zb+(zt-zb)*val-h));
p = rho*g*zval + 0.5*(1+tanh((press-0.98)*500))*100000;
endfunction
@end example
This will be automatically loaded into octave.
@node Unresolved constitutive relationships - c++, , Unresolved constitutive relationships - Octave, Constitutive Relationship (cr)
@subsection Unresolved constitutive relationships - c++
@cindex Unresolved constitutive relationships - Octave
Following the example of the previous section, the unresolved CR `tank'
can be expressed in c++ code. For example:
@example
inline double tank(const double rho,
const double g,
const double vol,
const double h,
const double topt,
const double bott,
const double press)
/* ## usage: p = tank (vol,h,topt,bott,press)
##
##
*/
double p, val, zval, zt, zb;
val = press;
zt = topt;
zb = bott;
zval = 0.5 * (abs(zb + (zt - zb) * val - h) + zb + (zt - zb) * val - h);
p = rho * g * zval + 0.5 * (1 + tanh((press - 0.98) * 500)) * 100000L;
return p;
@end example
To make sure that this is used in system `model', the model_cr.h file
must be as follows:
@example
// CR headers for system model
#include "tank.c"
@end example
@node Parameters, Causal bond graph (cbg), Constitutive Relationship (cr), Representations
@comment node-name, next, previous, up
@section Parameters
@cindex Parameters
In general, lbl (@pxref{Labels (lbl)}) files contain symbolic
parameters. @strong{MTT} provides three ways of substituting for these
parameters:
@itemize @bullet
@item
symbolic substitution
@item
symbolic substitution for simplification of displayed equations
@item
numeric
@end itemize
@menu
* Symbolic parameters (subs.r)::
* Symbolic parameters for simplification (simp.r)::
* Numeric parameters (numpar)::
@end menu
@node Symbolic parameters (subs.r), Symbolic parameters for simplification (simp.r), Parameters, Parameters
@comment node-name, next, previous, up
@subsection Symbolic parameters (subs.r)
@cindex Symbolic parameters
@vindex subs.r
This file contains reduce statements to symbolically change the
expressions describing the system.
For example, a useful set of trig substitutions is:
@example
LET cos(~x)*cos(~y) = (cos(x+y)+cos(x-y))/2;
LET cos(~x)*sin(~y) = (sin(x+y)-sin(x-y))/2;
LET sin(~x)*sin(~y) = (cos(x-y)-cos(x+y))/2;
LET cos(~x)^2 = (1+cos(2*x))/2;
LET sin(~x)^2 = (1-cos(2*x));
@end example
@node Symbolic parameters for simplification (simp.r), Numeric parameters (numpar), Symbolic parameters (subs.r), Parameters
@comment node-name, next, previous, up
@subsection Symbolic parameters for simplification (simp.r)
@cindex Symbolic parameters for simplification
@vindex simp.r
This file contains reduce statements to symbolically change the
expressions describing the system. Unlike the subs.r file
(@pxref{Symbolic parameters (subs.r)}) it does not affect all system
transformations; only those converting to LaTeX form.
@node Numeric parameters (numpar), , Symbolic parameters for simplification (simp.r), Parameters
@comment node-name, next, previous, up
@subsection Numeric parameters (numpar)
@cindex Numeric parameters
When computing time and frequency responses; or when evaluating
functions in Octave (@pxref{Octave}); symbolic parameters need numerical
instantiations.
The numpar representation provides the relevant @emph{numerical}
information. It comes in a number of languages:
@ftable @code
@item txt
a textual description of the parameter values -- this is the
defining representation (@pxref{Defining representations}).
@item m
readable by @code{octave} a high-level interactive language for numerical
computation -- translated by @strong{mtt} from the txt version.
@item c
readable by @code{gcc} a c compiler -- translated by @strong{mtt} from the txt version.
@end ftable
@menu
* Text form (numpar.txt)::
@end menu
@node Text form (numpar.txt), , Numeric parameters (numpar), Numeric parameters (numpar)
@comment node-name, next, previous, up
@subsubsection Text form (numpar.txt)
@cindex Numeric parameters
This is the textual form of the numerical parameters representation
(@pxref{Numeric parameters (numpar)}). Lines are either
@ftable @code
@item assignment statements
variable = value
@item comments
lines beginning with #
@item commented assignment statements
variable = value # comments
@end ftable
An example file is:
@example
# Numerical parameter file (rc_numpar.txt)
# Generated by MTT at Mon Jun 16 15:10:17 BST 1997
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% Version control history
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% $Id$
# %% $Log$
# %% Revision 1.9 2002/07/05 13:29:34 geraint
# %% Added notes about generating dynamically linked functions for Octave and Matlab.
# %%
# %% Revision 1.8 2002/07/04 21:34:12 geraint
# %% Updated gnuplot view description to describe Tcl/Tk interface instead of obsolete txt method.
# %%
# %% Revision 1.7 2002/04/23 09:51:54 gawthrop
# %% Changed incorrect statement about searching for components.
# %%
# %% Revision 1.6 2001/10/15 14:29:50 gawthrop
# %% Added documentaton on [1:N] style port labels
# %%
# %% Revision 1.5 2001/07/23 03:35:29 geraint
# %% Updated file structure (mtt/bin).
# %%
# %% Revision 1.4 2001/07/23 03:25:02 geraint
# %% Added notes on -ae hybrd, rk4, ode2odes.cc, .oct dependencies.
# %%
# %% Revision 1.3 2001/07/13 03:02:38 geraint
# %% Added notes on #ICD, gnuplot.txt and odes.sg rep.
# %%
# %% Revision 1.2 2001/07/03 22:59:10 gawthrop
# %% Fixed problems with argument passing for CRs
# %%
# %% Revision 1.1 2001/06/04 08:18:52 gawthrop
# %% Putting documentation under CVS
# %%
# %% Revision 1.66 2000/12/05 14:20:55 peterg
# %% Added the c++ anf m CR info.
# %%
# %% Revision 1.65 2000/11/27 15:36:15 peterg
# %% NOPAR --> NOTPAR
# %%
# %% Revision 1.64 2000/11/16 14:22:48 peterg
# %% added UNITS declaration
# %%
# %% Revision 1.63 2000/11/03 14:41:08 peterg
# %% Added PAR and NOTPAR stuff
# %%
# %% Revision 1.62 2000/10/17 17:53:34 peterg
# %% Added some simulation details
# %%
# %% Revision 1.61 2000/09/14 17:13:06 peterg
# %% New options table
# %%
# %% Revision 1.60 2000/09/14 17:09:20 peterg
# %% Tidied up valid name sections
# %% Tidied up defining represnetations table
# %% Verion 4.6
# %%
# %% Revision 1.59 2000/08/30 13:09:00 peterg
# %% Updated option table
# %%
# %% Revision 1.58 2000/08/01 13:30:19 peterg
# %% Version 4.4
# %% updated STEPFACTOR info
# %% describes octave and OCST interfaces
# %%
# %% Revision 1.57 2000/07/20 07:55:44 peterg
# %% Version 4.3
# %%
# %% Revision 1.56 2000/05/19 17:49:17 peterg
# %% Extended the user defined representation section -- new nppp rep.
# %%
# %% Revision 1.55 2000/03/16 13:53:31 peterg
# %% Correct date
# %%
# %% Revision 1.54 2000/03/15 21:22:57 peterg
# %% Updated to 4.1 -- old style SS no longer supported
# %%
# %% Revision 1.53 1999/12/22 05:33:10 peterg
# %% Updated for 4.0
# %%
# %% Revision 1.52 1999/11/23 00:25:11 peterg
# %% Added the sensitivity reps
# %%
# %% Revision 1.51 1999/11/16 04:43:47 peterg
# %% Added start of sensitivity section
# %%
# %% Revision 1.50 1999/11/16 00:30:35 peterg
# %% Updated simulation section
# %% Added vector components
# %%
# %% Revision 1.49 1999/07/20 23:44:58 peterg
# %% V 3.8
# %%
# %% Revision 1.48 1999/07/19 03:08:33 peterg
# %% Added documentation for (new) SS lbl fields
# %%
# %% Revision 1.47 1999/03/09 01:42:22 peterg
# %% Rearranged the User interface section
# %%
# %% Revision 1.46 1999/03/09 01:18:01 peterg
# %% Updated for 3.5 including xmtt
# %%
# %% Revision 1.45 1999/03/03 02:39:26 peterg
# %% Minor updates
# %%
# %% Revision 1.44 1999/02/17 06:52:14 peterg
# %% New level formula dor artwork
# %%
# %% Revision 1.43 1998/11/25 16:49:24 peterg
# %% Put in subs.r documentation (was called params.r)
# %%
# %% Revision 1.42 1998/11/24 12:24:59 peterg
# %% Added section on simulation output
# %% Version 3.4
# %%
# %% Revision 1.41 1998/09/02 12:04:15 peterg
# %% Version 3.2
# %%
# %% Revision 1.40 1998/08/27 08:36:39 peterg
# %% Removed in. methods except Euler anf implicit
# %%
# %% Revision 1.39 1998/08/18 10:44:28 peterg
# %% Typo
# %%
# %% Revision 1.38 1998/08/18 09:16:38 peterg
# %% Version 3.1
# %%
# %% Revision 1.37 1998/08/17 16:14:30 peterg
# %% Version 3.1 - includes documentation on METHOD=IMPLICIT
# %%
# %% Revision 1.36 1998/07/30 17:33:15 peterg
# %% VERSION 3.0
# %%
# %% Revision 1.35 1998/07/22 11:00:53 peterg
# %% Correct date!
# %%
# %% Revision 1.34 1998/07/22 11:00:13 peterg
# %% Version to BAe
# %%
# %% Revision 1.33 1998/07/17 19:32:19 peterg
# %% Added more about aliases
# %%
# %% Revision 1.32 1998/07/05 14:21:56 peterg
# %% Further additions (Carlisle-Glasgow)
# %%
# %% Revision 1.31 1998/07/04 11:35:57 peterg
# %% Strarted new lbl description
# %%
# %% Revision 1.30 1998/07/02 18:39:20 peterg
# %% Started 3.0
# %% Added alias and default sections.
# %%
# %% Revision 1.29 1998/05/19 19:46:58 peterg
# %% Added the odess description
# %%
# %% Revision 1.28 1998/05/14 09:17:22 peterg
# %% Added METHOD variable to the simpar file
# %%
# %% Revision 1.27 1998/05/13 10:03:09 peterg
# %% Added unknown/zero SS label documentation.
# %%
# %% Revision 1.26 1998/04/29 15:12:46 peterg
# %% Version 2.9.
# %%
# %% Revision 1.25 1998/04/12 17:00:26 peterg
# %% Added new port features: coerced direction and top-level behaviour.
# %%
# %% Revision 1.24 1998/04/05 18:27:20 peterg
# %% This was the 2.6 version
# %%
# Revision 1.23 1997/08/24 11:17:51 peterg
# This is the released version 2.5
#
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# Parameters
c = 1.0; # Default value
r = 1.0; # Default value
# Initial states
x(1) = 0.0; # Initial state for rc (c)
@end example
As usual, @strong{MTT} provides a default text file to be edited by the
user (@pxref{Text editors}).
@node Causal bond graph (cbg), Elementary system equations, Parameters, Representations
@comment node-name, next, previous, up
@section Causal bond graph (cbg)
@cindex Causal bond graph (cbg)
The causal bond graph is the causally complete version of the
Acausal bond graph (@pxref{Acausal bond graph (abg)}).
To create the causal bond graph of system `sys' in language fig type:
@example
mtt sys cbg fig
@end example
To create the causal bond graph of system `sys' in language m type:
@example
mtt sys cbg m
@end example
To view the causal bond graph of system `sys' type:
@example
mtt sys cbg view
@end example
@menu
* Language fig (cbg.fig)::
* Language m (cbg.m)::
@end menu
@node Language fig (cbg.fig), Language m (cbg.m), Causal bond graph (cbg), Causal bond graph (cbg)
@subsection Language fig (cbg.fig)
@cindex Language fig (cbg.fig)
@pindex Language fig (cbg.fig)
The fig file is created by @strong{MTT}. It is identical to the
corresponding acausal representation (@pxref{Language fig (abg.fig)})
except that
@itemize @bullet
@item
the new causal strokes are added (using a double thickness line in blue)
@item
components that are undercausal are bold and green
@item
components that are overcausal are bold and red
@end itemize
@node Language m (cbg.m), , Language fig (cbg.fig), Causal bond graph (cbg)
@comment node-name, next, previous, up
@subsection Language m (cbg.m)
@cindex Language m (cbg.m)
@cindex cbonds
@cindex status
The causal bond graph of system `sys' is represented as
an m file with heading:
@example
function [cbonds,status] = sys_cbg
@end example
The two outputs of this function are:
@itemize @bullet
@item
cbonds
@item
status
@end itemize
@emph{cbonds} is a matrix with
@itemize @bullet
@item
one row for each bond
@item
the first column contains the arrow-orientated
(@pxref{Arrow-orientated causality})
causality of the @emph{effort} variable.
@item
the second column contains the arrow-orientated
(@pxref{Arrow-orientated causality})
causality of the @emph{flow} variable.
@end itemize
@emph{status} is a matrix with
@itemize @bullet
@item
one row for each component
@item
the first column contains 1 if the component is overcausal; 0 if the
component is causally complete and -1 if the component is undercausal.
@end itemize
A successful model would therefore have all zeros in the status matrix.
@menu
* Transformation abg2cbg_m::
@end menu
@node Transformation abg2cbg_m, , Language m (cbg.m), Language m (cbg.m)
@comment node-name, next, previous, up
@subsubsection Transformation abg2cbg_m
@cindex Transformation abg2cbg_m
This transformation takes the acausal bond graph as an m file
(@pxref{Language m (abg.m)}) and transforms it into a causal bond graph in
m-file format (@pxref{Language m (cbg.m)}).
It is based on the m-function abg2cbg.m which iteratively tries to
complete causality whilst recursively searching the bond graph
structure.
If causality is incomplete, it picks the first acausal dynamic (C or I)
component, asserts integral causality, and tries again.
This is essentially the sequential causality assignment procedure of
Karnopp and Rosenberg.
The transformation informs the user of the final status in terms of the
percentage of causally complete components; a successful model will
yield 100% here.
@node Elementary system equations, Differential-Algebraic Equations, Causal bond graph (cbg), Representations
@comment node-name, next, previous, up
@section Elementary system equations (ese)
@cindex Elementary system equations
The elementary system equations are a complete set of assignment statements
describing the dynamic system corresponding to the bond graph.
They are in the Reduce (@pxref{Reduce}) language.
Because these are based on a causally complete system, these assignment
statements are directly soluble by substitution.
Unlike early versions of @strong{MTT}, @strong{MTT} does @emph{not} sort
the equations in order of solution, but rather leaves them sorted by
component and subsystem.
These are not supposed to be read by the user, so there is no view
facility as such. However, you may read these with your favourite text
editor and, to this end, helpful comment lines have been added.
Wherever components have an explicit constitutive relationship, the
corresponding RHS of the equation has a standard form.
@example
cr(arguments,out_causality,outport,
input_1, causality_1, port_1,
....
input_i, causality_i, port_i,
....
input_n, causality_n, port_n
);
@end example
where the symbols have the following meaning
@vtable @code
@item arguments
the constitutive relationship arguments
@item out_causality
the causality (effort or flow) of the output variable
(@pxref{Variables})
@item outport
the number (integer) of the output port of the system
@item input_i
the ith input to the component
@item causality_i
the causality (effort or flow) of the ith input variable
(@pxref{Variables})
@item port_i
the number (integer) of the ith input port of the system
@end vtable
An example for a resistor with linear constitutive relationship is:
@example
rc_1_bond4_flow := lin(flow,r,flow,1,
rc_1_bond4_effort,effort,1
);
@end example
@menu
* Transformation cbg2ese_m2r::
@end menu
@node Transformation cbg2ese_m2r, , Elementary system equations, Elementary system equations
@comment node-name, next, previous, up
@subsubsection Transformation cbg2ese_m2r
@cindex Transformation cbg2ese_m2r
@cindex Structure
@cindex def.r
This transformation takes the causal bond graph as an m file
(@pxref{Language m (cbg.m)}) and transforms it into elementary system
equations
in Reduce (@pxref{Reduce})
form.
It is based on the m-function cbg2ese.m which iteratively traverses the
causal bond graph writing equations as it goes.
It also writes out the system structure as the file @file{sys_def.r}.
@node Differential-Algebraic Equations, Constrained-state Equations, Elementary system equations, Representations
@section Differential-Algebraic Equations (dae)
@cindex Differential-Algebraic Equations
@cindex DAE
The system differential algebraic equations describe the system dynamics together
together with any algebraic constraints.
They are generated in language @code{lang} for system
@code{sys} by:
@example
mtt sys dae lang
@end example
Valid languages are:
@vtable @code
@item r
reduce (@pxref{Reduce}).
@item m
m (@pxref{m}).
@item view
reduce (@pxref{Views}).
@end vtable
There are five sets of variables describing the system:
@vtable @code
@item x
the system states (corresponding to C and I components with integral
causality.
@item z
the system nonstates (corresponding to C and I components with derivative
causality.
@item u
the system inputs (corresponding to SS components
with external attribute).
@item ui
the @emph{internal} system inputs (corresponding to SS components
with internal attribute) used to solve algebraic loops
(@pxref{Algebraic loops}).
@item y
the system outputs (corresponding to SS components
with external attribute).
@end vtable
In general there are four sets of equations. The right-hand side of
each is a function of x, dz/dt, u and ui and the left hand sides are:
@enumerate
@item
the derivative of x (dx/dt)
@item
z
@item
w=0 (the algebraic equations)
@item
y
@end enumerate
@menu
* Differential-Algebraic Equations (reduce)::
* Differential-Algebraic Equations (m)::
@end menu
@node Differential-Algebraic Equations (reduce), Differential-Algebraic Equations (m), Differential-Algebraic Equations, Differential-Algebraic Equations
@subsection Language reduce (dae.r)
@cindex Differential-Algebraic Equations (reduce)
@cindex dae.r
The system DAEs (@pxref{Differential-Algebraic Equations})
are represented in the reduce (@pxref{Reduce}) language as
arrays containing the algebraic expressions for the
right hand sides of each set of equations. The arrays are:
@vtable @code
@item MTTx
x -- the system states (corresponding to C and I components with integral
causality.
@item MTTz
z -- the system nonstates (corresponding to C and I components with derivative
causality.
@item MTTu
u -- the system inputs (corresponding to SS components
with external attribute).
@item mttv
ui -- the @emph{internal} system inputs (corresponding to SS components
with internal attribute) used to solve algebraic loops
(@pxref{Algebraic loops}).
@item MTTy
y -- the system outputs (corresponding to SS components
with external attribute).
@end vtable
@menu
* Transformation ese2dae_r::
@end menu
@node Transformation ese2dae_r, , Differential-Algebraic Equations (reduce), Differential-Algebraic Equations (reduce)
@subsubsection Transformation ese2dae_r
@cindex Transformation ese2dae_r
@pindex ese2dae_r
This transformation (@pxref{What is a Transformation?})
uses Reduce (@pxref{Reduce}) to combine the elementary system
equations (@pxref{Elementary system equations}) with the
constitutive relationships (@pxref{Constitutive relationship})
and simplify the result.
@node Differential-Algebraic Equations (m), , Differential-Algebraic Equations (reduce), Differential-Algebraic Equations
@subsection Language m (dae.m)
@cindex Differential-Algebraic Equations (m)
@cindex dae.m
The system DAEs (@pxref{Differential-Algebraic Equations})
are represented in the m (@pxref{m}) language as
two m-functions of the form:
@example
function resid = sys_dae(dx,x,t)
function y = sys_dae(dx,x,t)
@end example
Where x is the dae @emph{descriptor} vector and dx its
time derivative; t is the time.
The first function is of a form suitable for solution by DASSL;
the second function can then be used to find the coresponding system
output.
@menu
* Transformation dae_r2m::
@end menu
@node Transformation dae_r2m, , Differential-Algebraic Equations (m), Differential-Algebraic Equations (m)
@subsubsection Transformation dae_r2m
@cindex Transformation dae_r2m
@pindex dae_r2m
This transformation (@pxref{What is a Transformation?})
uses Reduce (@pxref{Reduce}) to rewrite the elementary system
equations (@pxref{Elementary system equations}) in m-file
format (@pxref{m}) . Numerical parameters are declared as global.
@node Constrained-state Equations, Ordinary Differential Equations, Differential-Algebraic Equations, Representations
@section Constrained-state Equations (cse)
@cindex Constrained-state Equations
@cindex ODE
The system constrained-state equations describe the system dynamics for
a special class of systems (see the book for details). The resuting
equations are of the form:
@example
E(x) dx/dt = f(x,u)
y = g(x,u)
@end example
They typically occure where two or more states are constrained to be equal, or
proportional, to each other. For example, two capacitors in parallel or
two inertias connected by a stiff shaft.
They are generated in language @code{lang} for system
@code{sys} by:
@example
mtt sys cse lang
@end example
Valid languages are:
@vtable @code
@item r
reduce (@pxref{Reduce}).
@item m
m (@pxref{m}).
@item view
reduce (@pxref{Views}).
@end vtable
There are three sets of variables describing the system:
@vtable @code
@item x
the system states (corresponding to C and I components with integral
causality.
@item u
the system inputs (corresponding to SS components
with external attribute).
@item y
the system outputs (corresponding to SS components
with external attribute).
@end vtable
In general there are two sets of equations. The right-hand side of
each is a function of x and u and the left hand sides are:
@enumerate
@item
the derivative of x (dx/dt)
y
@end enumerate
@menu
* Constrained-state Equations (reduce)::
* Constrained-state Equations (view)::
@end menu
@node Constrained-state Equations (reduce), Constrained-state Equations (view), Constrained-state Equations, Constrained-state Equations
@subsection Language reduce (cse.r)
@cindex Constrained-state Equations (reduce)
@cindex cse.r
The system CSEs (@pxref{Constrained-state Equations})
are represented in the reduce (@pxref{Reduce}) language as
arrays containing the algebraic expressions for the
right hand sides of each set of equations. The arrays are:
@vtable @code
@item MTTx
x -- the system states (corresponding to C and I components with integral
causality.
@item MTTu
u -- the system inputs (corresponding to SS components
with external attribute).
@item MTTy
y -- the system outputs (corresponding to SS components
with external attribute).
@end vtable
together with the array containing the elements of the E matrix.
@menu
* Transformation dae2cse_r::
@end menu
@node Transformation dae2cse_r, , Constrained-state Equations (reduce), Constrained-state Equations (reduce)
@subsubsection Transformation dae2cse_r
@cindex Transformation dae2cse_r
@pindex dae2cse_r
This transformation (@pxref{What is a Transformation?})
Reduce (@pxref{Reduce}) to find various Jacobians which are combined to
find the E matrix and the
constrained-state equations (@pxref{Constrained-state Equations}).
@node Constrained-state Equations (view), , Constrained-state Equations (reduce), Constrained-state Equations
@subsection Language m (view)
@cindex Constrained-state Equations (view)
@cindex view Constrained-state Equations
This representation has the standard text view
(@pxref{Views}).
@node Ordinary Differential Equations, Descriptor matrices, Constrained-state Equations, Representations
@section Ordinary Differential Equations
@cindex Ordinary Differential Equations
@cindex ODE
The system ordinary differential equations describe the system dynamics.
They are generated in language @code{lang} for system
@code{sys} by:
@example
mtt sys ode lang
@end example
Valid languages are:
@vtable @code
@item r
reduce (@pxref{Reduce}).
@item m
m (@pxref{m}).
@item view
reduce (@pxref{Views}).
@end vtable
There are three sets of variables describing the system:
@vtable @code
@item x
the system states (corresponding to C and I components with integral
causality.
@item u
the system inputs (corresponding to SS components
with external attribute).
@item y
the system outputs (corresponding to SS components
with external attribute).
@end vtable
In general there are two sets of equations. The right-hand side of
each is a function of x and u and the left hand sides are:
@enumerate
@item
the derivative of x (dx/dt)
y
@end enumerate
@menu
* Ordinary Differential Equations (reduce)::
* Ordinary Differential Equations (m)::
* Ordinary Differential Equations (view)::
@end menu
@node Ordinary Differential Equations (reduce), Ordinary Differential Equations (m), Ordinary Differential Equations, Ordinary Differential Equations
@subsection Language reduce (ode.r)
@cindex Ordinary Differential Equations (reduce)
@cindex ode.r
The system ODEs (@pxref{Ordinary Differential Equations})
are represented in the reduce (@pxref{Reduce}) language as
arrays containing the algebraic expressions for the
right hand sides of each set of equations. The arrays are:
@vtable @code
@item MTTx
x -- the system states (corresponding to C and I components with integral
causality.
@item MTTu
u -- the system inputs (corresponding to SS components
with external attribute).
@item MTTy
y -- the system outputs (corresponding to SS components
with external attribute).
@end vtable
@menu
* Transformation cse2ode_r::
@end menu
@node Transformation cse2ode_r, , Ordinary Differential Equations (reduce), Ordinary Differential Equations (reduce)
@subsubsection Transformation cse2ode_r
@cindex Transformation cse2ode_r
@pindex cse2ode_r
This transformation (@pxref{What is a Transformation?})
uses Reduce (@pxref{Reduce}) to invert the E matrix of the
constrained-state equations (@pxref{Constrained-state Equations})
and simplify the result.
@node Ordinary Differential Equations (m), Ordinary Differential Equations (view), Ordinary Differential Equations (reduce), Ordinary Differential Equations
@subsection Language m (ode.m)
@cindex Ordinary Differential Equations (m)
@cindex ode.m
The system ODEs (@pxref{Ordinary Differential Equations})
are represented in the m (@pxref{m}) language as
two m-functions of the form:
@example
function dx = sys_ODE(x,t)
function y = sys_ODE(dx,x,t)
@end example
Where x is the ODE @emph{state} vector and dx its
time derivative; t is the time.
The first function is of a form suitable for solution by odesol;
the second function can then be used to find the corresponding system
output.
@menu
* Transformation ode_r2m::
@end menu
@node Transformation ode_r2m, , Ordinary Differential Equations (m), Ordinary Differential Equations (m)
@subsubsection Transformation ode_r2m
@cindex Transformation ode_r2m
@pindex ode_r2m
This transformation (@pxref{What is a Transformation?})
uses Reduce (@pxref{Reduce}) to rewrite the
ordinary differential equations
(@pxref{Ordinary Differential Equations}) in m-file
format (@pxref{m}) . Numerical parameters are declared as global.
@node Ordinary Differential Equations (view), , Ordinary Differential Equations (m), Ordinary Differential Equations
@subsection Language m (view)
@cindex Ordinary Differential Equations (view)
@cindex view Ordinary Differential Equations
This representation has the standard text view
(@pxref{Views}).
@node Descriptor matrices, Report, Ordinary Differential Equations, Representations
@section Descriptor matrices (dm)
@cindex Descriptor matrices
@cindex dm
The system descriptor matrices A, B, C, D and E describe the
@emph{linearised} system dynamics in the form
@example
E dx/dt = Ax + Bu
y = Cx + Du
@end example
They are generated in language @code{lang} for system
@code{sys} by:
@example
mtt sys dm lang
@end example
Valid languages are:
@vtable @code
@item r
reduce (@pxref{Reduce}).
@item m
m (@pxref{m}).
@item view
reduce (@pxref{Views}).
@end vtable
@menu
* Descriptor matrices (reduce)::
* Descriptor matrices (m)::
@end menu
@node Descriptor matrices (reduce), Descriptor matrices (m), Descriptor matrices, Descriptor matrices
@subsection Language reduce (dm.r)
@cindex Descriptor matrices (reduce)
@cindex dm.r
The system descriptor matrices (@pxref{Descriptor matrices})
are represented in the reduce (@pxref{Reduce}) language as
arrays containing the four matrices. The arrays are:
@vtable @code
@item MTTA
A
@item MTTB
B
@item MTTA
C
@item MTTD
D
@item MTTE
E
@end vtable
@node Descriptor matrices (m), , Descriptor matrices (reduce), Descriptor matrices
@subsection Language m (dm.m)
@cindex Descriptor matrices (m)
@cindex dm.m
The system descriptor matrices (@pxref{Descriptor matrices})
are represented in the m (@pxref{m}) language as
an m-function of the form:
@example
function [A,B,C,D,E] = sys_dm
@end example
System numeric parameters (@pxref{Numeric parameters})
are passed via global variables defined in the _numpar.m file.
@c (@pxref{numpar.m}).
Thus the system descriptor matrices are
typically generated in Octave (@pxref{Octave}) as follows:
@example
sys_numpar
[A,B,C,D,E] = sys_dm
@end example
Parameters can be changed from their default values by entering
their values directly into Octave (@pxref{Octave}) and then invoking
@code{sys_dm}; for example
@example
sys_numpar
par_1 = 25
par_2 = par_1 + 3
[A,B,C,D,E] = sys_dm
@end example
@node Report, , Descriptor matrices, Representations
@section Report (rep)
@cindex Report
@cindex rep
@strong{MTT} has a report-generator feature. The user specifies the
report contents in a text file (@pxref{Report (text)}) using an
appropriate text editor (@pxref{Text editors}).
For example, the report can be viewed by typing
@example
mtt system rep view
@end example
@menu
* Report (text)::
* Report (view)::
@end menu
@node Report (text), Report (view), Report, Report
@subsection Language text (rep.txt)
@cindex Report (text)
@cindex rep.txt
The user specifies the report contents in a text file (@pxref{Report
(text)}) using an appropriate text editor (@pxref{Text editors}).
The text file contains lines which are either comments (indicated by %)
or valid @strong{MTT} commands. The report will then contain appropriate
sections. The following languages are supported by the report generator:
@ftable @code
@item m
@code{octave} a high-level interactive language for numerical
computation.
@item r
@code{reduce} a high-level interactive language for symbolic
computation.
@item tex
@code{latex} a text processor.
@item ps
@code{ghostview} another document viewer.
@item c
@code{gcc} a c compiler.
@end ftable
For example:
@example
mtt rc abg tex
mtt rc cbg ps
mtt rc struc tex
mtt rc ode tex
mtt rc sro ps
mtt rc tf tex
mtt rc lmfr ps
@end example
The acausal bond graph (abg) (@pxref{Acausal bond graph (abg)}) with the
tex language is handled in a special way: the acausal Bond Graph in
fig format (@pxref{Language fig (abg.fig)}), the label file (@pxref{Labels (lbl)})
the description file (@pxref{Description (desc)}), together with
corresponding subsystems are included in the report. It is recommended
that the first (non-comment line) in the file should be:
@example
mtt <system> abg tex
@end example
where @code{<system>} is the name of the (top-level) system.
As usual, @strong{MTT} provides a default text file to be edited by the
user (@pxref{Text editors}).
In the special case that the first argument to mtt (normally the system)
is a directory, a default text file is provided which generates a report
for all systems to be found in that directory tree.
@node Report (view), , Report (text), Report
@subsection Language view
@cindex Report (view)
@cindex view Report
This representation has the standard text view
(@pxref{Views}).
@node Extending MTT, Languages, Representations, Top
@comment node-name, next, previous, up
@chapter Extending MTT
@cindex Extending MTT
@cindex Make
@strong{MTT} has a number of built-in mechanisms for the user to extend
its capabilities. As @strong{MTT} is based on `Make' it is unsurprising
that some of these involve the creation of `make files'.
@menu
* Makefiles::
* New representations::
* Component library ::
@end menu
@node Makefiles, New representations, Extending MTT, Extending MTT
@comment node-name, next, previous, up
@section Makefiles
@cindex Makefiles
If a file called `Makefile' exists in the current directory,
@strong{MTT} executes it using make before doing anything else. This is
useful if one of the .txt files contains a reference to, for example, an
octave function of which @strong{MTT} unaware. Such a function can be
created using the makefile. An example `Makefile' is
@example
# Makefile for the Two link GMV example
all: msdP_tf.m TwoLinkP_obs.m TwoLinkP_sm.m twolinkp_sm.m TwoLinkGMV_numpar.m
msdP_tf.m: msdP_abg.fig
mtt -q msdP tf m
TwoLinkP_obs.m: TwoLinkP_abg.fig TwoLinkP_lbl.txt
mtt -q TwoLinkP obs m
TwoLinkP_sm.m: TwoLinkP_abg.fig TwoLinkP_lbl.txt
mtt -q TwoLinkP sm m
twolinkp_sm.m: TwoLinkP_sm.m
cp -v TwoLinkP_sm.m twolinkp_sm.m
TwoLinkGMV_numpar.m: TwoLinkGMV_numpar.txt
mtt -q TwoLinkGMV numpar m
@end example
All of the files in the line stating `all:' are created when
@strong{MTT} is executed (if they don't already exist).
@node New representations, Component library , Makefiles, Extending MTT
@comment node-name, next, previous, up
@section New representations
@cindex New representations
It may be convenient to create new representations for @strong{MTT}; in
particular, it is nice to be able to include the result of some
numerical or symbolic computations within an @strong{MTT} report
(@pxref{Report}).
To create a new representation `myrep' in a language `mylang', create a
file with the name
@example
myrep_rep.make
@end example
This file must contain text in `make' syntax. It is executed by
@strong{MTT} and the two arguments `SYS' (the system name) and `LANG'
(the language) are passed to it by @strong{MTT}. Note that @strong{MTT}
cannot know of any prerequisites, but these can be explicitly included in
the makefile (which may include execution of @strong{MTT} itself.
The following example declares the new representation `nppp' which is
created with the Octave script sys_nppp.m where `sys' is the system
name. This needs a number of files (for exaample `sys_ode2odes.out')
which are themselves created by @strong{MTT}.
@example
# -*-makefile-*-
# Makefile for representation nppp
# File nppp_rep.make
#Copyright (C) 2000 by Peter J. Gawthrop
all: $(SYS)_nppp.$(LANG)
$(SYS)_nppp.view: $(SYS)_nppp.ps
echo Viewing $(SYS)_nppp.ps; ghostview $(SYS)_nppp.ps&
$(SYS)_nppp.ps: $(SYS)_ode2odes.out s$(SYS)_ode2odes.out \
$(SYS)_sim.m s$(SYS)_sim.m \
$(SYS)_state.m $(SYS)_sympar.m $(SYS)_numpar.m \
s$(SYS)_state.m s$(SYS)_sympar.m s$(SYS)_numpar.m \
$(SYS)_sm.m $(SYS)_def.m s$(SYS)_def.m
octave $(SYS)_nppp.m
$(SYS)_ode2odes.out:
mtt -q -c -stdin $(SYS) ode2odes out
s$(SYS)_ode2odes.out:
mtt -q -c -stdin -s s$(SYS) ode2odes out
$(SYS)_sim.m:
mtt -q -c $(SYS) sim m
s$(SYS)_sim.m:
mtt -q -c -s s$(SYS) sim m
$(SYS)_state.m:
mtt -q $(SYS) state m
$(SYS)_sympar.m :
mtt -q $(SYS) sympar m
$(SYS)_numpar.m:
mtt -q $(SYS) numpar m
s$(SYS)_state.m:
mtt -q -s s$(SYS) state m
s$(SYS)_sympar.m :
mtt -q -s s$(SYS) sympar m
s$(SYS)_numpar.m:
mtt -q -s s$(SYS) numpar m
$(SYS)_sm.m:
mtt -q $(SYS) sm m
$(SYS)_def.m:
mtt -q $(SYS) def m
s$(SYS)_def.m:
mtt -q -s s$(SYS) def m
@end example
Future extensions of @strong{MTT} will use such representations stored
in $MTT_REP.
@node Component library , , New representations, Extending MTT
@comment node-name, next, previous, up
@section Component library
@cindex Component library
@cindex component
@cindex Component library
If @strong{MTT} does not recognise a component (eg named MyComponent) as
a simple component (@pxref{Simple components}) or as already existing,
it searches the library search path $MTT_COMPONENTS
(@pxref{$MTT_COMPONENTS}) for a directory called MyComponent containing
MyComponent_lbl.txt. It then copies the @emph{entire} directory into the
current working directory. Thus, for example, the directory could
contain MyComponent_desc.tex MyComponent_abg.fig MyComponent_lbl.txt and MyComponent_cr.r in
addition to MyComponent_lbl.txt.
@c node next prev up
@node Languages, Language tools, Extending MTT, Top
@chapter Languages
@cindex Languages
@pindex Languages
@c node next prev up
@menu
* Fig:: r
* m::
* Reduce::
* c::
@end menu
These are a number of languages used by @strong{MTT} to implement the
various representations.
Each has associated Language tools (@pxref{Language tools}) to
manipulate and/or view the representation.
@ftable @code
@item fig
@code{Fig} a graphical description language.
@item m
@code{octave} a high-level interactive language for numerical
computation.
@item r
@code{reduce} a high-level interactive language for symbolic
computation.
@item tex
@code{latex} a text processor.
@item dvi
@code{xdvi} a document viewer.
@item ps
@code{ghostview} another document viewer.
@item gdat
@code{gnuplot} a data viewer.
@item c
@code{gcc} a c compiler.
@item sg
@code{scigraphica} a plotting package.
@end ftable
These tools are automatically invoked as appropriate by @strong{MTT};
but for more advanced use, these tools can be used directly on files
(with the appropriate suffix) generated by @strong{MTT}.
@node Fig, m, Languages, Languages
@section Fig
@cindex Fig
@pindex Fig
Please see xfig documentation.
@node m, Reduce, Fig, Languages
@section m
@cindex m
@pindex m
Please see Octave documentation
@ifhtml
<A HREF="http://www.che.wisc.edu/octave/">Octave</A> documentation.
<A HREF="http://www.mathworks.com/homepage.html">Matlab</A> documentation.
@end ifhtml
@node Reduce, c, m, Languages
@section Reduce
@cindex Reduce
@pindex Reduce
Please see the reduce documentation.
@node c, , Reduce, Languages
@comment node-name, next, previous, up
@section c
@cindex c
@pindex c
Please see the gcc documentation.
@node Language tools, Administration, Languages, Top
@comment node-name, next, previous, up
@chapter Language tools
@cindex Language tools
@menu
* Views::
* Xfig::
* Text editors::
* Octave::
* LaTeX::
@end menu
@node Views, Xfig, Language tools, Language tools
@comment node-name, next, previous, up
@section Views
@cindex views
A number of representations (@pxref{Representations}) have a language
representation which is particularly useful for viewing by the
user. These views are
invoked, where appropriate by the command:
@example
mtt sys rep view
@end example
where @code{sys} is the system name and @code{rep} a corresponding representation.
@node Xfig, Text editors, Views, Language tools
@comment node-name, next, previous, up
@section Xfig
@cindex Xfig
@node Text editors, Octave, Xfig, Language tools
@comment node-name, next, previous, up
@section Text editors
@cindex Text editors
All representations live in text files and thus may be edited using your
favourite text editor; however, the Fig (@pxref{Fig}) representation is
pretty meaningless in this form and so you should use Xfig
(@pxref{Xfig}) for representation in this language.
Its up to you which text editor to use. I recommend emacs, but simpler
(and less powerful) editors such as xedit, textedit and vi are also ok.
I usually run @strong{MTT} out of an emacs shell window and keep the
rest of the files in emacs buffers.
@node Octave, LaTeX, Text editors, Language tools
@comment node-name, next, previous, up
@section Octave
@cindex Octave
@cindex Matlab
@cindex m-files
@cindex Octave interface
@cindex mtt.m
Octave is a numerical matrix-based language @xref{Top,
,Octave,Octave,Octave}. It is similar to Matlab in many ways. In most
cases, m-files generated by @strong{MTT} can be understood by both
Matlab and Octave (and no doubt other Matlab lookalikes).
@strong{MTT} provides the octave function @code{mtt}. The octave
command
@example
help mtt
@end example
gives the following information:
@example
usage: mtt (system[,representation,language])
Invokes mtt from octave to generate system_representation.language
Ie equivalent to "mtt system representation language" at the shell
Representation and language defualt to "sm" and "m" respectively
@end example
Thus for example, if octave is in the directory containing the system
rc the following session generates the state matrices of the system "rc"
with the defaut capacitance but resitance r=0.1.
@example
octave> mtt("rc");
Creating rc_rbg.m
Creating rc_cmp.m
Creating rc_fig.fig
Creating rc_sabg.fig
Creating rc_alias.txt
Creating rc_alias.m
Creating rc_sub.sh
Creating rc_abg.m
Creating rc_cbg.m (maximise integral causality)
Creating rc_type.sh
Creating rc_ese.r
Creating rc_def.r
Creating rc_struc.txt
Creating rc_rdae.r
Creating rc_subs.r
Creating rc_cr.txt
Creating rc_cr.r
Copying CR SS to here from
Copying CR lin to here from
Creating rc_dae.r
Creating rc_sympar.txt
Creating rc_sympar.r
Creating rc_cse.r
Creating rc_sspar.r
Creating rc_csm.r
Creating rc_ode.r
Creating rc_ss.r
Creating rc_sm.r
Creating rc_switch.txt
0 switches found
Creating rc_sympars.txt
Creating rc_sm.m
Copying rc_sm.m
octave> mtt("rc","numpar");
Creating rc_numpar.txt
Creating rc_numpar.m
Copying rc_numpar.m
octave> mtt("rc","sympar");
Creating rc_sympar.m
Copying rc_sympar.m
octave> par = rc_numpar
par =
1
1
octave> sym = rc_sympar;
octave> par(sym.r) = 0.1;
octave> [A,B,C,D] = rc_sm(par)
A = -10
B = 10
C = 1
D = 0
octave>
@end example
generates the data structure rc corresponding the the bond graph of the
system called `rc'.
The following octave commands then generate the step reponse and bode
diagram respectively:
@example
step(rc);
bode(rc);
@end example
@menu
* Octave control system toolbox (OCST)::
* Creating GNU Octave .oct files::
* Creating Matlab .mex files::
* Embedding MTT models in Simulink::
@end menu
@node Octave control system toolbox (OCST), Creating GNU Octave .oct files, Octave, Octave
@comment node-name, next, previous, up
@subsection Octave control system toolbox (OCST)
@cindex Octave
@cindex toolbox
@cindex OCST
@cindex control systems
@cindex mtt2sys
@strong{MTT} provides an interface to the Octave control system toolbox
(OCST) using the mfile @code{mtt2sys}. the octave command
@example
help mtt2sys
@end example
gives the following information.
@example
usage: sys = mtt2sys (Name[,par])
Creates a sys structure for the Octave Control Systems Toolbox
from an MTT system with name "Name"
Optional second argument is system parameter list
Assumes that Name_sm.m, Name_struc.m and Name_numpar.m exist
@end example
Thus for example, if octave is in the directory containing the system
rc:
@example
rc = mtt2sys("rc");
@end example
generates the data structure rc corresponding the the bond graph of the
system called `rc'.
The following octave commands then generate the step reponse and bode
diagram respectively:
@example
step(rc);
bode(rc);
@end example
@node Creating GNU Octave .oct files, Creating Matlab .mex files, Octave control system toolbox (OCST), Octave
@comment node-name, next, previous, up
@subsection Creating GNU Octave .oct files
@cindex Creating GNU Octave .oct files
GNU Octave dynamically loaded functions (.oct files) can be created by
instructing @strong{MTT} to create the ``oct'' representation:
@example
mtt [options] sys ode oct
@end example
This will cause @strong{MTT} to create the C++ representation of the system
(sys_ode.cc) and to then compile it as a shared object suitable for
use within Octave. The resultant file may be used in an identical
manner to the equivalent, but generally slower, interpreted .m file.
Usage information for the function may be obtained within Octave in the usual manner:
@example
octave:1> help rc_ode
rc_ode is the dynamically-linked function from the file
/home/mttuser/rc/rc_ode.oct
Usage: [mttdx] = rc_ode(mttx,mttu,mttt,mttpar)
Octave ode representation of system rc
Generated by MTT on Fri Jul 5 11:23:08 BST 2002
@end example
Note that the first line of output from Octave identifies whether the
compiled or interpreted function is being used.
Alternatively, standard representations may be generated using the
Octave DLDs by use of the ``-oct'' switch:
@example
mtt -oct rc odeso view
@end example
In order to successfully generate .oct files, Octave must be correctly
configured prior to compilation and certain headers and libraries must
be correctly installed on the system (@pxref{.oct file dependencies}).
@node Creating Matlab .mex files, Embedding MTT models in Simulink, Creating GNU Octave .oct files, Octave
@comment node-name, next, previous, up
@subsection Creating Matlab .mex files
@cindex Creating Matlab .mex files
On GNU/Linux systems, Matlab dynamically linked executables (.mexglx
files) can created by instructing @strong{MTT} to create the
``mexglx'' representation:
@example
mtt [options] sys ode mexglx
@end example
This will cause @strong{MTT} to create the C++ representation of the
system (sys_ode.cc) and to then compile it as a shared object suitable
for use within Matlab.
If it is necessary to compile mex files for another platform, then the
usual C++ representation (generated with the -cc flag) can be created
and the resultant file compiled with the -DCODEGENTARGET=MATLABMEX
flag on the target platform.
@example
mtt_machine:
mtt -cc rc ode cc
matlab_machine:
matlab> mex -DCODEGENTARGET=MATLABMEX rc_ode.cc
@end example
@node Embedding MTT models in Simulink, , Creating Matlab .mex files, Octave
@comment node-name, next, previous, up
@subsection Embedding MTT models in Simulink
@cindex Embedding MTT models in Simulink
It is possible to embed @strong{MTT} functions or entire @strong{MTT}
models within Simulink simulations as Sfun blocks. If the zip package
is installed on the system, the command
@example
mtt sys sfun zip
@end example
will create a compressed archive containing sys.mdl, which may be
embedded into a larger Simulink model. Also contained within the
archive will be four sys_sfun*.c files,
@itemize @bullet
@item
sys_sfun.c
model state and output equations
@item
sys_sfun_ae.c
model algebraic equations
@item
sys_sfun_input.c
model inputs
@item
sys_sfun_interface.c
interface between MTT model and Simulink
@end itemize
The last of these files must be edited to correctly map the inputs and
outputs between the @strong{MTT} and Simulink models. The two sections
to edit are clearly marked with
@example
@code{/* Start EDIT */}
@code{....}
@code{/* End EDIT */}
@end example
These four files should then be compiled with the Matlab ``mex''
compiler as described in the @emph{README} file in the archive.
If it is desired to compile the .mex files directly from within
@strong{MTT} on a machine which has the Matlab header files installed,
this may be done with the command
@example
mtt sys sfun mexglx
@end example
which will generated the four .mex files and the .mdl file. In this
case, the user must ensure that @emph{sys_sfun_interface.c} has been
correctly edited prior to compilation.
Note that solution of algebraic equations within Simulink is not
possible unless the @emph{Matlab Optimisation Toolbox} is installed.
@node LaTeX, , Octave, Language tools
@comment node-name, next, previous, up
@section LaTeX
@cindex LaTeX
LaTeX is a powerful text processor which @strong{MTT} uses to provide
visual output.
@node Administration, Glossary, Language tools, Top
@comment node-name, next, previous, up
@chapter Administration
@cindex Administration
@menu
* Software components::
* REDUCE setup::
* Octave setup::
* Paths::
* File structure::
@end menu
@node Software components, REDUCE setup, Administration, Administration
@comment node-name, next, previous, up
@section Software components
@cindex Software components
@strong{MTT} is built from a set of readily-available software tools.
These are:
@itemize @bullet
@item General purpose software tools.
@item Octave (@pxref{Octave setup})
@item REDUCE (@pxref{REDUCE setup})
@end itemize
The General purpose tools are (these will all be available with a
standard Linux distribution):
@vtable @code
@item sh
Bourne shell
@item gmake
Gnu make
@item gawk
Gnu awk
@item sed
Gnu sed
@item grep
Gnu grep
@item comm
Gnu Compare sorted files by line
@item xfig
Figure editor, version 3 or greater.
@item fig2dev
Fig file conversion, version 3 or greater.
@item ghostview
postscript viewer
@item xdvi
dvi viewer
@item dvips
dvi to postscript conversion
@item latex
the text processor (LaTeX2e needed)
@item latex2html
converts latex to html
@item perl
needed for latex2html
@item gnuplot
a graph plotting program
@item gnuscape
or other web/html browser such as netscape, Red Baron etc.
@item gcc
GNU c compiler
@end vtable
@ifhtml
<A HREF="http://home.pages.de/~GNU/">GNU</A> documentation.
@end ifhtml
@node REDUCE setup, Octave setup, Software components, Administration
@comment node-name, next, previous, up
@section REDUCE setup
@cindex REDUCE setup
Symbolic algebra is performed by REDUCE, which although not free
software is the the result of international collaboration. The version I
use is obtained from:
@quotation
ZIB ( http://www.zib.de )
@end quotation
@ifhtml
<A HREF="http://www.rrz.uni-koeln.de/REDUCE/">REDUCE</A> documentation.
<A HREF="http://www.zib.de">ZIB</A> documentation.
@end ifhtml
@node Octave setup, Paths, REDUCE setup, Administration
@comment node-name, next, previous, up
@section Octave setup
@cindex Octave setup
Octave is available at various web sites including:
@uref{http://www.octave.org}
@menu
* .octaverc::
* .oct file dependencies::
@end menu
@node .octaverc, .oct file dependencies, Octave setup, Octave setup
@comment node-name, next, previous, up
@subsection .octaverc
@vindex .octaverc
The @file{.octaverc} file should contain the following lines:
@example
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Startup file for Octave for use with MTT
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
implicit_str_to_num_ok = 1;
empty_list_elements_ok = 1;
@end example
@node .oct file dependencies, , .octaverc, Octave setup
@comment node-name, next, previous, up Additionally, it is necessary to
@subsection .oct file dependencies
Successful compilation of .oct code requires that Octave has been
configured to use dynamically linked libraries and that the Octave
libraries @code{liboctave}, @code{libcruft} and @code{liboctinterp}
are available on the system.
This can be acheived by compiling Octave from the source code, configured
with the options @code{--enable-shared} and @code{--enable-dl}.
A number of additional libraries and headers are also required to be
installed on a system. These include,
@itemize @bullet
@item
@emph{ncurses} and @emph{readline}
terminal control routines
@item
@emph{blas} or @emph{altas}
basic linear algebra subprograms, usually optimised for the specific processor
@item
@emph{fftw}
fast Fourier transform routines
@item
@emph{g2c}
GNU Fortran to C conversion routines
@item
@emph{kpathsea}
TeX path search routines
@end itemize
Note that on many GNU/Linux distributions, the necessary headers are
contained in development packages which must be installed in addition
to the standard library package.
Further information on configuring and installing Octave to handle dynamic
libraries (DLDs) can be found in the
@uref{http://www.octave.org/docs.html,Octave documentation}.
@node Paths, File structure, Octave setup, Administration
@comment node-name, next, previous, up
@section Paths
@cindex paths
@cindex mttrc
There are a number of paths that must be set correctely for @strong{MTT}
to work. These are normally set up by sourcing the file @code{mttrc} that
lives in the @strong{MTT} home directory.
@menu
* $MTTPATH::
* $MTT_COMPONENTS::
* $MTT_CRS::
* $MTT_EXAMPLES::
* $OCTAVE_PATH::
@end menu
@node $MTTPATH, $MTT_COMPONENTS, Paths, Paths
@comment node-name, next, previous, up
@subsection $MTTPATH
@vindex $MTTPATH
The environment variable $MTTPATH points to the mtt home directory.
This is usually @code{/usr/local/lib/mtt}.
@node $MTT_COMPONENTS, $MTT_CRS, $MTTPATH, Paths
@comment node-name, next, previous, up
@subsection $MTT_COMPONENTS
@vindex $MTT_COMPONENTS
The environment variable $MTT_COMPONENTS is a colon-separated path
pointing to directories containing components and subsystems.
By default
@example
MTT_COMPONENTS=.:$MTT_LIB/lib/comp/
@end example
but you may wish to add your own component libraries:
@example
MTT_COMPONENTS=my_library_path:$MTT_COMPONENTS
@end example
@node $MTT_CRS, $MTT_EXAMPLES, $MTT_COMPONENTS, Paths
@comment node-name, next, previous, up
@subsection $MTT_CRS
@vindex $MTT_CRS
The environment variable $MTT_CRS is a colon-separated path
pointing to directories containing constitutive relationships.
By default
@example
MTT_CRS=$MTTPATH/lib/cr
@end example
but you may wish to add your own component libraries:
@example
MTT_CRS=my_cr_path:$MTT_CRS
@end example
@node $MTT_EXAMPLES, $OCTAVE_PATH, $MTT_CRS, Paths
@comment node-name, next, previous, up
@subsection $MTT_EXAMPLES
@vindex $MTT_EXAMPLES
The environment variable $MTT_EXAMPLES is a colon-separated path
pointing to directories containing EXAMPLES and subsystems.
By default
@example
MTT_EXAMPLES=$MTTPATH/lib/examples
@end example
but you may wish to add your own component libraries:
@example
MTT_EXAMPLES=my_examples_path:$MTT_EXAMPLES
@end example
@node $OCTAVE_PATH, , $MTT_EXAMPLES, Paths
@comment node-name, next, previous, up
@subsection $OCTAVE_PATH
@vindex $OCTAVE_PATH
The @code{$OCTAVE_PATH} path must include the relevant paths for mtt to
work properly. In particular, it must include:
@example
$MTTPATH/trans/m
$MTTPATH/lib/comp/simple
$MTTPATH/lib/comp/compound
@end example
@node File structure, , Paths, Administration
@comment node-name, next, previous, up
@section File structure
@cindex File structure
The recommended installation of @strong{MTT} uses the following
directory structure with corresponding contents. Normally, each of the
listed directories is a subdirectory of @file{/usr/local}. The directory
@code{mtt} is pointed to by $MTTPATH (@pxref{$MTTPATH}).
@vtable @file
@item mtt/bin
This is the home directory for @strong{MTT}. @strong{MTT} itself lives
here along with @file{mttrc}.
@item mtt/bin/trans
The transformations executed by @strong{MTT}.
@item mtt/bin/trans/m
The @code{m-files} associated with the transformations.
@item mtt/bin/trans/awk
The @code{awk} scripts associated with the transformations.
@item mtt/lib
The place for components, examples and CRs which will be updated.
@item mtt/lib/comp/simple
@cindex simple components
The @code{m-files} defining the simple components.
@cindex compound components
@item mtt/lib/comp/compound
The @code{m-files} defining the compound components.
@item mtt/lib/cr/r
constitutive relationship definitions
@item mtt/lib/examples
Some examples.
@item mtt/examples/metamodelling
Examples from the book.
@item mtt/doc
The documentation files for @strong{MTT}.
@item mtt/doc/Examples
Examples used in the documentation.
@end vtable
@node Glossary, Index, Administration, Top
@comment node-name, next, previous, up
@unnumbered Glossary
@printindex fn
@node Index, , Glossary, Top
@comment node-name, next, previous, up
@unnumbered Index
@printindex cp
@contents
@bye
|
Added mttroot/mtt/lib/rep/ident_rep.make version [042982e678].
> > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 |
# -*-makefile-*-
# Makefile for representation ident
# File ident_rep.make
#Copyright (C) 2000,2001,2002 by Peter J. Gawthrop
## Model targets
model_reps = ${SYS}_sympar.m ${SYS}_simpar.m ${SYS}_state.m
model_reps += ${SYS}_numpar.m ${SYS}_input.m ${SYS}_ode2odes.m
model_reps += ${SYS}_def.m
## Prepend s to get the sensitivity targets
sensitivity_reps = ${model_reps:%=s%}
## Simulation targets
sims = ${SYS}_sim.m s${SYS}_ssim.m
## m-files needed for ident
ident_m = ${SYS}_ident.m ${SYS}_ident_numpar.m
## Targets for the ident simulation
ident_reps = ${ident_m} ${sims} ${model_reps} ${sensitivity_reps}
## ps output files
psfiles = ${SYS}_ident.ps ${SYS}_ident.basis.ps ${SYS}_ident.par.ps ${SYS}_ident.U.ps
figfiles = ${psfiles:%.ps=%.fig}
all: ${SYS}_ident.${LANG}
echo:
echo "sims: ${sims}"
echo "model_reps: ${model_reps}"
echo "sensitivity_reps: ${sensitivity_reps}"
echo "ident_reps: ${ident_reps}"
${SYS}_ident.view: ${SYS}_ident.ps
ident_rep.sh ${SYS} view
${psfiles}: ${SYS}_ident.fig
ident_rep.sh ${SYS} ps
${SYS}_ident.gdat: ${SYS}_ident.dat2
ident_rep.sh ${SYS} gdat
${SYS}_ident.fig ${SYS}_ident.dat2: ${ident_reps}
ident_rep.sh ${SYS} dat2
${SYS}_ident.m:
ident_rep.sh ${SYS} m
${SYS}_ident_numpar.m:
ident_rep.sh ${SYS} numpar.m
## System model reps
## Generic txt files
${SYS}_%.txt:
mtt ${OPTS} -q -stdin ${SYS} $* txt
## Specific m files
${SYS}_ode2odes.m: ${SYS}_rdae.r
mtt -q -stdin ${OPTS} ${SYS} ode2odes m
${SYS}_sim.m: ${SYS}_ode2odes.m
mtt ${OPTS} -q -stdin ${SYS} sim m
## Generic txt to m
${SYS}_%.m: ${SYS}_%.txt
mtt ${OPTS} -q -stdin ${SYS} $* m
## r files
${SYS}_def.r: ${SYS}_abg.fig
mtt ${OPTS} -q -stdin ${SYS} def r
${SYS}_rdae.r:
mtt ${OPTS} -q -stdin ${SYS} rdae r
## Sensitivity model reps
## Generic txt files
s${SYS}_%.txt:
mtt ${OPTS} -q -stdin -s s${SYS} $* txt
## Specific m files
s${SYS}_ode2odes.m: s${SYS}_rdae.r
mtt -q -stdin ${OPTS} -s s${SYS} ode2odes m
s${SYS}_ssim.m:
mtt -q -stdin ${OPTS} -s s${SYS} ssim m
s${SYS}_def.m:
mtt -q -stdin ${OPTS} -s s${SYS} def m
## Generic txt to m
s${SYS}_%.m: s${SYS}_%.txt
mtt ${OPTS} -q -stdin s${SYS} $* m
## r files
s${SYS}_rdae.r:
mtt ${OPTS} -q -stdin -s s${SYS} rdae r
|
Added mttroot/mtt/lib/rep/ident_rep.sh version [509586cb1e].
> > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 |
#! /bin/sh
## ident_rep.sh
## DIY representation "ident" for mtt
# Copyright (C) 2002 by Peter J. Gawthrop
sys=$1
rep=ident
lang=$2
mtt_parameters=$3
rep_parameters=$4
## Some names
target=${sys}_${rep}.${lang}
def_file=${sys}_def.r
dat2_file=${sys}_ident.dat2
dat2s_file=${sys}_idents.dat2
ident_numpar_file=${sys}_ident_numpar.m
option_file=${sys}_ident_mtt_options.txt
## Get system information
if [ -f "${def_file}" ]; then
echo Using ${def_file}
else
mtt -q ${sys} def r
fi
ny=`mtt_getsize $1 y`
nu=`mtt_getsize $1 u`
check_new_options() {
if [ -f "${option_file}" ]; then
old_options=`cat ${option_file}`
if [ "${mtt_options}" != "${old_options}" ]; then
echo ${mtt_options} > ${option_file}
fi
else
echo ${mtt_options} > ${option_file}
fi
}
## Make the _ident.m file
make_ident() {
filename=${sys}_${rep}.m
echo Creating ${filename}
cat > ${filename} <<EOF
function [y,u,t] = ${sys}_ident (last, ppp_names, par_names, A_u, A_w, w, Q, extras)
## usage: [y,u,t] = ${sys}_ident (last, ppp_names, par_names, A_u, A_w, w, Q, extras)
##
## last last time in run
## ppp_names Column vector of names of ppp params
## par_names Column vector of names of estimated params
## extras Structure containing additional info
##Sanity check
if nargin<2
printf("Usage: [y,u,t] = ${sys}_ident(N, ppp_names[, par_names, extras])\n");
return
endif
if nargin<4
## Set up optional parameters
extras.criterion = 1e-3;
extras.emulate_timing = 0;
extras.max_iterations = 15;
extras.simulate = 1;
extras.v = 1e-6;
extras.verbose = 0;
extras.visual = 1;
endif
## System info
[n_x,n_y,n_u,n_z,n_yz] = ${sys}_def;
sympar = ${sys}_sympar;
simpar = ${sys}_simpar;
sympars = s${sys}_sympar;
simpars = s${sys}_simpar;
t_ol = simpar.last;
## Number of intervals needed
N = ceil(last/t_ol);
## Setpoints
if extras.verbose
printf("Open-loop interval %3.2f \n", simpar.last);
printf(" -- using info in ${sys}_simpar.txt\n");
printf("PPP optimisation from %3.2f to %3.2f\n", simpars.first, simpars.last);
printf(" -- using info in s${sys}_simpar.txt\n");
endif
t_horizon = [simpars.first+simpars.dt:simpars.dt:simpars.last]';
w_s = ones(length(t_horizon)-1,1)*w';
## Setup the indices of the adjustable stuff
if nargin<2
i_ppp = []
else
i_ppp = ppp_indices (ppp_names,sympar,sympars); # Parameters
endif
n_ppp = length(i_ppp(:,1));
if nargin<3
i_par = []
else
i_par = ppp_indices (par_names,sympar,sympars); # Parameters
endif
## Do some simulations to check things out
## System itself
par = ${sys}_numpar;
x_0_ol = ${sys}_state(par);
[y_ol,x_ol, t_ol] = ${sys}_sim(x_0_ol, par, simpar, ones(1,n_u));
simpar_OL = simpar;
simpar_OL.last = simpars.last;
[y_OL,x_OL, t_OL] = ${sys}_sim(x_0_ol, par, simpar_OL, ones(1,n_u));
pars = s${sys}_numpar;
x_0_ppp = s${sys}_state(pars);
[y_ppp,y_par,x_ppp, t_ppp] = s${sys}_ssim(x_0_ppp, pars, simpars, ones(1,n_u));
simpar_PPP = simpars;
simpar_PPP.first = simpar.first;
[y_PPP,y_par,x_PPP, t_PPP] = s${sys}_ssim(x_0_ppp, pars, simpar_PPP, ones(1,n_u));
## Basis functions
Us = ppp_ustar(A_u,1,t_OL',0,0)';
if extras.visual #Show some graphs
figure(2);
grid; title("Outputs of ${sys}_sim and s${sys}_ssim");
plot(t_ol,y_ol, '*', t_ppp, y_ppp, '+', t_OL, y_OL, t_PPP, y_PPP);
figure(3);
grid; title("Basis functions");
plot(t_OL, Us);
endif
## Do it
[y,u,t,P,U,t_open,t_ppp,t_est,its_ppp,its_est] \
= ppp_nlin_run ("${sys}",i_ppp,i_par,A_u,w_s,N,Q,extras);
## Compute values at ends of ol intervals
T_open = cumsum(t_open);
T_open = T_open(1:length(T_open)-1); # Last point not in t
j=[];
for i = 1:length(T_open)
j = [j; find(T_open(i)*ones(size(t))==t)];
endfor
y_open = y(j,:);
u_open = u(j,:);
## Plots
gset nokey
gset nogrid
#eval(sprintf("gset xtics %g", simpar.last));
#gset noytics
gset format x "%.1f"
gset format y "%.2f"
gset term fig monochrome portrait fontsize 20 size 20 20 metric \
thickness 4
gset output "${sys}_ident.fig"
title("");
xlabel("Time (s)");
ylabel("u");
subplot(2,1,2); plot(t,u,'-', T_open, u_open,"+");
#subplot(2,1,2); plot(t,u);
ylabel("y");
subplot(2,1,1); plot(t,y,'-', T_open, y_open,"+");
#subplot(2,1,1); plot(t,y);
oneplot;
gset term fig monochrome portrait fontsize 20 size 20 10 metric \
thickness 4
gset output "${sys}_ident.basis.fig"
title("");
xlabel("Time (s)");
ylabel("Basis functions");
plot(t_OL, Us);
## Create plot against time
TTT = [ [0;T_open] [T_open; last] ]';
TT = TTT(:);
[n,m] = size(P);
if m>0
P = P(1:n-1,:); # Loose last point
PP = [];
for j=1:m
pp = [P(:,j) P(:,j)]';
PP = [PP pp(:)];
endfor
oneplot;
gset output "${sys}_ident.par.fig"
title("");
xlabel("Time (s)");
ylabel("Parameters");
plot(TT,PP);
endif
[n,m] = size(U);
if m>0 oneplot;
gset output "${sys}_ident.U.fig"
title("");
xlabel("Time (s)");
ylabel("U");
[n,m] = size(U);
U = U(1:n-1,:); # Loose last point
UU = [];
for j=1:m
uu = [U(:,j) U(:,j)]';
UU = [UU uu(:)];
endfor
plot(TT,UU);
endif
endfunction
EOF
}
make_ident_numpar() {
echo Creating ${ident_numpar_file}
cat > ${sys}_ident_numpar.m <<EOF
function [last, ppp_names, par_names, A_u, A_w, w, Q, extras] = ${sys}_ident_numpar
## usage: [last, ppp_names, par_names, A_u, A_w, w, Q, extras] = ${sys}_ident_numpar ()
##
##
## Last time of run
last = 10;
## Specify basis functions
A_w = zeros(1,1);
n_ppp = ${nu};
A_u = ppp_aug(A_w,laguerre_matrix(n_ppp-1,2.0));
## Names of ppp parameters
ppp_names = "";
for i=1:n_ppp
name = sprintf("ppp_%i", i);
ppp_names = [ppp_names; name];
endfor
## Estimated parameters
par_names = [];
## Weights
Q = ones(${ny},1);
## Setpoint
w = zeros(${ny},1); w(1) = 1;
## Set up optional parameters
extras.criterion = 1e-3;
extras.emulate_timing = 0;
extras.max_iterations = 15;
extras.simulate = 1;
extras.v = 1e-6;
extras.verbose = 0;
extras.visual = 0;
endfunction
EOF
}
make_dat2() {
## Inform user
echo Creating ${dat2_file}
## Use octave to generate the data
octave -q <<EOF
[last, ppp_names, par_names, A_u, A_w, w, Q, extras] = ${sys}_ident_numpar;
[y,u,t] = ${sys}_ident(last, ppp_names, par_names, A_u, A_w, w, Q, extras);
data = [t,y,u];
save -ascii ${dat2_file} data
EOF
}
case ${lang} in
numpar.m)
## Make the numpar stuff
make_ident_numpar;
;;
m)
## Make the code
make_ident;
;;
dat2|fig|basis.fig|par.fig|U.fig)
## The dat2 language (output data) & fig file
rm ${sys}_ident*.fig
make_dat2;
;;
gdat)
cp ${dat2_file} ${dat2s_file}
dat22dat ${sys} ${rep}
dat2gdat ${sys} ${rep}
;;
ps|basis.ps|par.ps|U.ps)
figs=`ls ${sys}_ident*.fig | sed -e 's/\.fig//'`
echo $figs
for fig in ${figs}; do
fig2dev -Leps ${fig}.fig > ${fig}.ps
done
;;
view)
pss=`ls ${sys}_ident*.ps`
echo Viewing ${pss}
for ps in ${pss}; do
gv ${ps}&
done
;;
*)
echo Language ${lang} not supported by ${rep} representation
exit 3
esac
|