## Makes the figures

par = ReactorTQ_numpar;		# Parameters
sym = ReactorTQ_sympar;		# Parameter indices

F_s= [90:10:500];		# Range of flows

Z = [];
for f_s=F_s
  par(sym.f_s) = f_s;
  z = sort(eig(ReactorTQ_sm(par)));
  Z = [Z z];
endfor


grid; xlabel("f_s"); ylabel("z");
plot(F_s,Z);
psfig("ReactorTQ_zero");

## Makes the schematic diagram and the zero figure
all: ReactorTQ_pic.ps ReactorTQ_zero.ps

ReactorTQ_pic.ps: ReactorTQ_pic.fig
	fig2dev -Lps ReactorTQ_pic.fig> ReactorTQ_pic.ps

ReactorTQ_zero.ps: ReactorTQ_abg.fig
	mtt -q ReactorTQ sm m; mtt -q ReactorTQ numpar m;
	mtt -q ReactorTQ sympar m;
	octave MakeFigure.m

#FIG 3.2
Portrait
Center
Inches
A4      
100.00
Single
-2
1200 2
2 1 0 2 0 0 0 0 -1 0.000 0 0 0 0 0 3
	 3001 8701 3001 7801 3151 7951
2 1 0 2 0 0 0 0 -1 0.000 0 0 0 0 0 3
	 1801 9001 2701 9001 2551 9151
2 1 0 2 -1 -1 0 0 -1 0.000 0 0 -1 0 0 2
	 2701 8776 2701 9226
2 1 0 2 0 0 0 0 -1 0.000 0 0 0 0 0 3
	 3301 9001 4201 9001 4051 9151
2 1 0 2 -1 -1 0 0 -1 0.000 0 0 -1 0 0 3
	 4201 9301 3601 9901 3826 9901
2 1 0 2 0 0 0 0 -1 0.000 0 0 0 0 0 3
	 5701 9001 4801 9001 4951 9151
2 1 0 2 0 0 0 0 -1 0.000 0 0 0 0 0 3
	 1800 6000 2700 6000 2550 6150
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 1
	 10350 5025
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 1800 6000 1800 5775
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 1800 6225 1800 6000
2 4 1 2 1 7 0 0 -1 4.000 0 0 7 0 0 5
	 11100 10200 600 10200 600 7500 11100 7500 11100 10200
2 4 1 2 1 7 0 0 -1 4.000 0 0 7 0 0 5
	 11100 6600 600 6600 600 5400 11100 5400 11100 6600
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4500 4800 4500 8700 4650 8550
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 6000 4800 4800 8700 5025 8625
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 9000 4800 5100 8700 5400 8700
2 1 0 2 -1 -1 0 0 -1 0.000 0 0 -1 0 0 2
	 4725 4800 4275 4800
2 1 0 2 -1 -1 0 0 -1 0.000 0 0 -1 0 0 2
	 4725 4200 4275 4200
2 1 0 2 -1 -1 0 0 -1 0.000 0 0 -1 0 0 2
	 6225 4800 5775 4800
2 1 0 2 -1 -1 0 0 -1 0.000 0 0 -1 0 0 2
	 6225 4200 5775 4200
2 1 0 2 -1 -1 0 0 -1 0.000 0 0 -1 0 0 2
	 9225 4800 8775 4800
2 1 0 2 -1 -1 0 0 -1 0.000 0 0 -1 0 0 2
	 9225 4200 8775 4200
2 1 0 2 0 0 0 0 -1 0.000 0 0 0 0 0 3
	 3000 7200 3000 6300 3150 6450
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 10500 4800 3300 6000 3525 6075
2 4 1 2 1 7 0 0 -1 4.000 0 0 7 0 0 5
	 11100 5100 600 5100 600 3300 11100 3300 11100 5100
2 1 0 2 0 0 0 0 -1 0.000 0 0 0 0 0 3
	 4485 2395 4485 4130 4633 3841
2 1 0 2 0 0 0 0 -1 0.000 0 0 0 0 0 3
	 2999 2395 2999 4130 3148 3841
2 1 0 2 0 0 0 0 -1 0.000 0 0 0 0 0 3
	 5970 2395 5970 4130 6119 3841
2 1 0 2 0 0 0 0 -1 0.000 0 0 0 0 0 3
	 10428 2397 10428 4132 10577 3843
2 1 0 2 0 0 0 0 -1 0.000 0 0 0 0 0 3
	 8943 2397 8943 4132 9091 3843
2 1 0 2 0 0 0 0 -1 0.000 0 0 0 0 0 3
	 1800 2100 2700 2100 2550 2250
2 1 0 2 0 0 0 0 -1 0.000 0 0 0 0 0 3
	 3300 2100 4200 2100 4050 2250
2 1 0 2 0 0 0 0 -1 0.000 0 0 0 0 0 3
	 4800 2100 5700 2100 5550 2250
2 1 0 2 -1 -1 0 0 -1 0.000 0 0 -1 0 0 3
	 4200 1800 3600 1200 3600 1425
2 1 0 2 -1 -1 0 0 -1 0.000 0 0 -1 0 0 2
	 2700 1875 2700 2325
2 1 0 2 -1 -1 0 0 -1 0.000 0 0 -1 0 0 3
	 8701 1801 8101 1201 8101 1426
2 1 0 2 0 0 0 0 -1 0.000 0 0 0 0 0 3
	 9301 2101 10201 2101 10051 2251
2 1 0 2 -1 -1 0 0 -1 0.000 0 0 -1 0 0 3
	 9301 1801 9901 1201 9901 1426
2 1 0 2 0 0 0 0 -1 0.000 0 0 0 0 0 3
	 6300 2100 7200 2100 7050 2250
2 1 0 2 0 0 0 0 -1 0.000 0 0 0 0 0 3
	 7800 2100 8700 2100 8550 2250
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 4050 1950 4350 1650
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 10050 1350 9900 1200
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 9900 1200 9750 1050
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 8550 1950 8850 1650
2 4 1 2 1 7 0 0 -1 4.000 0 0 7 0 0 5
	 11100 300 600 300 600 2700 11100 2700 11100 300
2 1 0 2 0 0 0 0 -1 0.000 0 0 0 0 0 3
	 3000 4800 3000 5700 3150 5550
2 1 0 2 0 0 0 0 -1 0.000 0 0 0 0 0 2
	 4800 8775 4800 9225
4 1 0 0 0 0 20 0.0000 4 210 1035 3075 4575 FMR:rfa\001
4 1 0 0 0 0 20 0.0000 4 210 1065 4575 4575 Rate:AD\001
4 1 0 0 0 0 20 0.0000 4 210 1050 6000 4575 Rate:AB\001
4 2 0 0 0 0 20 0.0000 4 285 780 1651 9076 SS:t_0\001
4 2 0 0 0 0 20 0.0000 4 285 690 3451 9976 C:h_r\001
4 1 0 0 0 0 20 0.0000 4 210 150 3000 6075 1\001
4 2 0 0 0 0 20 0.0000 4 210 480 1725 6075 SS:f\001
4 1 0 0 0 0 20 0.0000 4 210 150 3001 9076 1\001
4 1 0 0 0 0 20 0.0000 4 210 150 4501 9076 0\001
4 1 0 0 0 0 20 0.0000 4 210 1005 9001 4576 Rate:BC\001
4 1 0 0 0 0 20 0.0000 4 210 1050 10576 4576 FMR:rfb\001
4 1 1 1 0 3 20 0.0000 4 210 2625 9600 7800 THERMAL MODEL\001
4 1 1 1 0 3 20 0.0000 4 210 2940 9450 5700 HYDRAULIC MODEL\001
4 1 0 0 0 0 20 0.0000 4 210 900 3000 7575 FMR:rt\001
4 1 1 1 0 3 20 0.0000 4 210 2700 9675 3750 REACTION MODEL\001
4 2 0 0 0 0 20 0.0000 4 285 825 1650 2175 SS:c_0\001
4 1 0 0 0 0 20 0.0000 4 210 150 3000 2175 1\001
4 1 0 0 0 0 20 0.0000 4 210 150 4500 2175 0\001
4 1 0 0 0 0 20 0.0000 4 210 150 6000 2175 1\001
4 1 0 0 0 0 20 0.0000 4 210 150 9001 2176 0\001
4 1 0 0 0 0 20 0.0000 4 210 150 10501 2176 1\001
4 1 0 0 0 0 20 0.0000 4 210 420 7500 2175 AF\001
4 1 0 0 0 0 20 0.0000 4 285 795 8100 1050 C:m_b\001
4 1 0 0 0 0 20 0.0000 4 285 825 9975 1050 SS:c_b\001
4 1 0 0 0 0 20 0.0000 4 285 780 3600 1050 C:m_a\001
4 1 1 0 0 3 20 0.0000 4 210 3735 9075 600 CONCENTRATION MODEL\001
4 1 0 0 0 0 20 0.0000 4 210 480 6151 9076 SS:t\001

% -*-latex-*- Put EMACS into LaTeX-mode
% Verbal description for system ReactorTQ (ReactorTQ_desc.tex)
% Generated by MTT on Fri Mar 3 12:43:33 GMT 2000.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\fig{ReactorTQ_pic}
{ReactorTQ_pic} {0.9} {System \textbf{ReactorTQ}, Schematic}

Figure \Ref{fig:ReactorTQ_pic} is the schematic diagram of a chemical
reactor.

The acausal bond graph of system \textbf{ReactorTQ} is displayed in
Figure \Ref{fig:ReactorTQ_abg.ps} and its label file is listed in
Section \Ref{sec:ReactorTQ_lbl}.  The subsystems are listed in Section
\Ref{sec:ReactorTQ_sub}.

This example of a (nonlinear) chemical reactor is due to Trickett and
Bogle\footnote{ K. J. Tricket, \emph{Quantification of Inverse
    Responses for Controllability Assessment of Nonlinear Processes},
  PhD Thesis, University College London, 1994} is used in this
section.  The reactor has two reaction mechanisms: $\text{A}
\rightarrow \text{B} \rightarrow \text{C}$ and $\text{2A} \rightarrow
\text{D}$.  The reactor mass inflow and outflow $f_r$ are identical.
$q$ represents the heat inflow to the reactor.

The control loop $t$/$q$ has been inverted. The resulting SISO
system has two interpretations:
\begin{enumerate}
\item the \emph{dynamics} of the $c_b$/$f$ loop when the $t$/$q$ loop
  is under perfect control and
\item the \emph{inverse} dynamics of the  $t$/$q$ loop.
\end{enumerate}

\fig{ReactorTQ_zero} {ReactorTQ_zero} {0.9}
{System\textbf{ReactorTQ}: zeros v flow} 

Figure \Ref{fig:ReactorTQ_zero}
shows the poles of the linearised system as the steady-state flow
varies: these are the \emph{zeros} of the $c_b$/$f$ control-loop when
the $t$/$q$ loop is \emph{open}.

# -*-octave-*- Put Emacs into octave-mode
# Input specification (ReactorTQ_input.txt)
# Generated by MTT at Fri Mar  3 11:52:23 GMT 2000
###############################################################
## Version control history
###############################################################
## $Id$
## $Log$
###############################################################

## Reduce steady-state parameter file (ReactorTQ_sspar.r)
## as siso_sspar ecxept that inputs/states have different meaning
## Steady state for constant c_a, c_b and t=t_s and f=f_s

## Unit volume ReactorTQ:
v_r = 1;


## The exponentials.
e_1 = exp(-q_1/t_s);
e_2 = exp(-q_2/t_s);
e_3 = exp(-q_3/t_s);

## Solve for the steady-state concentrations
## Solve for ca - a quadratic.
a 	= k_3*e_3;	#ca^2 
b 	= k_1*e_1 + f_s;	#ca^1 
c 	= -c_0*f_s;

c_a	= (-b + sqrt(b^2 - 4*a*c))/(2*a);

## solve for c_b
c_b 	= c_a*k_1*e_1/(f_s+k_2*e_2);


#States (masses)
x1 = c_a*v_r;
x2 = c_b*v_r;

#Thermal state
x3 = c_p*t_s*v_r;

# Set the inputs
mttu(1) = f_s + 0.1*f_s*(t>0.01); # f (ReactorTQ)

%% Label file for system ReactorTQ (ReactorTQ_lbl.txt)
%SUMMARY ReactorTQ: Simple reactor model - with TQ loop inverted
%DESCRIPTION Pseudo bond graph reactor model (based on ancient version)

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%ALIAS Rate Chemical/Rate

% Extra variables
%VAR t_s
%VAR f_s
%VAR t_0
%VAR c_0
%VAR rho
%VAR v_r
%VAR e_1
%VAR e_2
%VAR e_3
%VAR a
%VAR b
%VAR c
%VAR c_A
%VAR c_B
%VAR x1
%VAR x2
%VAR x3
%VAR q_S


% Port aliases

% Argument aliases

%% 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
	m_a	lin		effort,1
	m_b	lin		effort,1
	h_r	lin		effort,c_p

% Component type FMR
	rfa	lin		effort,1		
	rfb	lin		effort,1		
	rt	lin		effort,c_p

% Component type Rate
        AB	Rate	k_1,q_1,h_1,1
	BC	Rate	k_2,q_2,h_2,1
	AD	Rate	k_3,q_3,h_3,2

% Component type SS
	c_0	SS		c_0,internal
	c_b	SS		external,0
	f	SS		internal,external
	t	SS		t_s,internal
	t_0	SS		t_0,internal

function mttpar = ReactorTQ_numpar();
% mttpar = ReactorTQ_numpar();
%System ReactorTQ, representation numpar, language m;
%File ReactorTQ_numpar.m;
%Generated by MTT on Thu Aug 24 14:29:20 BST 2000;
%

#====== Set up the global variables ======#
global ...
     a ...
     b ...
     c ...
     c_0 ...
     c_a ...
     c_b ...
     c_p ...
     e_1 ...
     e_2 ...
     e_3 ...
     f_s ...
     h ...
     h_1 ...
     h_2 ...
     h_3 ...
     k ...
     k_1 ...
     k_2 ...
     k_3 ...
     n ...
     q ...
     q_1 ...
     q_2 ...
     q_3 ...
     q_s ...
     rho ...
     t_0 ...
     t_s ...
     v_r ...
     x1 ...
     x2 ...
     x3 ;
## Set parameters to zero
 a = 0.0;
 b = 0.0;
 c = 0.0;
 c_0 = 0.0;
 c_a = 0.0;
 c_b = 0.0;
 c_p = 0.0;
 e_1 = 0.0;
 e_2 = 0.0;
 e_3 = 0.0;
 f_s = 0.0;
 h = 0.0;
 h_1 = 0.0;
 h_2 = 0.0;
 h_3 = 0.0;
 k = 0.0;
 k_1 = 0.0;
 k_2 = 0.0;
 k_3 = 0.0;
 n = 0.0;
 q = 0.0;
 q_1 = 0.0;
 q_2 = 0.0;
 q_3 = 0.0;
 q_s = 0.0;
 rho = 0.0;
 t_0 = 0.0;
 t_s = 0.0;
 v_r = 0.0;
 x1 = 0.0;
 x2 = 0.0;
 x3 = 0.0;
 %  -*-octave-*- Put Emacs into octave-mode
 %  Numerical parameter file (ReactorTQ_numpar.txt)
 %  Generated by MTT at Fri Mar  3 09:22:56 GMT 2000

 %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %  %% Version control history
 %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %  %% $Id$
 %  %% $Log$
 %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

 % 
a =  0;				 %  Dummy
b =  0;				 %  Dummy
c =  0;				 %  Dummy
c_0 =  0;			 %  Dummy
c_a =  0;			 %  Dummy
c_b =  0;			 %  Dummy
c_p =  0;			 %  Dummy
e_1 =  0;			 %  Dummy
e_2 =  0;			 %  Dummy
e_3 =  0;			 %  Dummy
f_s =  0;			 %  Dummy
h =  0;				 %  Dummy
h_1 =  0;			 %  Dummy
h_2 =  0;			 %  Dummy
h_3 =  0;			 %  Dummy
k =  0;				 %  Dummy
k_1 =  0;			 %  Dummy
k_2 =  0;			 %  Dummy
k_3 =  0;			 %  Dummy
n =  0;				 %  Dummy
q =  0;				 %  Dummy
q_1 =  0;			 %  Dummy
q_2 =  0;			 %  Dummy
q_3 =  0;			 %  Dummy
q_s =  0;			 %  Dummy
rho =  0;			 %  Dummy
t_0 =  0;			 %  Dummy
t_s =  0;			 %  Dummy
v_r =  0;			 %  Dummy
x1 =  0;				 %  Dummy
x2 =  0;				 %  Dummy
x3 =  0;				 %  Dummy

 % 
rho =  900;			 %  Density
c_p =  5.0;			 %  Specific heat

 % 
k_1 =  2.5e10;			 %  Reaction rate constant
q_1 =  1e4;			 %  Exotherm constant
h_1 =  1e4;			 %  Heat of reaction

 % 
k_2 =  2.65e12;			 %  Reaction rate constant
q_2 =  1.2e4;			 %  Exotherm constant
h_2 =  1.2e4;			 %  Heat of reaction

 % 
k_3 =  6e7;			 %  Reaction rate constant
q_3 =  8e3;			 %  Exotherm constant
h_3 =  3e4;			 %  Heat of reaction

 % 
c_0 =  10;			 %  Inflow conc
t_0 =  530;			 %  Inflow temp

 % 
t_s =  530;			 %  Steady-state temp
f_s =  100;			 %  Steady-state flow








## Set up the parameter vector
  mttpar(1) 	= a;
  mttpar(2) 	= b;
  mttpar(3) 	= c;
  mttpar(4) 	= c_0;
  mttpar(5) 	= c_a;
  mttpar(6) 	= c_b;
  mttpar(7) 	= c_p;
  mttpar(8) 	= e_1;
  mttpar(9) 	= e_2;
  mttpar(10) 	= e_3;
  mttpar(11) 	= f_s;
  mttpar(12) 	= h;
  mttpar(13) 	= h_1;
  mttpar(14) 	= h_2;
  mttpar(15) 	= h_3;
  mttpar(16) 	= k;
  mttpar(17) 	= k_1;
  mttpar(18) 	= k_2;
  mttpar(19) 	= k_3;
  mttpar(20) 	= n;
  mttpar(21) 	= q;
  mttpar(22) 	= q_1;
  mttpar(23) 	= q_2;
  mttpar(24) 	= q_3;
  mttpar(25) 	= q_s;
  mttpar(26) 	= rho;
  mttpar(27) 	= t_0;
  mttpar(28) 	= t_s;
  mttpar(29) 	= v_r;
  mttpar(30) 	= x1;
  mttpar(31) 	= x2;
  mttpar(32) 	= x3;

# -*-octave-*- Put Emacs into octave-mode
# Numerical parameter file (ReactorTQ_numpar.txt)
# Generated by MTT at Fri Mar  3 09:22:56 GMT 2000

# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% Version control history
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% $Id$
# %% $Log$
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

## Dummies
a = 0;				# Dummy
b = 0;				# Dummy
c = 0;				# Dummy
c_0 = 0;			# Dummy
c_a = 0;			# Dummy
c_b = 0;			# Dummy
c_p = 0;			# Dummy
e_1 = 0;			# Dummy
e_2 = 0;			# Dummy
e_3 = 0;			# Dummy
f_s = 0;			# Dummy
h = 0;				# Dummy
h_1 = 0;			# Dummy
h_2 = 0;			# Dummy
h_3 = 0;			# Dummy
k = 0;				# Dummy
k_1 = 0;			# Dummy
k_2 = 0;			# Dummy
k_3 = 0;			# Dummy
n = 0;				# Dummy
q = 0;				# Dummy
q_1 = 0;			# Dummy
q_2 = 0;			# Dummy
q_3 = 0;			# Dummy
q_s = 0;			# Dummy
rho = 0;			# Dummy
t_0 = 0;			# Dummy
t_s = 0;			# Dummy
v_r = 0;			# Dummy
x1 = 0;				# Dummy
x2 = 0;				# Dummy
x3 = 0;				# Dummy

## The bulk liquid
rho = 900;			# Density
c_p = 5.0;			# Specific heat

## Substance A
k_1 = 2.5e10;			# Reaction rate constant
q_1 = 1e4;			# Exotherm constant
h_1 = 1e4;			# Heat of reaction

## Substance B
k_2 = 2.65e12;			# Reaction rate constant
q_2 = 1.2e4;			# Exotherm constant
h_2 = 1.2e4;			# Heat of reaction

## Substance C
k_3 = 6e7;			# Reaction rate constant
q_3 = 8e3;			# Exotherm constant
h_3 = 3e4;			# Heat of reaction

## Inflow parameters
c_0 = 10;			# Inflow conc
t_0 = 530;			# Inflow temp

## Steady-state values
t_s = 530;			# Steady-state temp
f_s = 100;			# Steady-state flow

#FIG 3.2
Landscape
Center
Inches
Letter  
100.00
Single
-2
1200 2
6 2400 3150 3225 3375
2 1 0 1 -1 -1 0 0 -1 0.000 0 0 -1 1 0 2
	0 0 1.00 60.00 120.00
	 2625 3300 2925 3300
4 0 -1 0 0 2 20 0.0000 4 210 210 2400 3375 A\001
4 0 -1 0 0 2 20 0.0000 4 210 225 3000 3375 D\001
-6
2 1 0 2 -1 -1 0 0 -1 0.000 0 0 -1 0 0 3
	 2100 2100 2100 3900 1500 3900
2 1 0 2 -1 -1 0 0 -1 0.000 0 0 -1 0 0 2
	 1500 4050 3900 4050
2 1 0 2 -1 -1 0 0 -1 0.000 0 0 -1 1 0 2
	0 0 2.00 120.00 240.00
	 1500 4350 2100 4350
2 1 0 2 -1 -1 0 0 -1 0.000 0 0 -1 0 0 3
	 3600 2100 3600 3900 4200 3900
2 1 0 2 -1 -1 0 0 -1 0.000 0 0 -1 1 0 2
	0 0 2.00 120.00 240.00
	 3600 4350 4200 4350
2 1 0 2 -1 -1 0 0 -1 0.000 0 0 -1 0 0 2
	 3900 4050 4200 4050
2 1 1 2 -1 -1 0 0 -1 6.000 0 0 -1 0 0 2
	 2100 2400 3600 2400
2 1 0 1 -1 -1 0 0 -1 0.000 0 0 -1 1 0 2
	0 0 1.00 60.00 120.00
	 2400 2925 2700 2925
2 1 0 1 -1 -1 0 0 -1 0.000 0 0 -1 1 0 2
	0 0 1.00 60.00 120.00
	 3000 2925 3300 2925
2 1 0 2 -1 -1 0 0 -1 0.000 0 0 -1 1 0 2
	0 0 2.00 120.00 240.00
	 2850 4800 2850 3750
4 0 -1 0 0 2 20 0.0000 4 210 210 2175 3000 A\001
4 0 -1 0 0 2 20 0.0000 4 210 195 2775 3000 B\001
4 0 -1 0 0 2 20 0.0000 4 210 210 3375 3000 C\001
4 0 -1 0 0 2 20 0.0000 4 210 150 2250 3375 2\001
4 0 -1 0 0 3 12 0.0000 4 135 90 1875 4950 0\001
4 0 -1 0 0 3 12 0.0000 4 135 90 2250 4950 0\001
4 0 -1 0 0 3 20 0.0000 4 210 150 2775 5025 q\001
4 0 -1 0 0 3 20 0.0000 4 285 765 1500 4800 f , c  , t\001
4 0 -1 0 0 3 20 0.0000 4 285 765 3600 4800 f , c  , t\001
4 0 -1 0 0 3 12 0.0000 4 135 90 3975 4950 b\001
4 0 -1 0 0 3 12 0.0000 4 90 75 4350 4950 r\001

## -*-octave-*- Put Emacs into octave-mode
## Outline report file for system ReactorTQ (ReactorTQ_rep.txt)
## Generated by MTT on" Fri Mar  3 12:13:34 GMT 2000.

###############################################################
## Version control history
###############################################################
## $Id$
## $Log$
###############################################################

mtt ReactorTQ abg tex			# The system description
mtt ReactorTQ cbg ps 		        # The causal bond graph
## Uncomment the following lines or add others
mtt ReactorTQ struc tex	        # The system structure
## mtt ReactorTQ dae tex	        # The system dae
mtt ReactorTQ ode tex	        # The system ode 
## mtt ReactorTQ sspar tex		# Steady-state parameters
## mtt ReactorTQ ss tex 		# Steady state
## mtt ReactorTQ dm tex		# Descriptor matrices (of linearised system)
mtt ReactorTQ sm tex		# State matrices (of linearised system)
## mtt ReactorTQ tf tex		# Transfer function (of linearised system)
## mtt ReactorTQ lmfr ps		# log modulus of frequency response (of linearised system)
mtt ReactorTQ simpar tex		# Simulation parameters
mtt ReactorTQ numpar tex		# Numerical simulation parameters
mtt ReactorTQ input tex		# Simulation input
mtt ReactorTQ state tex		# Simulation initial state

mtt -c ReactorTQ odeso ps

%% Reduce comands to simplify output (mimo_sim.r)
m_r   := rho*v_r;
%mttx1 := c_a*v_r;
%mttx2 := c_b*v_r;

% THIS MUST BE CHANGED - probs with cp and FMRs
%c_p := 1;

%let mttx3/c_p = t;

let  e^(q_1/(mttx3/c_p)) = 1/epsilon_1;
let  e^(q_2/(mttx3/c_p)) = 1/epsilon_2;
let  e^(q_3/(mttx3/c_p)) = 1/epsilon_3;

let  e^(q_1/t_s) = 1/epsilon_1;
let  e^(q_2/t_s) = 1/epsilon_2;
let  e^(q_3/t_s) = 1/epsilon_3;

FACTOR mttx1,mttx2;

END;

# -*-octave-*- Put Emacs into octave-mode
# Simulation parameters for system ReactorTQ (ReactorTQ_simpar.txt)
# Generated by MTT on Fri Mar 3 12:11:48 GMT 2000.
###############################################################
## Version control history
###############################################################
## $Id$
## $Log$
###############################################################


LAST        = 0.05;       # Last time in simulation
DT          = 0.0002;        # Print interval
STEPFACTOR  = 1;          # Integration steps per print interval
WMIN        = -1;         # Minimum frequency = 10^WMIN
WMAX        = 2;          # Maximum frequency = 10^WMAX
WSTEPS      = 100;        # Number of frequency steps
INPUT       = 1;          # Index of the input

function [mtta,mttb,mttc,mttd] = ReactorTQ_sm(mttpar);
% [mtta,mttb,mttc,mttd] = ReactorTQ_sm(mttpar);
%System ReactorTQ, representation sm, language m;
%File ReactorTQ_sm.m;
%Generated by MTT on Thu Aug 24 14:47:46 BST 2000;
%
%====== Set up the global variables ======%
global ...
a ...
b ...
c ...
c_0 ...
c_a ...
c_b ...
c_p ...
e_1 ...
e_2 ...
e_3 ...
f_s ...
h ...
h_1 ...
h_2 ...
h_3 ...
k ...
k_1 ...
k_2 ...
k_3 ...
n ...
q ...
q_1 ...
q_2 ...
q_3 ...
q_s ...
rho ...
t_0 ...
t_s ...
v_r ...
x1 ...
x2 ...
x3 ;
a 	= mttpar(1);
b 	= mttpar(2);
c 	= mttpar(3);
c_0 	= mttpar(4);
c_a 	= mttpar(5);
c_b 	= mttpar(6);
c_p 	= mttpar(7);
e_1 	= mttpar(8);
e_2 	= mttpar(9);
e_3 	= mttpar(10);
f_s 	= mttpar(11);
h 	= mttpar(12);
h_1 	= mttpar(13);
h_2 	= mttpar(14);
h_3 	= mttpar(15);
k 	= mttpar(16);
k_1 	= mttpar(17);
k_2 	= mttpar(18);
k_3 	= mttpar(19);
n 	= mttpar(20);
q 	= mttpar(21);
q_1 	= mttpar(22);
q_2 	= mttpar(23);
q_3 	= mttpar(24);
q_s 	= mttpar(25);
rho 	= mttpar(26);
t_0 	= mttpar(27);
t_s 	= mttpar(28);
v_r 	= mttpar(29);
x1 	= mttpar(30);
x2 	= mttpar(31);
x3 	= mttpar(32);
%a matrix%
mtta = zeros(2,2);
mtt_t1 = exp((2.0*q_1+q_3)/t_s)*f_s^2+4.0*exp((2.0*q_1)/t_s)*c_0*f_s*k_3;
mtt_t1 = -sqrt((mtt_t1+2.0*exp((q_1+q_3)/t_s)*f_s*k_1+exp(q_3/t_s)*k_1^2)/exp(q_3/t_s));
mtta(1,1) = mtt_t1/abs(exp(q_1/t_s));
mtta(2,1) = k_1/exp(q_1/t_s);
mtta(2,2) = (-(exp(q_2/t_s)*f_s)-k_2)/exp(q_2/t_s);
%b matrix%
mttb = zeros(2,1);
mtt_t1 = exp((q_1+q_3)/t_s)*abs(exp(q_1/t_s))*f_s+2.0*exp(q_1/t_s)*abs(exp(q_1/t_s))*c_0*k_3;
mtt_t1 = mtt_t1+exp(q_3/t_s)*abs(exp(q_1/t_s))*k_1;
mtt_t3 = exp((q_1+q_3)/t_s);
mtt_t2 = exp((2.0*q_1+q_3)/t_s)*f_s^2+4.0*exp((2.0*q_1)/t_s)*c_0*f_s*k_3;
mtt_t1 = mtt_t1-(mtt_t3*sqrt((mtt_t2+2.0*exp((q_1+q_3)/t_s)*f_s*k_1+exp(q_3/t_s)*k_1^2)/exp(q_3/t_s)));
mttb(1) = mtt_t1/(2.0*exp(q_1/t_s)*abs(exp(q_1/t_s))*k_3);
mtt_t1 = exp((q_1+q_2+q_3)/t_s)*abs(exp(q_1/t_s))*f_s*k_1;
mtt_t3 = exp((q_1+q_2+q_3)/t_s);
mtt_t2 = exp((2.0*q_1+q_3)/t_s)*f_s^2+4.0*exp((2.0*q_1)/t_s)*c_0*f_s*k_3;
mtt_t3 = mtt_t3*sqrt((mtt_t2+2.0*exp((q_1+q_3)/t_s)*f_s*k_1+exp(q_3/t_s)*k_1^2)/exp(q_3/t_s));
mtt_t1 = mtt_t1+exp((q_2+q_3)/t_s)*abs(exp(q_1/t_s))*k_1^2-(mtt_t3*k_1);
mtt_t2 = 2.0*exp((2.0*q_1+q_2)/t_s)*abs(exp(q_1/t_s))*f_s*k_3;
mttb(2) = mtt_t1/(mtt_t2+2.0*exp((2.0*q_1)/t_s)*abs(exp(q_1/t_s))*k_2*k_3);
%c matrix%
mttc = zeros(1,2);
mttc(1,2) = 1.0;
%d matrix%
mttd = zeros(1,1);

%% Reduce steady-state parameter file (ReactorTQ_sspar.r)
%% as siso_sspar ecxept that inputs/states have different meaning
%% Steady state for constant c_a, c_b and t=t_s and f=f_s

%% Unit volume ReactorTQ:
v_r := 1;

%% Do the inputs first -- this avoids problems with reduce not
%% recognising that complicated expressions are zero

%% The exponentials.
e_1 := e^(-q_1/t_s);
e_2 := e^(-q_2/t_s);
e_3 := e^(-q_3/t_s);

%Steady-state input q needed to achieve steady-state t_s
q_s := -( 
        + (t_0-t_s)*f_s
        + e_1*h_1*k_1*x1
        + e_2*h_2*k_2*x2
        + e_3*h_3*k_3*x1^2
       );

%% The input at steady-state
MTTu1 := f_s;

%States (masses)
x1 := c_a*v_r;
x2 := c_b*v_r;

%Load up the vectors
MTTx1 := x1;
MTTx2 := x2;

MTTy1 := c_b;

%% Finally, solve for the steady-state concentrations
%% Solve for ca - a quadratic.
a 	:= k_3*e_3;	%ca^2 
b 	:= k_1*e_1 + f_s;	%ca^1 
c 	:= -c_0*f_s;

c_a	:= (-b + sqrt(b^2 - 4*a*c))/(2*a);

%% solve for c_b
c_b 	:= c_a*k_1*e_1/(f_s+k_2*e_2);


END;

# -*-octave-*- Put Emacs into octave-mode
# State specification (ReactorTQ_state.txt)
# Generated by MTT at Fri Mar  3 11:52:23 GMT 2000
###############################################################
## Version control history
###############################################################
## $Id$
## $Log$
###############################################################

## Reduce steady-state parameter file (ReactorTQ_sspar.r)
## as siso_sspar ecxept that states/states have different meaning
## Steady state for constant c_a, c_b and t=t_s and f=f_s

## Unit volume ReactorTQ:
v_r = 1;


## The exponentials.
e_1 = exp(-q_1/t_s);
e_2 = exp(-q_2/t_s);
e_3 = exp(-q_3/t_s);

## Solve for the steady-state concentrations
## Solve for ca - a quadratic.
a 	= k_3*e_3;	#ca^2 
b 	= k_1*e_1 + f_s;	#ca^1 
c 	= -c_0*f_s;

c_a	= (-b + sqrt(b^2 - 4*a*c))/(2*a);

## solve for c_b
c_b 	= c_a*k_1*e_1/(f_s+k_2*e_2);


#States (masses)
x1 = c_a*v_r;
x2 = c_b*v_r;


## The two inputs at steady-state
##mttu(1) = f_s;

## Load up the states
mttx(1) = x1;
mttx(2) = x2;

function sympar = ReactorTQ_sympar();
% sympar = ReactorTQ_sympar();
%System ReactorTQ, representation sympar, language m;
%File ReactorTQ_sympar.m;
%Generated by MTT on Thu Aug 24 14:47:48 BST 2000;
%
global ...
mtt_no_globals ;
  sympar.a 	= 1; # ReactorTQ
  sympar.b 	= 2; # ReactorTQ
  sympar.c 	= 3; # ReactorTQ
  sympar.c_0 	= 4; # ReactorTQ
  sympar.c_A 	= 5; # ReactorTQ
  sympar.c_B 	= 6; # ReactorTQ
  sympar.c_p 	= 7; # ReactorTQ
  sympar.e_1 	= 8; # ReactorTQ
  sympar.e_2 	= 9; # ReactorTQ
  sympar.e_3 	= 10; # ReactorTQ
  sympar.f_s 	= 11; # ReactorTQ
  sympar.h 	= 12; # Rate
  sympar.h_1 	= 13; # ReactorTQ
  sympar.h_2 	= 14; # ReactorTQ
  sympar.h_3 	= 15; # ReactorTQ
  sympar.k 	= 16; # Rate
  sympar.k_1 	= 17; # ReactorTQ
  sympar.k_2 	= 18; # ReactorTQ
  sympar.k_3 	= 19; # ReactorTQ
  sympar.n 	= 20; # Rate
  sympar.q 	= 21; # Rate
  sympar.q_1 	= 22; # ReactorTQ
  sympar.q_2 	= 23; # ReactorTQ
  sympar.q_3 	= 24; # ReactorTQ
  sympar.q_S 	= 25; # ReactorTQ
  sympar.rho 	= 26; # ReactorTQ
  sympar.t_0 	= 27; # ReactorTQ
  sympar.t_s 	= 28; # ReactorTQ
  sympar.v_r 	= 29; # ReactorTQ
  sympar.x1 	= 30; # ReactorTQ
  sympar.x2 	= 31; # ReactorTQ
  sympar.x3 	= 32; # ReactorTQ

#FIG 3.1
Portrait
Center
Metric
1200 2
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 1801 3151 2701 3151 2476 3376
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3601 3151 4501 3151 4276 3376
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4726 2926 4726 2026 4951 2251
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4951 3151 5851 3151 5626 3376
2 4 0 1 31 7 1 0 -1 0.000 0 0 7 0 0 5
	 6975 4050 6975 1350 450 1350 450 4050 6975 4050
4 1 -1 0 0 0 20 0.0000 4 195 375 3151 3241 AF\001
4 1 -1 0 0 0 20 0.0000 4 195 135 4726 3241 0\001
4 1 -1 0 0 0 20 0.0000 4 195 600 4726 1891 CX:c\001
4 1 -1 0 0 0 20 0.0000 4 240 810 1306 3241 SS:[in]\001
4 1 -1 0 0 0 20 0.0000 4 240 960 6346 3241 SS:[out]\001

% Verbal description for system INTFX (INTFX_desc.tex)
% Generated by MTT on Fri Aug 15 09:53:16 BST 1997.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.1  1997/08/24 11:20:18  peterg
% %% Initial revision
% %%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   The acausal bond graph of system \textbf{INTFX} is
   displayed in Figure \Ref{INTFX_abg} and its label
   file is listed in Section \Ref{sec:INTFX_lbl}.
   The subsystems are listed in Section \Ref{sec:INTFX_sub}.

\textbf{INTFX} is a two-port component where the effort on port [out]
   is the integral of the flow on port [in].

%SUMMARY INTFX
%DESCRIPTION <Detailed description here>
%% Label file for system INTFX (INTFX_lbl.txt)

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Each line should be of one of the following forms:
%	a comment (ie starting with %)
%	Component-name	CR_name	arg1,arg2,..argn
%	blank



% Component type CX
	c		lin	effort,1

% Component type SS
	[in]		SS	external,external
	[out]		SS	external,external

# Makefile for the Two link GMV example

all: msdp_tf.m twolinkp_obs.m twolinkp_sm.m TwoLinkGMV_numpar.m 

msdP_tf.m: msdP_abg.fig 
	mtt -q msdP tf m

msdp_tf.m: msdP_tf.m
	tr [A-Z] [a-z] <msdP_tf.m >msdp_tf.m

TwoLinkP_obs.m: TwoLinkP_abg.fig TwoLinkP_lbl.txt
	mtt -q TwoLinkP obs m

twolinkp_obs.m: TwoLinkP_obs.m
	tr [A-Z] [a-z] <TwoLinkP_obs.m >twolinkp_obs.m

TwoLinkP_sm.m: TwoLinkP_abg.fig TwoLinkP_lbl.txt
	mtt -q TwoLinkP sm m

twolinkp_sm.m: TwoLinkP_sm.m
	tr [A-Z] [a-z] <TwoLinkP_sm.m >twolinkp_sm.m

TwoLinkGMV_numpar.m: TwoLinkGMV_numpar.txt
	mtt -q TwoLinkGMV numpar m

#FIG 3.1
Portrait
Center
Metric
1200 2
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4728 4278 5403 4953 5178 4953
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5854 5404 6529 6079 6304 6079
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4728 6078 5403 5403 5403 5628
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5853 4953 6528 4278 6528 4503
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 1
	 4277 3827
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3152 2702 4277 3827 4052 3827
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 6977 6527 8102 7652 7877 7652
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3152 7652 4277 6527 4277 6752
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 6977 3827 8102 2702 8102 2927
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5852 5177 6527 5177 6392 5312
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2927 2927 2927 4952 3152 4727
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2927 5402 2927 7427 3152 7202
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2701 5176 2026 5176 2161 5311
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2926 1351 2926 2476 3196 2206
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2926 7876 2926 9001 3196 8731
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 8328 2928 8328 4953 8553 4728
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 8328 5403 8328 7428 8553 7203
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 8327 1352 8327 2477 8597 2207
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 8327 7877 8327 9002 8597 8732
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5626 1351 5626 4951 5851 4726
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5626 5401 5626 9001 5851 8776
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 1
	 6526 5401
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 6526 4951 6526 5401
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 8551 5176 9226 5176 9091 5311
2 1 0 1 5 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3826 4951 6526 4051 6436 4231
2 1 0 1 5 7 0 0 -1 0.000 0 0 -1 0 0 2
	 3826 4996 3826 5356
2 1 0 1 5 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4276 5176 3826 5176 3961 5311
2 1 0 1 5 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3826 5401 6301 6301 6121 6301
2 1 0 1 5 -1 0 0 -1 0.000 0 0 -1 0 0 3
	 3601 5401 4051 6301 3826 6301
2 1 0 1 5 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3601 4951 4051 4051 4051 4276
2 1 0 1 5 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5536 5176 5086 5176 5221 5311
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 6300 9675 6300 675 4950 675 4950 9675 6300 9675
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 9000 9675 9000 675 7650 675 7650 9675 9000 9675
2 4 0 1 31 7 1 0 -1 0.000 0 0 7 0 0 5
	 11025 10305 11025 225 225 225 225 10305 11025 10305
2 4 0 1 1 7 0 0 -1 0.000 0 0 7 0 0 5
	 3600 9675 2250 9675 2250 675 3600 675 3600 9675
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 10125 2250 990 2250 990 900 10125 900 10125 2250
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 10125 5850 990 5850 990 4500 10125 4500 10125 5850
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 10125 9450 990 9450 990 8100 10125 8100 10125 9450
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3375 4950 1800 3375 1800 3600
4 1 -1 0 0 0 20 0.0000 4 195 135 5628 5268 1\001
4 1 -1 0 0 0 20 0.0000 4 195 270 6933 5268 IX:J\001
4 1 -1 0 0 0 20 0.0000 4 195 135 2927 5312 1\001
4 1 -1 0 0 0 20 0.0000 4 195 135 2972 2792 0\001
4 1 -1 0 0 0 20 0.0000 4 195 135 2927 7742 0\001
4 1 -1 0 0 0 20 0.0000 4 195 135 8328 5313 1\001
4 1 -1 0 0 0 20 0.0000 4 195 135 8373 2793 0\001
4 1 -1 0 0 0 20 0.0000 4 195 135 8328 7743 0\001
4 1 -1 0 0 0 20 0.0000 4 255 660 9676 5266 I:m_y\001
4 1 -1 0 0 0 20 0.0000 4 255 660 1531 5221 I:m_x\001
4 1 -1 0 0 0 20 0.0000 4 195 1110 4636 4141 EMTF:c1\001
4 1 -1 0 0 0 20 0.0000 4 195 1110 4681 6391 EMTF:c2\001
4 1 -1 0 0 0 20 0.0000 4 195 1095 7156 4141 EMTF:s1\001
4 1 -1 0 0 0 20 0.0000 4 195 1095 7156 6391 EMTF:s2\001
4 1 5 0 0 0 20 0.0000 4 195 135 3603 5313 0\001
4 1 26 0 0 0 16 0.0000 4 210 345 6751 4456 [in]\001
4 1 26 0 0 0 16 0.0000 4 210 465 6751 3781 [out]\001
4 1 26 0 0 0 16 0.0000 4 210 345 6751 6076 [in]\001
4 1 26 0 0 0 16 0.0000 4 210 465 6751 6706 [out]\001
4 1 26 0 0 0 16 0.0000 4 210 585 6211 6526 [mod]\001
4 1 5 0 0 0 20 0.0000 4 195 960 4681 5266 INTFX:th\001
4 1 1 1 0 0 20 0.0000 4 195 210 2925 10035 X\001
4 1 1 1 0 32 20 0.0000 4 135 180 5580 9990 a\001
4 1 1 1 0 0 20 0.0000 4 195 210 8280 9990 Y\001
4 2 26 0 0 0 16 0.0000 4 210 585 3960 4140 [mod]\001
4 2 26 0 0 0 16 0.0000 4 210 585 6345 4095 [mod]\001
4 2 26 0 0 0 16 0.0000 4 210 585 3960 6210 [mod]\001
4 1 26 0 0 0 16 0.0000 4 210 345 4590 4455 [in]\001
4 1 26 0 0 0 16 0.0000 4 210 465 4545 3780 [out]\001
4 1 26 0 0 0 16 0.0000 4 210 465 4590 6660 [out]\001
4 0 26 0 0 0 16 0.0000 4 210 345 4365 6030 [in]\001
4 1 4 0 0 0 20 0.0000 4 255 990 2971 1216 SS:[x_a]\001
4 1 4 0 0 0 20 0.0000 4 255 990 2971 9361 SS:[x_b]\001
4 1 4 0 0 0 20 0.0000 4 255 990 8372 1217 SS:[y_a]\001
4 1 4 0 0 0 20 0.0000 4 255 990 8417 9362 SS:[y_b]\001
4 1 4 0 0 0 20 0.0000 4 255 1485 5671 1216 SS:[alpha_a]\001
4 1 4 0 0 0 20 0.0000 4 255 1485 5671 9361 SS:[alpha_b]\001
4 1 1 1 0 0 20 0.0000 4 255 600 1350 2700 Tip a\001
4 1 1 1 0 0 20 0.0000 4 195 1380 1260 6300 Mass centre\001
4 1 1 1 0 0 20 0.0000 4 255 600 1350 9855 Tip b\001
4 1 4 0 0 0 20 0.0000 4 255 1215 1756 3286 SS:[alpha]\001

% Verbal description for system RODaX (RODaX_desc.tex)
% Generated by MTT on Fri Aug 15 09:53:23 BST 1997.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.1  1998/04/12 15:25:35  peterg
% %% Initial revision
% %%
% Revision 1.1  1997/08/15  09:41:19  peterg
% Initial revision
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   The acausal bond graph of system \textbf{RODaX} is
   displayed in Figure \Ref{RODaX_abg} and its label
   file is listed in Section \Ref{sec:RODaX_lbl}.
   The subsystems are listed in Section \Ref{sec:RODaX_sub}.

{\bf RODaX} is essentially as described in Figure 10.2 of
``Metamodelling''. It has an additional port ``[angle]'' to provide
access to the rod angle.

%SUMMARY	RODaX: rigid rod in two dimensions - angle port.
%DESCRIPTION	Port [alpha_a]:	Angular torque/velocity - end a
%DESCRIPTION	Port [alpha_b]:	Angular torque/velocity - end b
%DESCRIPTION	Port [x_a]:	x force/velocity - end a
%DESCRIPTION	Port [x_b]:	x force/velocity - end b
%DESCRIPTION	Port [y_a]:	y force/velocity - end a
%DESCRIPTION	Port [y_b]:	y force/velocity - end b
%DESCRIPTION	Port [alpha]:	rod angle
%DESCRIPTION
%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"


%% Label file for system RODaX (RODaX_lbl.txt)




% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % $Id$
% % $Log$
% % Revision 1.1  1998/04/12 15:24:06  peterg
% % Initial revision
% %
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%% Each line should be of one of the following forms:
%	a comment (ie starting with %)
%	Component-name	CR_name	arg1,arg2,..argn
%	blank

%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



	

#FIG 3.1
Portrait
Center
Metric
1200 2
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 7875 8550 9225 8550 9000 8775
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 9225 8325 9225 8775
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 7875 9450 9225 9450 9000 9675
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 9225 9225 9225 9675
2 4 0 2 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 11025 10215 2475 10215 2475 7650 11025 7650 11025 10215
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 5625 8325 5625 8775
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 5625 9225 5625 9675
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 4
	 3825 5625 3825 8550 5625 8550 5400 8775
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 4
	 3375 6525 3375 9450 5625 9450 5400 9675
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 7875 5400 9225 5400 9000 5625
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 9225 5175 9225 5625
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 7875 6300 9225 6300 9000 6525
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 9225 6075 9225 6525
2 4 0 2 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 11025 7065 2475 7065 2475 4500 11025 4500 11025 7065
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4050 5400 5625 5400 5400 5625
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 5625 5175 5625 5625
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3600 6300 5625 6300 5400 6525
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 5625 6075 5625 6525
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2025 5400 3600 5400 3375 5625
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 3600 5175 3600 5625
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2025 6300 3150 6300 2925 6525
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 3150 6075 3150 6525
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 7875 2250 9225 2250 9000 2475
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 9225 2025 9225 2475
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 7875 3150 9225 3150 9000 3375
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 9225 2925 9225 3375
2 4 0 2 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 11025 3915 2475 3915 2475 1350 11025 1350 11025 3915
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4050 2250 5625 2250 5400 2475
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 5625 2025 5625 2475
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4050 3150 5625 3150 5400 3375
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 5625 2925 5625 3375
4 0 -1 0 0 22 20 0.0000 4 270 1935 9315 8640 SS:Theta_1_m\001
4 0 -1 0 0 22 20 0.0000 4 270 1935 9315 9540 SS:Theta_2_m\001
4 1 -1 0 0 22 20 0.0000 4 210 2445 6750 9090 TwoLinkPX:model\001
4 0 4 0 0 22 20 0.0000 4 270 1230 7920 8415 [Theta_1]\001
4 0 4 0 0 22 20 0.0000 4 270 1230 7920 9315 [Theta_2]\001
4 2 4 0 0 22 20 0.0000 4 270 1140 5535 8415 [Joint_1]\001
4 2 4 0 0 22 20 0.0000 4 270 1140 5535 9315 [Joint_2]\001
4 1 1 1 0 3 26 0.0000 4 270 1005 6750 10080 Model\001
4 1 -1 0 0 22 20 0.0000 4 270 2415 6750 5940 TwoLinkP:system\001
4 0 4 0 0 22 20 0.0000 4 270 1230 7920 5265 [Theta_1]\001
4 0 4 0 0 22 20 0.0000 4 270 1230 7920 6165 [Theta_2]\001
4 0 -1 0 0 22 20 0.0000 4 270 1530 9315 5490 SS:Theta_1\001
4 0 -1 0 0 22 20 0.0000 4 270 1530 9315 6390 SS:Theta_2\001
4 2 4 0 0 22 20 0.0000 4 270 1140 5535 5265 [Joint_1]\001
4 2 4 0 0 22 20 0.0000 4 270 1140 5535 6165 [Joint_2]\001
4 1 -1 0 0 22 20 0.0000 4 195 150 3825 5490 0\001
4 2 -1 0 0 22 20 0.0000 4 270 1275 1935 6390 SS:Tau_2\001
4 2 -1 0 0 22 20 0.0000 4 270 1275 1980 5490 SS:Tau_1\001
4 1 -1 0 0 22 20 0.0000 4 195 150 3375 6390 0\001
4 1 1 1 0 3 26 0.0000 4 360 1110 6705 6885 System\001
4 0 -1 0 0 22 20 0.0000 4 270 1785 9315 2340 SS:Theta_1_r\001
4 0 -1 0 0 22 20 0.0000 4 270 1785 9315 3240 SS:Theta_2_r\001
4 1 1 1 0 3 26 0.0000 4 360 2055 6705 3735 Specification\001
4 1 -1 0 0 22 20 0.0000 4 270 1860 6795 2340 msdP:spec_1\001
4 1 -1 0 0 22 20 0.0000 4 270 1860 6795 3195 msdP:spec_2\001
4 2 -1 0 0 22 20 0.0000 4 270 1260 4005 2340 SS:Ref_1\001
4 2 -1 0 0 22 20 0.0000 4 270 1260 3960 3240 SS:Ref_2\001

% -*-latex-*- Put EMACS into LaTeX-mode
% Verbal description for system TwoLinkGMV (TwoLinkGMV_desc.tex)
% Generated by MTT on Wed Apr 15 18:15:23 BST 1998.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.1  1998/04/15 18:41:58  peterg
% %% Initial revision
% %%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   The acausal bond graph of system \textbf{TwoLinkGMV} is
   displayed in Figure \Ref{TwoLinkGMV_abg} and its label
   file is listed in Section \Ref{sec:TwoLinkGMV_lbl}.
   The subsystems are listed in Section \Ref{sec:TwoLinkGMV_sub}.

This composite system provides an illustration of nonlinear
generalised minimum variance (GMV) control (continuous-time) operating on a
twolink manipulator. GMV can also be interpreted as:
\begin{itemize}
\item the exact linearisation (by feedback) followed by a
  pole-placement design on the resulting linear system and
\item a special case of generalised predictive control (GPC) were the
  prediction horizon is zero and the $P(s)$ polynomial is the same as
  the system relative degree and
\item One possible instance of physical-model-based control.
\end{itemize}

The composite system of Figure \Ref{TwoLinkGMV_abg} has three
(visible) parts:
\begin{enumerate}
\item a linear decoupled \emph{specification} system that describes the desired
  closed-loop system in terms of a physical system (two decoupled
  mass-spring-damper systems),
\item the system itself (a two-link manipulator) representing the
  system to be controlled, more details are given in Sections
  \Ref{sec:TwoLinkP_ode.tex} and \Ref{sec:TwoLinkP_rfe.tex}.
\item a model of the system with additional state inputs to be used as
  a state observer.
\end{enumerate}
The invisible parts are implemented in the text file
``TwoLinkGMV\_input.txt'' (see Section \Ref{sec:TwoLinkGMV_input.txt}).
These parts are:
\begin{itemize}
\item the reference signal (joint angles)
  \begin{equation}
    w(t) = 
    \begin{cases}
      \begin{pmatrix}
        \pi \\
        0
      \end{pmatrix} & 0 \ge t > 10 \\
      \begin{pmatrix}
        2\pi \\
        0
      \end{pmatrix} & 10 \ge t > 15 \\
      \begin{pmatrix}
        2\pi \\
        \pi
      \end{pmatrix} & 15 \ge t > 30 \\
    \end{cases}
  \end{equation}
\item The control signal (joint torques) being the solution of 
  \begin{equation}
    \phi^*(t) = O_o(\hat x(t)) + O_h(\hat x(t)) u(t) = w(t)
  \end{equation}
where $\hat x$ is the observed state.
\item The observer feedback signal
  \begin{equation}
    u_x = K ( y - \hat y)
  \end{equation}
where $K$ is the observer gain matrix and $y$ and $\hat y$ are the
system and model outputs respectively.
\end{itemize}
The observer gain is set up on the basis of the \emph{linearised}
system using LQ theory. This is implemented in the text file
``TwoLinkGMV\_state.txt'' (see Section \Ref{sec:TwoLinkGMV_state.txt})
using the Octave function ``lqe'' together with the MTT-generated
linearised system ``TwoLink\_sm''.


The system was simulated using Octave under MTT with the results given
in Figures
\Ref{fig:TwoLinkGMV_odeso.ps-TwoLinkGMV-Theta-1,TwoLinkGMV-Theta-1-r}
and
\Ref{fig:TwoLinkGMV_odeso.ps-TwoLinkGMV-Theta-2,TwoLinkGMV-Theta-2-r}
giving the actual and specification angles for joints 1 and 2
respectively.

The initial \emph{system} state was zero except that the angle of the
first rod was $\frac{\pi}{4}$. The initial \emph{observer} state was
(erroneously but deliberately) set at zero. This explains the
(decaying) discrepancy between the actual and specification angles.
Simulations with zero initial state gave precise matching.

# Numerical parameter file (TwoLinkGMV_input.txt)
# Generated by MTT at Mon Apr 13 11:02:37 BST 1998

# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% Version control history
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# %% $Log$
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

global ObserverGain;

# Reference signals
u(1) =	 pi + pi*(t>10) ;			# TwoLinkGMV (Ref_1)
u(2) =	 pi*(t>15) ;			# TwoLinkGMV (Ref_2)

# Control signals
w = u(1:2);			# Reference signal
x_model = x(9:12);		# Observed states
[O_o, O_h] = TwoLinkP_obs(x_model) #GPC O function (affine case)
[spec_n,spec_d] = msdP_tf;	# Spec transfer function
P = spec_d(3:-1:1);		# P poly with ascending coeffs
PP = [eye(2)*P(1) eye(2)*P(2) eye(2)*P(3)]; 
PO_o = PP*O_o;			# Compute Py with u zero
PO_h = PP*O_h;			# Coefficient of u
u_control =  PO_h\(w - PO_o);	# GMV control signal

u(3:4) = u_control;		# TwoLinkGMV (Tau_1)

# Observer
x_system = x(5:8);		# System states
error = x_system-x_model;	# Error in states
ObserverInput = ObserverGain*error;
u(5:8) = ObserverInput;		# Set the state-input to the observer

%SUMMARY TwoLinkGMV - GMV control of two-link manipulator
%DESCRIPTION This composite system provides an illustration
%DESCRIPTION of nonlinear generalised minimum variance (GMV) control
%DESCRIPTION (continuous-time) operating on a twolink manipulator. 

%% Label file for system TwoLinkGMV (TwoLinkGMV_lbl.txt)

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
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%% Each line should be of one of the following forms:
%	a comment (ie starting with %)
%	Component-name	CR_name	arg1,arg2,..argn
%	blank



% Component type SS
	Ref_1		SS	external,internal
	Ref_2		SS	external,internal
	Tau_1		SS	external,internal
	Tau_2		SS	external,internal

	Theta_1		SS	external,0
	Theta_2		SS	external,0

	Theta_1_m	SS	external,0
	Theta_2_m	SS	external,0

	Theta_1_r	SS	external,0
	Theta_2_r	SS	external,0

% Component type msdP
	spec_1
	spec_2

% Component type TwoLinkP
	system

% Component type TwoLinkPX
	model

# Numerical parameter file (TwoLinkGMV_numpar.txt)
# Generated by MTT at Mon Apr 13 10:57:02 BST 1998

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# Parameters
c_s = 	1.0; # msdP
j_s = 	1.0; # msdP
r_s = 	1.414; # msdP

j_r = 	1.0; # TwoLinkP,TwoLinkPX
l_r = 	1.0; # TwoLinkP,TwoLinkPX
m_r = 	1.0; # TwoLinkP,TwoLinkPX

%% Reduce  GPC observability function parameters for system TwoLinkGMV (TwoLinkGMV_obspar.r)

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MTTGPCNy := 2;
MTTGPCNu := 0;
Matrix MTTdU(5,1);
MTTdU(1,1) := MTTdU1;
MTTdU(2,1) := MTTdU2;
MTTdU(3,1) := MTTdU3;
MTTdU(4,1) := MTTdU4;
MTTdU(5,1) := MTTdU5;
Matrix MTTUU(2,5);
MTTUU(1,1) := MTTu1;
MTTUU(1,2) := MTTu11;
MTTUU(1,3) := MTTu12;
MTTUU(1,4) := MTTu13;
MTTUU(1,5) := MTTu14;
MTTUU(2,1) := MTTu2;
MTTUU(2,2) := MTTu21;
MTTUU(2,3) := MTTu22;
MTTUU(2,4) := MTTu23;
MTTUU(2,5) := MTTu24;
END;

# Outline report file for system TwoLinkGMV (TwoLinkGMV_rep.txt)

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mtt TwoLinkGMV abg tex
mtt TwoLinkGMV struc tex
mtt TwoLinkGMV sympar tex

mtt TwoLinkP struc tex
mtt TwoLinkP rfe tex
mtt TwoLinkP ode tex
mtt TwoLinkP obs tex

mtt TwoLinkP ss tex
mtt TwoLinkP sm tex

mtt msdP tf tex

mtt TwoLinkGMV numpar txt
mtt TwoLinkGMV state txt
mtt TwoLinkGMV input txt
mtt TwoLinkGMV odeso ps 'TwoLinkGMV_Theta_1,TwoLinkGMV_Theta_1_r'
mtt TwoLinkGMV odeso ps 'TwoLinkGMV_Theta_2,TwoLinkGMV_Theta_2_r'

%% Simulation parameters for system TwoLinkGMV (TwoLinkGMV_simpar.txt)

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LAST=30.0
DT=0.2
STEPFACTOR=1

%% Simulation parameters for system TwoLinkGMV (TwoLinkGMV_simpar.txt)

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LAST=30.0
DT=0.2
STEPFACTOR=1

% Steady-state parameter file (TwoLinkGMV_sspar.r)
% Generated by MTT at Tue Apr 14 08:47:47 BST 1998

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% % $Id$
% % $Log$
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% Steady-state states
MTTX1 := 	0; % TwoLinkGMV_spec_1 (c_s)
MTTX2 := 	0; % TwoLinkGMV_spec_1 (j_s)
MTTX3 := 	0; % TwoLinkGMV_spec_2 (c_s)
MTTX4 := 	0; % TwoLinkGMV_spec_2 (j_s)
MTTX5 := 	0; % TwoLinkGMV_system_rod1 (J)
MTTX6 := 	0; % TwoLinkGMV_system_rod1_th (3)
MTTX7 := 	0; % TwoLinkGMV_system_rod2 (J)
MTTX8 := 	0; % TwoLinkGMV_system_rod2_th (3)
MTTX9 := 	0; % TwoLinkGMV_model_rod1_J (i)
MTTX10 := 	0; % TwoLinkGMV_model_rod1_th_c (c)
MTTX11 := 	0; % TwoLinkGMV_model_rod2_J (i)
MTTX12 := 	0; % TwoLinkGMV_model_rod2_th_c (c)
% Steady-state inputs
MTTU1 := 	1; % TwoLinkGMV (Ref_1)
MTTU2 := 	1; % TwoLinkGMV (Ref_2)
MTTU3 := 	0; % TwoLinkGMV (Tau_1)
MTTU4 := 	0; % TwoLinkGMV (Tau_2)
MTTU5 := 	0; % TwoLinkGMV_model_rod1_J (X)
MTTU6 := 	0; % TwoLinkGMV_model_rod1_th_c (X)
MTTU7 := 	0; % TwoLinkGMV_model_rod2_J (X)
MTTU8 := 	0; % TwoLinkGMV_model_rod2_th_c (X)
;;END;

# Numerical parameter file (TwoLinkGMV_state.txt)
# Generated by MTT at Tue Apr 14 08:54:28 BST 1998

# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% Version control history
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# %% $Log$
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

global ObserverGain;

# Set the states
x(1) =	 0 ; # TwoLinkGMV_spec_1 (c_s)
x(2) =	 0 ; # TwoLinkGMV_spec_1 (j_s)
x(3) =	 0 ; # TwoLinkGMV_spec_2 (c_s)
x(4) =	 0 ; # TwoLinkGMV_spec_2 (j_s)
x(5) =	 0 ; # TwoLinkGMV_system_rod1 (J)
x(6) =	 pi/4 ; # TwoLinkGMV_system_rod1_th (3)
x(7) =	 0 ; # TwoLinkGMV_system_rod2 (J)
x(8) =	 0 ; # TwoLinkGMV_system_rod2_th (3)
x(9) =	 0 ; # TwoLinkGMV_model_rod1_J (i)
x(10) =	 0 ; # TwoLinkGMV_model_rod1_th_c (c)
x(11) =	 0 ; # TwoLinkGMV_model_rod2_J (i)
x(12) =	 0 ; # TwoLinkGMV_model_rod2_th_c (c)

# Observer design
[A,B,C] = TwoLinkP_sm;		# Get the linearised system
sigma = 0.1;			# Measurement noise variance (pretend)
k = lqe(A,eye(4),C,eye(4),sigma*eye(2))
ObserverGain = k*C;		# This system happens to have a linear output

#FIG 3.1
Portrait
Center
Metric
1200 2
1 3 0 2 1 7 1 0 -1 0.000 1 0.0000 8550 1125 485 485 8550 1125 8730 1575
1 3 0 2 1 7 1 0 -1 0.000 1 0.0000 8550 5625 485 485 8550 5625 9035 6110
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 3468 1128 3738 1128
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 5720 1130 5990 1130
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 4593 2703 4863 2703
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4728 1128 4728 2703 4953 2478
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 4502 5492 4502 5762
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2927 5627 4502 5627 4277 5852
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4726 5851 4726 7426 4951 7201
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 3472 8647 3742 8647
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 4597 8647 4867 8647
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 5724 8649 5994 8649
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4730 8645 4730 10220 4955 9995
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5855 8645 5855 10220 6080 9995
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3601 3826 3601 7426 3826 7201
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5851 3826 5851 7426 6076 7201
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 6525 8775 6525 7200 2925 7200 2925 8775 6525 8775
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 6525 2025 6525 450 2925 450 2925 2025 6525 2025
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 6525 6435 6525 4860 2925 4860 2925 6435 6525 6435
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 6525 11250 6525 9675 2925 9675 2925 11250 6525 11250
2 4 0 1 31 7 1 0 -1 0.000 0 0 7 0 0 5
	 9450 11475 9450 225 180 225 180 11475 9450 11475
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3603 1128 3603 2703 3828 2478
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5853 1128 5853 2703 6078 2478
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4726 3826 4726 5401 4951 5176
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 6525 4050 2925 4050 2925 2475 6525 2475 6525 4050
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3600 8622 3600 10197 3825 9972
2 4 0 2 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 8775 5175 8775 1575 8325 1575 8325 5175 8775 5175
2 4 0 2 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 8775 9675 8775 6075 8325 6075 8325 9675 8775 9675
2 2 0 2 1 7 1 0 -1 0.000 0 0 0 0 0 5
	 7650 450 9405 450 9405 675 7650 675 7650 450
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3150 3285 1575 3285 1800 3510
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3195 8055 1620 8055 1845 8280
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 1350 3150 1350 2025 1575 2250
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 1350 8325 1350 9450 1575 9225
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 1350 7875 1350 3600 1575 3825
4 1 -1 0 0 0 20 0.0000 4 255 810 3603 948 SS:v_x\001
4 0 -1 0 0 0 20 0.0000 4 195 135 4683 5718 0\001
4 1 -1 0 0 0 20 0.0000 4 255 840 3608 10673 SS:F_x\001
4 1 -1 0 0 0 20 0.0000 4 255 840 4733 10673 SS:F_a\001
4 1 -1 0 0 0 20 0.0000 4 255 840 5903 10673 SS:F_y\001
4 1 -1 0 0 0 20 0.0000 4 195 1335 4729 3379 RODaX:rod1\001
4 1 -1 0 0 0 20 0.0000 4 195 1335 4731 8196 RODaX:rod2\001
4 1 4 0 0 0 20 0.0000 4 255 1410 4771 946 SS:[Joint_1]\001
4 0 1 1 0 3 20 0.0000 4 210 720 6795 3375 Link 1\001
4 0 1 1 0 3 20 0.0000 4 225 795 6750 5760 Joint 2\001
4 0 1 1 0 3 20 0.0000 4 210 720 6750 8190 Link 2\001
4 0 1 1 0 3 20 0.0000 4 270 375 6750 10485 Tip\001
4 0 1 1 0 3 20 0.0000 4 225 795 6750 1260 Joint 1\001
4 1 4 0 0 0 16 0.0000 4 225 900 4725 2970 [alpha_a]\001
4 1 4 0 0 0 16 0.0000 4 210 510 3600 3780 [x_b]\001
4 1 4 0 0 0 16 0.0000 4 225 915 4725 3780 [alpha_b]\001
4 1 4 0 0 0 16 0.0000 4 225 510 5850 3780 [y_b]\001
4 1 4 0 0 0 16 0.0000 4 225 495 5850 2970 [y_a]\001
4 1 4 0 0 0 16 0.0000 4 210 495 3605 7835 [x_a]\001
4 1 4 0 0 0 16 0.0000 4 225 900 4730 7835 [alpha_a]\001
4 1 4 0 0 0 16 0.0000 4 225 495 5855 7835 [y_a]\001
4 1 4 0 0 0 16 0.0000 4 210 510 3607 8512 [x_b]\001
4 1 4 0 0 0 16 0.0000 4 225 915 4733 8513 [alpha_b]\001
4 1 4 0 0 0 16 0.0000 4 225 510 5859 8514 [y_b]\001
4 1 -1 0 0 0 20 0.0000 4 255 810 5850 945 SS:v_y\001
4 2 4 0 0 0 20 0.0000 4 255 1410 2882 5717 SS:[Joint_2]\001
4 1 4 0 0 0 16 0.0000 4 210 495 3600 2970 [x_a]\001
4 1 4 0 0 0 16 0.0000 4 225 675 3510 3375 [alpha]\001
4 1 4 0 0 0 16 0.0000 4 225 675 3555 8145 [alpha]\001
4 0 -1 0 0 0 20 0.0000 4 195 135 1308 8193 1\001
4 1 4 0 0 0 20 0.0000 4 255 1530 1397 1892 SS:[Theta_1]\001
4 1 4 0 0 0 20 0.0000 4 255 1530 1352 9767 SS:[Theta_2]\001
4 0 -1 0 0 0 20 0.0000 4 195 135 1263 3468 0\001

% Verbal description for system TwoLinkPX (TwoLinkPX_desc.tex)
% Generated by MTT on Fri Jun 13 16:30:23 BST 1997.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.1  1998/01/19 14:20:07  peterg
% %% Initial revision
% %%
% Revision 1.1  1997/08/15  13:31:00  peterg
% Initial revision
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   The acausal bond graph of system \textbf{TwoLinkPX} is
   displayed in Figure \Ref{TwoLinkPX_abg} and its label
   file is listed in Section \Ref{sec:TwoLinkPX_lbl}.
   The subsystems are listed in Section \Ref{sec:TwoLinkPX_sub}.

This is a heirachical version of the example from Section 10.5 of
"Metamodelling".  It uses the compound components: {\bf ROD}.  {\bf
ROD} is essentially as described in Figure 10.2.
There is no gravity included in this model.

This system has a number of dynamic elements (those corresponding to translation
motion) in derivative causality, thus the system is represnted as a
Differential-Algebraic Equation (Section
\Ref{sec:TwoLinkPX_dae.tex}). Hovever, this is of contrained-state form and
therfore can be written as a set of constrained-state equations (Section
\Ref{sec:TwoLinkPX_cse.tex}). The corresponding ordinary differential
equation is complicated due to the trig functions involved in
inverting the E matrix.

As well as the standard representation the ``robot-form'' equations
appear in Section  \Ref{sec:TwoLinkPX_rfe}. 

%%% Local Variables: 
%%% mode: plain-tex
%%% TeX-master: t
%%% End: 

%SUMMARY TwoLinkPX: two-link manipulator from Section 10.5 of "Metamodelling"
%DESCRIPTION This is a heirachical version of the 
%DESCRIPTION example from Section 10.5 of "Metamodelling".
%DESCRIPTION It uses two compound components: ROD and GRA
%DESCRIPTION ROD is essentially as described in Figure 10.2
%DESCRIPTION GRAV represents gravity by a vertical accelleration
%DESCRIPTION as in Section 10.9 of "Metamodelling"


%% Label (TwoLinkPX_lbl.txt)

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.2  1996/12/05  12:39:49  peterg
% %% Documentation
% %%
% %% Revision 1.1  1996/12/05 12:17:15  peterg
% %% Initial revision
% %%
% %% Revision 1.1  1996/11/14  10:48:42  peterg
% %% Initial revision
% %%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Each line should be of one of the following forms:
%	a comment (ie starting with %)
%	Component-name	CR_name	arg1,arg2,..argn
%	blank

%Rod parameters - uniform rods
rod1	none	l_r;l_r;j_r;m_r
rod2	none	l_r;l_r;j_r;m_r

%Zero velocity sources
v_x	SS     internal,0
v_y	SS     internal,0


%Zero force/torque sources
F_x	SS	   0,internal
F_a	SS	   0,internal
F_y	SS	   0,internal

%Named ports
[Joint_1]		SS	external,internal
[Joint_2]		SS	external,internal
[Theta_1]		SS	external,0
[Theta_2]		SS	external,0

%Torque/velocity at joints
%f_a1	SS	 external,external
%f_a2	SS	 external,external

#FIG 3.1
Portrait
Center
Metric
1200 2
1 3 0 2 1 7 1 0 -1 0.000 1 0.0000 8550 1125 485 485 8550 1125 8730 1575
1 3 0 2 1 7 1 0 -1 0.000 1 0.0000 8550 5625 485 485 8550 5625 9035 6110
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 3468 1128 3738 1128
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 5720 1130 5990 1130
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 4593 2703 4863 2703
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4728 1128 4728 2703 4953 2478
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 4502 5492 4502 5762
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2927 5627 4502 5627 4277 5852
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4726 5851 4726 7426 4951 7201
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 3472 8647 3742 8647
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 4597 8647 4867 8647
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 5724 8649 5994 8649
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4730 8645 4730 10220 4955 9995
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5855 8645 5855 10220 6080 9995
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3601 3826 3601 7426 3826 7201
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5851 3826 5851 7426 6076 7201
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 6525 8775 6525 7200 2925 7200 2925 8775 6525 8775
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 6525 2025 6525 450 2925 450 2925 2025 6525 2025
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 6525 6435 6525 4860 2925 4860 2925 6435 6525 6435
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 6525 11250 6525 9675 2925 9675 2925 11250 6525 11250
2 4 0 1 31 7 1 0 -1 0.000 0 0 7 0 0 5
	 9450 11475 9450 225 180 225 180 11475 9450 11475
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3603 1128 3603 2703 3828 2478
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5853 1128 5853 2703 6078 2478
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4726 3826 4726 5401 4951 5176
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 6525 4050 2925 4050 2925 2475 6525 2475 6525 4050
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3600 8622 3600 10197 3825 9972
2 4 0 2 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 8775 5175 8775 1575 8325 1575 8325 5175 8775 5175
2 4 0 2 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 8775 9675 8775 6075 8325 6075 8325 9675 8775 9675
2 2 0 2 1 7 1 0 -1 0.000 0 0 0 0 0 5
	 7650 450 9405 450 9405 675 7650 675 7650 450
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3150 3285 1575 3285 1800 3510
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3195 8055 1620 8055 1845 8280
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 1350 3150 1350 2025 1575 2250
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 1350 8325 1350 9450 1575 9225
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 1350 7875 1350 3600 1575 3825
4 1 -1 0 0 0 20 0.0000 4 255 810 3603 948 SS:v_x\001
4 0 -1 0 0 0 20 0.0000 4 195 135 4683 5718 0\001
4 1 -1 0 0 0 20 0.0000 4 255 840 3608 10673 SS:F_x\001
4 1 -1 0 0 0 20 0.0000 4 255 840 4733 10673 SS:F_a\001
4 1 -1 0 0 0 20 0.0000 4 255 840 5903 10673 SS:F_y\001
4 1 -1 0 0 0 20 0.0000 4 195 1335 4729 3379 RODa:rod1\001
4 1 -1 0 0 0 20 0.0000 4 195 1335 4731 8196 RODa:rod2\001
4 1 4 0 0 0 20 0.0000 4 255 1410 4771 946 SS:[Joint_1]\001
4 0 1 1 0 3 20 0.0000 4 210 720 6795 3375 Link 1\001
4 0 1 1 0 3 20 0.0000 4 225 795 6750 5760 Joint 2\001
4 0 1 1 0 3 20 0.0000 4 210 720 6750 8190 Link 2\001
4 0 1 1 0 3 20 0.0000 4 270 375 6750 10485 Tip\001
4 0 1 1 0 3 20 0.0000 4 225 795 6750 1260 Joint 1\001
4 1 4 0 0 0 16 0.0000 4 225 900 4725 2970 [alpha_a]\001
4 1 4 0 0 0 16 0.0000 4 210 510 3600 3780 [x_b]\001
4 1 4 0 0 0 16 0.0000 4 225 915 4725 3780 [alpha_b]\001
4 1 4 0 0 0 16 0.0000 4 225 510 5850 3780 [y_b]\001
4 1 4 0 0 0 16 0.0000 4 225 495 5850 2970 [y_a]\001
4 1 4 0 0 0 16 0.0000 4 210 495 3605 7835 [x_a]\001
4 1 4 0 0 0 16 0.0000 4 225 900 4730 7835 [alpha_a]\001
4 1 4 0 0 0 16 0.0000 4 225 495 5855 7835 [y_a]\001
4 1 4 0 0 0 16 0.0000 4 210 510 3607 8512 [x_b]\001
4 1 4 0 0 0 16 0.0000 4 225 915 4733 8513 [alpha_b]\001
4 1 4 0 0 0 16 0.0000 4 225 510 5859 8514 [y_b]\001
4 1 -1 0 0 0 20 0.0000 4 255 810 5850 945 SS:v_y\001
4 2 4 0 0 0 20 0.0000 4 255 1410 2882 5717 SS:[Joint_2]\001
4 1 4 0 0 0 16 0.0000 4 210 495 3600 2970 [x_a]\001
4 1 4 0 0 0 16 0.0000 4 225 675 3510 3375 [alpha]\001
4 1 4 0 0 0 16 0.0000 4 225 675 3555 8145 [alpha]\001
4 0 -1 0 0 0 20 0.0000 4 195 135 1308 8193 1\001
4 1 4 0 0 0 20 0.0000 4 255 1530 1397 1892 SS:[Theta_1]\001
4 1 4 0 0 0 20 0.0000 4 255 1530 1352 9767 SS:[Theta_2]\001
4 0 -1 0 0 0 20 0.0000 4 195 135 1263 3468 0\001

lcos
lin
lsin

% Verbal description for system TwoLinkP (TwoLinkP_desc.tex)
% Generated by MTT on Fri Jun 13 16:30:23 BST 1997.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.1  1998/01/19 14:20:07  peterg
% %% Initial revision
% %%
% Revision 1.1  1997/08/15  13:31:00  peterg
% Initial revision
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   The acausal bond graph of system \textbf{TwoLinkP} is
   displayed in Figure \Ref{TwoLinkP_abg} and its label
   file is listed in Section \Ref{sec:TwoLinkP_lbl}.
   The subsystems are listed in Section \Ref{sec:TwoLinkP_sub}.

This is a heirachical version of the example from Section 10.5 of
"Metamodelling".  It uses the compound components: {\bf ROD}.  {\bf
ROD} is essentially as described in Figure 10.2.
There is no gravity included in this model.

This system has a number of dynamic elements (those corresponding to translation
motion) in derivative causality, thus the system is represnted as a
Differential-Algebraic Equation (Section
\Ref{sec:TwoLinkP_dae.tex}). Hovever, this is of contrained-state form and
therfore can be written as a set of constrained-state equations (Section
\Ref{sec:TwoLinkP_cse.tex}). The corresponding ordinary differential
equation is complicated due to the trig functions involved in
inverting the E matrix.

As well as the standard representation the ``robot-form'' equations
appear in Section  \Ref{sec:TwoLinkP_rfe}. 

%%% Local Variables: 
%%% mode: plain-tex
%%% TeX-master: t
%%% End: 

%SUMMARY TwoLinkP: two-link manipulator from Section 10.5 of "Metamodelling"
%DESCRIPTION This is a heirachical version of the 
%DESCRIPTION example from Section 10.5 of "Metamodelling".
%DESCRIPTION It uses two compound components: ROD and GRA
%DESCRIPTION ROD is essentially as described in Figure 10.2
%DESCRIPTION GRAV represents gravity by a vertical accelleration
%DESCRIPTION as in Section 10.9 of "Metamodelling"


%% Label (TwoLinkP_lbl.txt)

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.2  1996/12/05  12:39:49  peterg
% %% Documentation
% %%
% %% Revision 1.1  1996/12/05 12:17:15  peterg
% %% Initial revision
% %%
% %% Revision 1.1  1996/11/14  10:48:42  peterg
% %% Initial revision
% %%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Each line should be of one of the following forms:
%	a comment (ie starting with %)
%	Component-name	CR_name	arg1,arg2,..argn
%	blank

%Rod parameters - uniform rods
rod1	none	l_r;l_r;j_r;m_r
rod2	none	l_r;l_r;j_r;m_r

%Zero velocity sources
v_x	SS     internal,0
v_y	SS     internal,0


%Zero force/torque sources
F_x	SS	   0,internal
F_a	SS	   0,internal
F_y	SS	   0,internal

%Named ports
[Joint_1]		SS	external,internal
[Joint_2]		SS	external,internal
[Theta_1]		SS	external,0
[Theta_2]		SS	external,0

%Torque/velocity at joints
%f_a1	SS	 external,external
%f_a2	SS	 external,external

%% Reduce  GPC observability function parameters for system TwoLinkP (TwoLinkP_obspar.r)

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

MTTGPCNy := 2;
MTTGPCNu := 0;
Matrix MTTdU(5,1);
MTTdU(1,1) := MTTdU1;
MTTdU(2,1) := MTTdU2;
MTTdU(3,1) := MTTdU3;
MTTdU(4,1) := MTTdU4;
MTTdU(5,1) := MTTdU5;
Matrix MTTUU(2,5);
MTTUU(1,1) := MTTu1;
MTTUU(1,2) := MTTu11;
MTTUU(1,3) := MTTu12;
MTTUU(1,4) := MTTu13;
MTTUU(1,5) := MTTu14;
MTTUU(2,1) := MTTu2;
MTTUU(2,2) := MTTu21;
MTTUU(2,3) := MTTu22;
MTTUU(2,4) := MTTu23;
MTTUU(2,5) := MTTu24;
END;

%% Reduce  substitution statements for system TwoLinkPX (TwoLinkPX_subs.r)

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.2  1998/03/22 20:13:25  peterg
% %% Trig simplification added
% %%
% %% Revision 1.1  1998/03/22 20:12:51  peterg
% %% Initial revision
% %%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

        trig1 := {cos(~x)*cos(~y) => (cos(x+y)+cos(x-y))/2,
                  cos(~x)*sin(~y) => (sin(x+y)-sin(x-y))/2,
                  sin(~x)*sin(~y) => (cos(x-y)-cos(x+y))/2,
                  cos(~x)^2       => (1+cos(2*x))/2,
                  sin(~x)^2       => (1-cos(2*x))/2};
       LET trig1;

END;

#FIG 3.1
Portrait
Center
Metric
1200 2
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3825 4050 4950 4050 4725 4275
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3600 4275 3600 5400 3825 5175
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2250 4050 3375 4050 3150 4275
2 4 0 2 31 7 1 0 -1 0.000 0 0 7 0 0 5
	 8325 6975 8325 1125 1125 1125 1125 6975 8325 6975
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5400 4050 6525 4050 6300 4275
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5175 3825 5175 2700 5400 2925
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3600 3825 3600 2700 3825 2925
4 1 -1 0 0 0 20 0.0000 4 195 135 3600 4185 1\001
4 2 4 0 0 0 20 0.0000 4 240 810 2160 4140 SS:[in]\001
4 1 -1 0 0 0 20 0.0000 4 255 480 3600 5715 I:j_s\001
4 1 1 1 0 0 20 0.0000 4 255 5355 4815 6345 Mass-spring-damper system (position output)\001
4 1 -1 0 0 0 20 0.0000 4 195 135 5175 4140 0\001
4 0 4 0 0 0 20 0.0000 4 240 960 6660 4140 SS:[out]\001
4 1 -1 0 0 0 20 0.0000 4 255 615 3600 2565 R:r_s\001
4 1 -1 0 0 0 20 0.0000 4 255 630 5175 2565 C:c_s\001

% Verbal description for system msdP (msdP_desc.tex)
% Generated by MTT on Thu Nov 13 09:38:17 GMT 1997.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   The acausal bond graph of system \textbf{msdP} is
   displayed in Figure \Ref{msdP_abg} and its label
   file is listed in Section \Ref{sec:msdP_lbl}.
   The subsystems are listed in Section \Ref{sec:msdP_sub}.


 \textbf{msdP} is a simple Mass-Spring-Damper system with 
 force input and position output. It is set up to provide a specification system
 for each link of the two-link maipulator. This is appropriate because
 \begin{itemize}
 \item  it has compatible physical behaviour with the system itself,
 \item it specifies two decoupled systems,
 \item it has linear behaviour and
 \item it has a simple performance interpretation in terms of system
   rise-time and overshoot.
 \end{itemize}

%%% Local Variables: 
%%% mode: latex
%%% TeX-master: t
%%% End: 

%SUMMARY msdP
%DESCRIPTION <Detailed description here>
%% Label file for system msdP (msdP_lbl.txt)

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Each line should be of one of the following forms:
%	a comment (ie starting with %)
%	Component-name	CR_name	arg1,arg2,..argn
%	blank



% Component type C
	c_s		lin	effort,c_s

% Component type I
	j_s		lin	flow,j_s

% Component type R
	r_s		lin	flow,r_s

% Component type SS
	[in]		SS	external,internal
	[out]		SS	external,0

#FIG 3.1
Portrait
Center
Metric
1200 2
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 1801 3151 2701 3151 2476 3376
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3601 3151 4501 3151 4276 3376
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4726 2926 4726 2026 4951 2251
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4951 3151 5851 3151 5626 3376
2 4 0 1 31 7 1 0 -1 0.000 0 0 7 0 0 5
	 6975 4050 6975 1350 450 1350 450 4050 6975 4050
4 1 -1 0 0 0 20 0.0000 4 195 375 3151 3241 AF\001
4 1 -1 0 0 0 20 0.0000 4 195 135 4726 3241 0\001
4 1 -1 0 0 0 20 0.0000 4 195 600 4726 1891 CX:c\001
4 1 -1 0 0 0 20 0.0000 4 240 810 1306 3241 SS:[in]\001
4 1 -1 0 0 0 20 0.0000 4 240 960 6346 3241 SS:[out]\001

% Verbal description for system INTFX (INTFX_desc.tex)
% Generated by MTT on Fri Aug 15 09:53:16 BST 1997.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.1  1997/08/24 11:20:18  peterg
% %% Initial revision
% %%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   The acausal bond graph of system \textbf{INTFX} is
   displayed in Figure \Ref{INTFX_abg} and its label
   file is listed in Section \Ref{sec:INTFX_lbl}.
   The subsystems are listed in Section \Ref{sec:INTFX_sub}.

\textbf{INTFX} is a two-port component where the effort on port [out]
   is the integral of the flow on port [in].

%SUMMARY INTFX
%DESCRIPTION <Detailed description here>
%% Label file for system INTFX (INTFX_lbl.txt)

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Each line should be of one of the following forms:
%	a comment (ie starting with %)
%	Component-name	CR_name	arg1,arg2,..argn
%	blank



% Component type CX
	c		lin	effort,1

% Component type SS
	[in]		SS	external,external
	[out]		SS	external,external

#FIG 3.1
Portrait
Center
Metric
1200 2
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4728 4278 5403 4953 5178 4953
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5854 5404 6529 6079 6304 6079
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4728 6078 5403 5403 5403 5628
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5853 4953 6528 4278 6528 4503
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 1
	 4277 3827
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3152 2702 4277 3827 4052 3827
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 6977 6527 8102 7652 7877 7652
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3152 7652 4277 6527 4277 6752
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 6977 3827 8102 2702 8102 2927
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5852 5177 6527 5177 6392 5312
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2927 2927 2927 4952 3152 4727
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2927 5402 2927 7427 3152 7202
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2701 5176 2026 5176 2161 5311
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2926 1351 2926 2476 3196 2206
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2926 7876 2926 9001 3196 8731
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 8328 2928 8328 4953 8553 4728
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 8328 5403 8328 7428 8553 7203
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 8327 1352 8327 2477 8597 2207
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 8327 7877 8327 9002 8597 8732
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5626 1351 5626 4951 5851 4726
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5626 5401 5626 9001 5851 8776
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 1
	 6526 5401
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 6526 4951 6526 5401
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 8551 5176 9226 5176 9091 5311
2 1 0 1 5 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3826 4951 6526 4051 6436 4231
2 1 0 1 5 7 0 0 -1 0.000 0 0 -1 0 0 2
	 3826 4996 3826 5356
2 1 0 1 5 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4276 5176 3826 5176 3961 5311
2 1 0 1 5 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3826 5401 6301 6301 6121 6301
2 1 0 1 5 -1 0 0 -1 0.000 0 0 -1 0 0 3
	 3601 5401 4051 6301 3826 6301
2 1 0 1 5 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3601 4951 4051 4051 4051 4276
2 1 0 1 5 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5536 5176 5086 5176 5221 5311
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 6300 9675 6300 675 4950 675 4950 9675 6300 9675
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 9000 9675 9000 675 7650 675 7650 9675 9000 9675
2 4 0 1 31 7 1 0 -1 0.000 0 0 7 0 0 5
	 11025 10305 11025 225 225 225 225 10305 11025 10305
2 4 0 1 1 7 0 0 -1 0.000 0 0 7 0 0 5
	 3600 9675 2250 9675 2250 675 3600 675 3600 9675
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 10125 2250 990 2250 990 900 10125 900 10125 2250
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 10125 5850 990 5850 990 4500 10125 4500 10125 5850
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 10125 9450 990 9450 990 8100 10125 8100 10125 9450
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3375 4950 1800 3375 1800 3600
4 1 -1 0 0 0 20 0.0000 4 195 135 5628 5268 1\001
4 1 -1 0 0 0 20 0.0000 4 195 270 6933 5268 IX:J\001
4 1 -1 0 0 0 20 0.0000 4 195 135 2927 5312 1\001
4 1 -1 0 0 0 20 0.0000 4 195 135 2972 2792 0\001
4 1 -1 0 0 0 20 0.0000 4 195 135 2927 7742 0\001
4 1 -1 0 0 0 20 0.0000 4 195 135 8328 5313 1\001
4 1 -1 0 0 0 20 0.0000 4 195 135 8373 2793 0\001
4 1 -1 0 0 0 20 0.0000 4 195 135 8328 7743 0\001
4 1 -1 0 0 0 20 0.0000 4 255 660 9676 5266 I:m_y\001
4 1 -1 0 0 0 20 0.0000 4 255 660 1531 5221 I:m_x\001
4 1 -1 0 0 0 20 0.0000 4 195 1110 4636 4141 EMTF:c1\001
4 1 -1 0 0 0 20 0.0000 4 195 1110 4681 6391 EMTF:c2\001
4 1 -1 0 0 0 20 0.0000 4 195 1095 7156 4141 EMTF:s1\001
4 1 -1 0 0 0 20 0.0000 4 195 1095 7156 6391 EMTF:s2\001
4 1 5 0 0 0 20 0.0000 4 195 135 3603 5313 0\001
4 1 26 0 0 0 16 0.0000 4 210 345 6751 4456 [in]\001
4 1 26 0 0 0 16 0.0000 4 210 465 6751 3781 [out]\001
4 1 26 0 0 0 16 0.0000 4 210 345 6751 6076 [in]\001
4 1 26 0 0 0 16 0.0000 4 210 465 6751 6706 [out]\001
4 1 26 0 0 0 16 0.0000 4 210 585 6211 6526 [mod]\001
4 1 5 0 0 0 20 0.0000 4 195 960 4681 5266 INTFX:th\001
4 1 1 1 0 0 20 0.0000 4 195 210 2925 10035 X\001
4 1 1 1 0 32 20 0.0000 4 135 180 5580 9990 a\001
4 1 1 1 0 0 20 0.0000 4 195 210 8280 9990 Y\001
4 2 26 0 0 0 16 0.0000 4 210 585 3960 4140 [mod]\001
4 2 26 0 0 0 16 0.0000 4 210 585 6345 4095 [mod]\001
4 2 26 0 0 0 16 0.0000 4 210 585 3960 6210 [mod]\001
4 1 26 0 0 0 16 0.0000 4 210 345 4590 4455 [in]\001
4 1 26 0 0 0 16 0.0000 4 210 465 4545 3780 [out]\001
4 1 26 0 0 0 16 0.0000 4 210 465 4590 6660 [out]\001
4 0 26 0 0 0 16 0.0000 4 210 345 4365 6030 [in]\001
4 1 4 0 0 0 20 0.0000 4 255 990 2971 1216 SS:[x_a]\001
4 1 4 0 0 0 20 0.0000 4 255 990 2971 9361 SS:[x_b]\001
4 1 4 0 0 0 20 0.0000 4 255 990 8372 1217 SS:[y_a]\001
4 1 4 0 0 0 20 0.0000 4 255 990 8417 9362 SS:[y_b]\001
4 1 4 0 0 0 20 0.0000 4 255 1485 5671 1216 SS:[alpha_a]\001
4 1 4 0 0 0 20 0.0000 4 255 1485 5671 9361 SS:[alpha_b]\001
4 1 1 1 0 0 20 0.0000 4 255 600 1350 2700 Tip a\001
4 1 1 1 0 0 20 0.0000 4 195 1380 1260 6300 Mass centre\001
4 1 1 1 0 0 20 0.0000 4 255 600 1350 9855 Tip b\001
4 1 4 0 0 0 20 0.0000 4 255 1215 1756 3286 SS:[alpha]\001

% Verbal description for system RODaX (RODaX_desc.tex)
% Generated by MTT on Fri Aug 15 09:53:23 BST 1997.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.1  1998/04/12 15:25:35  peterg
% %% Initial revision
% %%
% Revision 1.1  1997/08/15  09:41:19  peterg
% Initial revision
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   The acausal bond graph of system \textbf{RODaX} is
   displayed in Figure \Ref{RODaX_abg} and its label
   file is listed in Section \Ref{sec:RODaX_lbl}.
   The subsystems are listed in Section \Ref{sec:RODaX_sub}.

{\bf RODaX} is essentially as described in Figure 10.2 of
``Metamodelling''. It has an additional port ``[angle]'' to provide
access to the rod angle.

%SUMMARY	RODaX: rigid rod in two dimensions - angle port.
%DESCRIPTION	Port [alpha_a]:	Angular torque/velocity - end a
%DESCRIPTION	Port [alpha_b]:	Angular torque/velocity - end b
%DESCRIPTION	Port [x_a]:	x force/velocity - end a
%DESCRIPTION	Port [x_b]:	x force/velocity - end b
%DESCRIPTION	Port [y_a]:	y force/velocity - end a
%DESCRIPTION	Port [y_b]:	y force/velocity - end b
%DESCRIPTION	Port [alpha]:	rod angle
%DESCRIPTION
%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"


%% Label file for system RODaX (RODaX_lbl.txt)




% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% % $Id$
% % $Log$
% % Revision 1.1  1998/04/12 15:24:06  peterg
% % Initial revision
% %
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%% Each line should be of one of the following forms:
%	a comment (ie starting with %)
%	Component-name	CR_name	arg1,arg2,..argn
%	blank

%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

#FIG 3.1
Portrait
Center
Metric
1200 2
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2475 2025 3825 2025 3600 2250
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4500 2025 5850 2025 5625 2250
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 6525 3600 7875 3600 7650 3825
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 2475 1800 2475 2295
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 6075 3375 6075 3825
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 5850 1800 5850 2295
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2475 3600 3825 3600 3600 3825
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4500 3600 6075 3600 5850 3825
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 6300 3330 6300 2205 6525 2430
4 2 4 0 0 0 20 0.0000 4 240 720 2385 2115 SS:[v]\001
4 1 -1 0 0 0 20 0.0000 4 195 420 4140 2115 GY\001
4 1 -1 0 0 0 20 0.0000 4 195 840 6345 2070 AE:tau\001
4 1 -1 0 0 0 20 0.0000 4 195 135 6300 3690 1\001
4 2 4 0 0 0 20 0.0000 4 255 720 2475 3690 SS:[p]\001
4 0 4 0 0 0 20 0.0000 4 240 690 8055 3645 SS:[s]\001
4 1 -1 0 0 0 20 0.0000 4 195 390 4050 3690 AE\001
4 2 4 0 0 0 20 0.0000 4 240 405 5760 1755 [in]\001
4 2 4 0 0 0 20 0.0000 4 240 555 6255 2565 [out]\001

%SUMMARY Sensor
%DESCRIPTION <Detailed description here>
%% Label file for system Sensor (Sensor_lbl.txt)

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Each line should be of one of the following forms:
%	a comment (ie starting with %)
%	Component-name	CR_name	arg1,arg2,..argn
%	blank



% Component type AE
	tau		lin	tau

% Component type SS
	[p]		SS	external,external
	[s]		SS	external,external
	[v]		SS	external,external

#FIG 3.1
Portrait
Center
Metric
1200 2
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 7875 8550 9225 8550 9000 8775
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 9225 8325 9225 8775
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 7875 9450 9225 9450 9000 9675
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 9225 9225 9225 9675
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 5625 8325 5625 8775
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 5625 9225 5625 9675
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 4
	 3825 5625 3825 8550 5625 8550 5400 8775
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 4
	 3375 6525 3375 9450 5625 9450 5400 9675
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 7875 5400 9225 5400 9000 5625
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 9225 5175 9225 5625
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 7875 6300 9225 6300 9000 6525
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 9225 6075 9225 6525
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4050 5400 5625 5400 5400 5625
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 5625 5175 5625 5625
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3600 6300 5625 6300 5400 6525
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 5625 6075 5625 6525
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2025 5400 3600 5400 3375 5625
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 3600 5175 3600 5625
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2025 6300 3150 6300 2925 6525
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 3150 6075 3150 6525
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 7875 2250 9225 2250 9000 2475
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 9225 2025 9225 2475
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 7875 3150 9225 3150 9000 3375
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 9225 2925 9225 3375
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4050 2250 5625 2250 5400 2475
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 5625 2025 5625 2475
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4050 3150 5625 3150 5400 3375
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 5625 2925 5625 3375
2 4 0 2 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 11475 3915 2475 3915 2475 1350 11475 1350 11475 3915
2 4 0 2 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 11475 7020 2475 7020 2475 4500 11475 4500 11475 7020
2 4 0 2 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 11475 10215 2475 10215 2475 7650 11475 7650 11475 10215
4 0 -1 0 0 22 20 0.0000 4 270 1935 9315 8640 SS:Theta_1_m\001
4 0 -1 0 0 22 20 0.0000 4 270 1935 9315 9540 SS:Theta_2_m\001
4 1 -1 0 0 22 20 0.0000 4 210 2640 6750 9090 TwoLinkPSX:model\001
4 0 4 0 0 22 20 0.0000 4 270 1230 7920 8415 [Theta_1]\001
4 0 4 0 0 22 20 0.0000 4 270 1230 7920 9315 [Theta_2]\001
4 2 4 0 0 22 20 0.0000 4 270 1140 5535 8415 [Joint_1]\001
4 2 4 0 0 22 20 0.0000 4 270 1140 5535 9315 [Joint_2]\001
4 1 1 1 0 3 26 0.0000 4 270 1005 6750 10080 Model\001
4 1 -1 0 0 22 20 0.0000 4 270 2610 6750 5940 TwoLinkPS:system\001
4 0 4 0 0 22 20 0.0000 4 270 1230 7920 5265 [Theta_1]\001
4 0 4 0 0 22 20 0.0000 4 270 1230 7920 6165 [Theta_2]\001
4 0 -1 0 0 22 20 0.0000 4 270 1530 9315 5490 SS:Theta_1\001
4 0 -1 0 0 22 20 0.0000 4 270 1530 9315 6390 SS:Theta_2\001
4 2 4 0 0 22 20 0.0000 4 270 1140 5535 5265 [Joint_1]\001
4 2 4 0 0 22 20 0.0000 4 270 1140 5535 6165 [Joint_2]\001
4 1 -1 0 0 22 20 0.0000 4 195 150 3825 5490 0\001
4 2 -1 0 0 22 20 0.0000 4 270 1275 1935 6390 SS:Tau_2\001
4 2 -1 0 0 22 20 0.0000 4 270 1275 1980 5490 SS:Tau_1\001
4 1 -1 0 0 22 20 0.0000 4 195 150 3375 6390 0\001
4 1 1 1 0 3 26 0.0000 4 360 1110 6705 6885 System\001
4 0 -1 0 0 22 20 0.0000 4 270 1785 9315 2340 SS:Theta_1_r\001
4 0 -1 0 0 22 20 0.0000 4 270 1785 9315 3240 SS:Theta_2_r\001
4 1 1 1 0 3 26 0.0000 4 360 2055 6705 3735 Specification\001
4 1 -1 0 0 22 20 0.0000 4 270 1860 6795 2340 msdP:spec_1\001
4 1 -1 0 0 22 20 0.0000 4 270 1860 6795 3195 msdP:spec_2\001
4 2 -1 0 0 22 20 0.0000 4 270 1260 4005 2340 SS:Ref_1\001
4 2 -1 0 0 22 20 0.0000 4 270 1260 3960 3240 SS:Ref_2\001

% -*-latex-*- Put EMACS into LaTeX-mode
% Verbal description for system TwoLinkGPC (TwoLinkGPC_desc.tex)
% Generated by MTT on Wed Apr 15 18:15:23 BST 1998.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.1  1998/04/15 18:41:58  peterg
% %% Initial revision
% %%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   The acausal bond graph of system \textbf{TwoLinkGPC} is
   displayed in Figure \Ref{TwoLinkGPC_abg} and its label
   file is listed in Section \Ref{sec:TwoLinkGPC_lbl}.
   The subsystems are listed in Section \Ref{sec:TwoLinkGPC_sub}.
   
   This example provides an illustration of nonlinear generalised
   predictive control (GPC) (continuous-time) operating on a twolink
   manipulator with a modified sensor.  The  sensor is modified in a
   rather contrived way to give a nonlinear system with an
   \emph{unstable} inverse. The idea is that the sensor approximates a
   pure delay of $\tau$ as:
   \begin{equation}
     e^{-s\tau} \approx 1 - s \tau
   \end{equation}
   
   The example contrasts GPC with GMV, which can also be interpreted
   as:
\begin{itemize}
\item the exact linearisation (by feedback) followed by a
  pole-placement design on the resulting linear system and
\item a special case of generalised predictive control (GPC) were the
  prediction horizon is zero and the $P(s)$ polynomial is the same as
  the system relative degree and
\end{itemize}


The composite system of Figure \Ref{TwoLinkGPC_abg} has three
(visible) parts:
\begin{enumerate}
\item a linear decoupled \emph{specification} system that describes the desired
  closed-loop system in terms of a physical system (two decoupled
  mass-spring-damper systems),
\item the system itself (a two-link manipulator) representing the
  system to be controlled, more details are given in Sections
  \Ref{sec:TwoLinkP_ode.tex} and \Ref{sec:TwoLinkP_rfe.tex}.
\item a model of the system with additional state inputs to be used as
  a state observer.
\end{enumerate}
The invisible parts are implemented in the text file
``TwoLinkGPC\_input.txt'' (see Section \Ref{sec:TwoLinkGPC_input.txt}).
These parts are:
\begin{itemize}
\item the reference signal (joint angles)
  \begin{equation}
    w(t) = 
    \begin{cases}
      \begin{pmatrix}
        \pi \\
        0
      \end{pmatrix} & 0 \ge t > 10 \\
      \begin{pmatrix}
        2\pi \\
        0
      \end{pmatrix} & 10 \ge t > 15 \\
      \begin{pmatrix}
        2\pi \\
        \pi
      \end{pmatrix} & 15 \ge t > 30 \\
    \end{cases}
  \end{equation}
\item The control signal (joint torques) being the solution of 
  \begin{equation}
    \phi^*(t) = O_o(\hat x(t)) + O_h(\hat x(t)) u(t) = w(t)
  \end{equation}
where $\hat x$ is the observed state.
\item The observer feedback signal
  \begin{equation}
    u_x = K ( y - \hat y)
  \end{equation}
where $K$ is the observer gain matrix and $y$ and $\hat y$ are the
system and model outputs respectively.
\end{itemize}
The observer gain is set up on the basis of the \emph{linearised}
system using LQ theory. This is implemented in the text file
``TwoLinkGPC\_state.txt'' (see Section \Ref{sec:TwoLinkGPC_state.txt})
using the Octave function ``lqe'' together with the MTT-generated
linearised system ``TwoLink\_sm''.


The system was simulated using Octave under MTT with the results given
in Figures
\Ref{fig:TwoLinkGPC_odeso.ps-TwoLinkGPC-Theta-1,TwoLinkGPC-Theta-1-r}
and
\Ref{fig:TwoLinkGPC_odeso.ps-TwoLinkGPC-Theta-2,TwoLinkGPC-Theta-2-r}
giving the actual and specification angles for joints 1 and 2
respectively.

The initial \emph{system} state was zero except that the angle of the
first rod was $\frac{\pi}{4}$. The initial \emph{observer} state was
(erroneously but deliberately) set at zero. This explains the
(decaying) discrepancy between the actual and specification angles.
Simulations with zero initial state gave precise matching.

%%% Local Variables: 
%%% mode: latex
%%% TeX-master: t
%%% End: 

%% Tex file (TwoLinkGPC_input.txt)
%% Generated by MTT at Wed Apr 29 11:21:32 BST 1998
\begin{verbatim}
# Numerical parameter file (TwoLinkGPC_input.txt)
# Generated by MTT at Mon Apr 13 11:02:37 BST 1998

# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% Version control history
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% $Id$
# %% $Log$
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

global ObserverGain;

if t<10
  tau = 0;
elseif t<20
  tau = 0.1;
else
  tau = 0.2;
end

# Reference signals
Period = 20;
u(1) =	 -pi*sign(cos(2*pi*t/Period))*(t>5); # TwoLinkGPC (Ref_1)
u(2) =	 pi*sign(sin(2*pi*t/Period)); # TwoLinkGPC (Ref_2)
w = u(1:2);			      # Reference signal

# Control signals
x_model = x(9:12);		# Observed states
[O_o, O_h] = TwoLinkPS_obs(x_model) #GPC O function (affine case)
[spec_n,spec_d] = msdP_tf;	# Spec transfer function
P = spec_d(3:-1:1);		# P poly with ascending coeffs
PP = [eye(2)*P(1) eye(2)*P(2) eye(2)*P(3)]; # Matrix version
PO_o = PP*O_o;			# Compute Py with u zero
PO_h = PP*O_h;			# Coefficient of u
u_control =  PO_h\(w - PO_o);	# GMV control signal

u(3:4) = u_control;		# TwoLinkGPC (Tau_1)

# Observer
x_system = x(5:8);		# System states
error = x_system-x_model;	# Error in states
ObserverInput = ObserverGain*error;
u(5:8) = ObserverInput;		# Set the state-input to the observer

\end{verbatim}

# Numerical parameter file (TwoLinkGPC_input.txt)
# Generated by MTT at Mon Apr 13 11:02:37 BST 1998

# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% Version control history
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% $Id$
# %% $Log$
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

global ObserverGain;

if t<10
  tau = 0;
else
  tau = 0.1;
end

# Reference signals
Period = 20;
u(1) =	 -pi*sign(cos(2*pi*t/Period))*(t>5); # TwoLinkGPC (Ref_1)
u(2) =	 pi*sign(sin(2*pi*t/Period)); # TwoLinkGPC (Ref_2)
w = u(1:2);			      # Reference signal

# Control signals
x_model = x(9:12);		# Observed states
[O_o, O_h] = TwoLinkPS_obs(x_model) #GPC O function (affine case)
[spec_n,spec_d] = msdP_tf;	# Spec transfer function
P = spec_d(3:-1:1);		# P poly with ascending coeffs
PP = [eye(2)*P(1) eye(2)*P(2) eye(2)*P(3)]; # Matrix version
PO_o = PP*O_o;			# Compute Py with u zero
PO_h = PP*O_h;			# Coefficient of u
u_control =  PO_h\(w - PO_o);	# GMV control signal

u(3:4) = u_control;		# TwoLinkGPC (Tau_1)

# Observer
x_system = x(5:8);		# System states
error = x_system-x_model;	# Error in states
ObserverInput = ObserverGain*error;
u(5:8) = ObserverInput;		# Set the state-input to the observer

%SUMMARY TwoLinkGPC - GPC control of two-link manipulator with delay
%DESCRIPTION This composite system provides an illustration
%DESCRIPTION of nonlinear GPC (Generalised Predictive Control) control
%DESCRIPTION (continuous-time) operating on a twolink manipulator. 

%% Label file for system TwoLinkGPC (TwoLinkGPC_lbl.txt)

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.1  1998/04/29 09:01:43  peterg
% %% Initial revision
% %%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Each line should be of one of the following forms:
%	a comment (ie starting with %)
%	Component-name	CR_name	arg1,arg2,..argn
%	blank



% Component type SS
	Ref_1		SS	external,internal
	Ref_2		SS	external,internal
	Tau_1		SS	external,internal
	Tau_2		SS	external,internal
	Theta_1		SS	external,0
	Theta_2		SS	external,0
	Theta_1_m	SS	external,0
	Theta_2_m	SS	external,0
	Theta_1_r	SS	external,0
	Theta_2_r	SS	external,0

% Component type msdP
	spec_1
	spec_2

% Component type TwoLinkP
	system

% Component type TwoLinkPX
	model

# Numerical parameter file (TwoLinkGPC_numpar.txt)
# Generated by MTT at Mon Apr 13 10:57:02 BST 1998

# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% Version control history
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% $Id$
# %% $Log$
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

# Parameters
c_s = 	1.0; # msdP
j_s = 	1.0; # msdP
r_s = 	2.0; # msdP
tau =   0.1; # msdP
l_r = 	0.5; # TwoLinkP,TwoLinkPX
m_r = 	1.0; # TwoLinkP,TwoLinkPX
j_r = 	m_r*l_r*l_r/3; # TwoLinkP,TwoLinkPX

%% Reduce  GPC observability function parameters for system TwoLinkGPC (TwoLinkGPC_obspar.r)

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
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% %% $Id$
% %% $Log$
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MTTGPCNy := 2;
MTTGPCNu := 0;
Matrix MTTdU(5,1);
MTTdU(1,1) := MTTdU1;
MTTdU(2,1) := MTTdU2;
MTTdU(3,1) := MTTdU3;
MTTdU(4,1) := MTTdU4;
MTTdU(5,1) := MTTdU5;
Matrix MTTUU(2,5);
MTTUU(1,1) := MTTu1;
MTTUU(1,2) := MTTu11;
MTTUU(1,3) := MTTu12;
MTTUU(1,4) := MTTu13;
MTTUU(1,5) := MTTu14;
MTTUU(2,1) := MTTu2;
MTTUU(2,2) := MTTu21;
MTTUU(2,3) := MTTu22;
MTTUU(2,4) := MTTu23;
MTTUU(2,5) := MTTu24;
END;

# Outline report file for system TwoLinkGPC (TwoLinkGPC_rep.txt)

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

mtt TwoLinkGPC abg tex
mtt TwoLinkGPC struc tex
mtt TwoLinkGPC sympar tex

mtt TwoLinkPS struc tex
mtt TwoLinkPS rfe tex
mtt TwoLinkPS ode tex
mtt TwoLinkPS obs tex

mtt TwoLinkPS ss tex
mtt TwoLinkPS sm tex

mtt msdP tf tex

mtt TwoLinkGPC numpar txt
mtt TwoLinkGPC state txt
mtt TwoLinkGPC input txt

mtt TwoLinkGPC odeso ps 'TwoLinkGPC_Theta_1,TwoLinkGPC_Theta_1_r'
mtt TwoLinkGPC odeso ps 'TwoLinkGPC_Theta_2,TwoLinkGPC_Theta_2_r'

%% Simulation parameters for system TwoLinkGPC (TwoLinkGPC_simpar.txt)

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

LAST=30
DT=0.1
STEPFACTOR=2

%% Simulation parameters for system TwoLinkGPC (TwoLinkGPC_simpar.txt)

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

LAST=30
DT=0.1
STEPFACTOR=2

# Numerical parameter file (TwoLinkGPC_state.txt)
# Generated by MTT at Thu Apr 23 09:10:43 BST 1998

# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% Version control history
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% $Id$
# %% $Log$
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

global ObserverGain;

# Set the states
x(1) =	 0 ; # TwoLinkGPC_spec_1 (c_s)
x(2) =	 0 ; # TwoLinkGPC_spec_1 (j_s)
x(3) =	 0 ; # TwoLinkGPC_spec_2 (c_s)
x(4) =	 0 ; # TwoLinkGPC_spec_2 (j_s)
x(5) =	 0 ; # TwoLinkGPC_system_rod1 (J)
x(6) =	 0 ; # TwoLinkGPC_system_rod1_th (3)
x(7) =	 0 ; # TwoLinkGPC_system_rod2 (J)
x(8) =	 0 ; # TwoLinkGPC_system_rod2_th (3)
x(9) =	 0 ; # TwoLinkGPC_model_rod1_J (i)
x(10) =	 0 ; # TwoLinkGPC_model_rod1_th_c (c)
x(11) =	 0 ; # TwoLinkGPC_model_rod2_J (i)
x(12) =	 0 ; # TwoLinkGPC_model_rod2_th_c (c)

# Observer design
[A,B,C] = TwoLinkPS_sm;		# Get the linearised system
sigma = 0.1;			# Measurement noise variance (pretend)
k = lqe(A,eye(4),C,eye(4),sigma*eye(2))
ObserverGain = k*C;		# This system happens to have a linear output

#FIG 3.1
Portrait
Center
Metric
1200 2
1 3 0 2 1 7 1 0 -1 0.000 1 0.0000 8550 1125 485 485 8550 1125 8730 1575
1 3 0 2 1 7 1 0 -1 0.000 1 0.0000 8550 5625 485 485 8550 5625 9035 6110
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 3468 1128 3738 1128
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 5720 1130 5990 1130
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 4593 2703 4863 2703
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4728 1128 4728 2703 4953 2478
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 4502 5492 4502 5762
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2927 5627 4502 5627 4277 5852
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4726 5851 4726 7426 4951 7201
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 3472 8647 3742 8647
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 4597 8647 4867 8647
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 5724 8649 5994 8649
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4730 8645 4730 10220 4955 9995
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5855 8645 5855 10220 6080 9995
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3601 3826 3601 7426 3826 7201
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5851 3826 5851 7426 6076 7201
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 6525 8775 6525 7200 2925 7200 2925 8775 6525 8775
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 6525 2025 6525 450 2925 450 2925 2025 6525 2025
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 6525 6435 6525 4860 2925 4860 2925 6435 6525 6435
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 6525 11250 6525 9675 2925 9675 2925 11250 6525 11250
2 4 0 1 31 7 1 0 -1 0.000 0 0 7 0 0 5
	 9450 11475 9450 225 180 225 180 11475 9450 11475
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3603 1128 3603 2703 3828 2478
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5853 1128 5853 2703 6078 2478
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4726 3826 4726 5401 4951 5176
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 6525 4050 2925 4050 2925 2475 6525 2475 6525 4050
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3600 8622 3600 10197 3825 9972
2 4 0 2 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 8775 5175 8775 1575 8325 1575 8325 5175 8775 5175
2 4 0 2 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 8775 9675 8775 6075 8325 6075 8325 9675 8775 9675
2 2 0 2 1 7 1 0 -1 0.000 0 0 0 0 0 5
	 7650 450 9405 450 9405 675 7650 675 7650 450
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3150 3285 1575 3285 1800 3510
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3195 8055 1620 8055 1845 8280
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 1350 3150 1350 2025 1575 2250
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 1350 8325 1350 9450 1575 9225
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 1350 7875 1350 3600 1575 3825
4 1 -1 0 0 0 20 0.0000 4 255 810 3603 948 SS:v_x\001
4 0 -1 0 0 0 20 0.0000 4 195 135 4683 5718 0\001
4 1 -1 0 0 0 20 0.0000 4 255 840 3608 10673 SS:F_x\001
4 1 -1 0 0 0 20 0.0000 4 255 840 4733 10673 SS:F_a\001
4 1 -1 0 0 0 20 0.0000 4 255 840 5903 10673 SS:F_y\001
4 1 -1 0 0 0 20 0.0000 4 195 1335 4729 3379 RODaX:rod1\001
4 1 -1 0 0 0 20 0.0000 4 195 1335 4731 8196 RODaX:rod2\001
4 1 4 0 0 0 20 0.0000 4 255 1410 4771 946 SS:[Joint_1]\001
4 0 1 1 0 3 20 0.0000 4 210 720 6795 3375 Link 1\001
4 0 1 1 0 3 20 0.0000 4 225 795 6750 5760 Joint 2\001
4 0 1 1 0 3 20 0.0000 4 210 720 6750 8190 Link 2\001
4 0 1 1 0 3 20 0.0000 4 270 375 6750 10485 Tip\001
4 0 1 1 0 3 20 0.0000 4 225 795 6750 1260 Joint 1\001
4 1 4 0 0 0 16 0.0000 4 225 900 4725 2970 [alpha_a]\001
4 1 4 0 0 0 16 0.0000 4 210 510 3600 3780 [x_b]\001
4 1 4 0 0 0 16 0.0000 4 225 915 4725 3780 [alpha_b]\001
4 1 4 0 0 0 16 0.0000 4 225 510 5850 3780 [y_b]\001
4 1 4 0 0 0 16 0.0000 4 225 495 5850 2970 [y_a]\001
4 1 4 0 0 0 16 0.0000 4 210 495 3605 7835 [x_a]\001
4 1 4 0 0 0 16 0.0000 4 225 900 4730 7835 [alpha_a]\001
4 1 4 0 0 0 16 0.0000 4 225 495 5855 7835 [y_a]\001
4 1 4 0 0 0 16 0.0000 4 210 510 3607 8512 [x_b]\001
4 1 4 0 0 0 16 0.0000 4 225 915 4733 8513 [alpha_b]\001
4 1 4 0 0 0 16 0.0000 4 225 510 5859 8514 [y_b]\001
4 1 -1 0 0 0 20 0.0000 4 255 810 5850 945 SS:v_y\001
4 2 4 0 0 0 20 0.0000 4 255 1410 2882 5717 SS:[Joint_2]\001
4 1 4 0 0 0 16 0.0000 4 210 495 3600 2970 [x_a]\001
4 1 4 0 0 0 16 0.0000 4 225 675 3510 3375 [alpha]\001
4 1 4 0 0 0 16 0.0000 4 225 675 3555 8145 [alpha]\001
4 0 -1 0 0 0 20 0.0000 4 195 135 1308 8193 1\001
4 1 4 0 0 0 20 0.0000 4 255 1530 1397 1892 SS:[Theta_1]\001
4 1 4 0 0 0 20 0.0000 4 255 1530 1352 9767 SS:[Theta_2]\001
4 0 -1 0 0 0 20 0.0000 4 195 135 1263 3468 0\001

% Verbal description for system TwoLinkPSX (TwoLinkPSX_desc.tex)
% Generated by MTT on Fri Jun 13 16:30:23 BST 1997.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.1  1998/01/19 14:20:07  peterg
% %% Initial revision
% %%
% Revision 1.1  1997/08/15  13:31:00  peterg
% Initial revision
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   The acausal bond graph of system \textbf{TwoLinkPSX} is
   displayed in Figure \Ref{TwoLinkPSX_abg} and its label
   file is listed in Section \Ref{sec:TwoLinkPSX_lbl}.
   The subsystems are listed in Section \Ref{sec:TwoLinkPSX_sub}.

This is a heirachical version of the example from Section 10.5 of
"Metamodelling".  It uses the compound components: {\bf ROD}.  {\bf
ROD} is essentially as described in Figure 10.2.
There is no gravity included in this model.

This system has a number of dynamic elements (those corresponding to translation
motion) in derivative causality, thus the system is represnted as a
Differential-Algebraic Equation (Section
\Ref{sec:TwoLinkPSX_dae.tex}). Hovever, this is of contrained-state form and
therfore can be written as a set of constrained-state equations (Section
\Ref{sec:TwoLinkPSX_cse.tex}). The corresponding ordinary differential
equation is complicated due to the trig functions involved in
inverting the E matrix.

As well as the standard representation the ``robot-form'' equations
appear in Section  \Ref{sec:TwoLinkPSX_rfe}. 

%%% Local Variables: 
%%% mode: plain-tex
%%% TeX-master: t
%%% End: 

%SUMMARY TwoLinkPSX: two-link manipulator from Section 10.5 of "Metamodelling"
%DESCRIPTION This is a heirachical version of the 
%DESCRIPTION example from Section 10.5 of "Metamodelling".
%DESCRIPTION It uses two compound components: ROD and GRA
%DESCRIPTION ROD is essentially as described in Figure 10.2
%DESCRIPTION GRAV represents gravity by a vertical accelleration
%DESCRIPTION as in Section 10.9 of "Metamodelling"


%% Label (TwoLinkPSX_lbl.txt)

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.2  1996/12/05  12:39:49  peterg
% %% Documentation
% %%
% %% Revision 1.1  1996/12/05 12:17:15  peterg
% %% Initial revision
% %%
% %% Revision 1.1  1996/11/14  10:48:42  peterg
% %% Initial revision
% %%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Each line should be of one of the following forms:
%	a comment (ie starting with %)
%	Component-name	CR_name	arg1,arg2,..argn
%	blank

%Rod parameters - uniform rods
rod1	none	l_r;l_r;j_r;m_r
rod2	none	l_r;l_r;j_r;m_r

%Zero velocity sources
v_x	SS     internal,0
v_y	SS     internal,0


%Zero force/torque sources
F_x	SS	   0,internal
F_a	SS	   0,internal
F_y	SS	   0,internal

%Named ports
[Joint_1]		SS	external,internal
[Joint_2]		SS	external,internal
[Theta_1]		SS	external,0
[Theta_2]		SS	external,0

%Torque/velocity at joints
%f_a1	SS	 external,external
%f_a2	SS	 external,external

#FIG 3.1
Portrait
Center
Metric
1200 2
1 3 0 2 1 7 1 0 -1 0.000 1 0.0000 11700 1800 485 485 11700 1800 11880 2250
1 3 0 2 1 7 1 0 -1 0.000 1 0.0000 11700 6300 485 485 11700 6300 12185 6785
2 4 0 1 31 7 1 0 -1 0.000 0 0 7 0 0 5
	 11745 11925 11745 450 45 450 45 11925 11745 11925
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 5
	 7650 900 4725 900 4725 3375 3375 3375 3600 3600
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4950 8505 4950 4230 5175 4455
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2925 6300 4052 6302 3827 6527
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 4
	 4275 6525 4275 8325 3150 8325 3375 8550
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4500 6300 7652 6300 7427 6525
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 6618 1803 6888 1803
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 8870 1805 9140 1805
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 7743 3378 8013 3378
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 7878 1125 7878 3378 8103 3153
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2
	 7652 6167 7652 6437
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 7876 6526 7876 8101 8101 7876
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 6622 9322 6892 9322
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 7747 9322 8017 9322
2 1 0 1 25 7 0 0 -1 0.000 0 0 -1 0 0 2
	 8874 9324 9144 9324
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 7880 9320 7880 10895 8105 10670
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 9005 9320 9005 10895 9230 10670
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 6751 4501 6751 8101 6976 7876
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 9001 4501 9001 8101 9226 7876
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 9675 9450 9675 7875 6075 7875 6075 9450 9675 9450
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 9675 7110 9675 5535 6075 5535 6075 7110 9675 7110
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 9675 11925 9675 10350 6075 10350 6075 11925 9675 11925
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 6753 1803 6753 3378 6978 3153
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 9003 1803 9003 3378 9228 3153
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 7876 4501 7876 6076 8101 5851
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 9675 4725 6075 4725 6075 3150 9675 3150 9675 4725
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 6750 9297 6750 10872 6975 10647
2 4 0 2 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 11925 5850 11925 2250 11475 2250 11475 5850 11925 5850
2 4 0 2 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 11925 10350 11925 6750 11475 6750 11475 10350 11925 10350
2 2 0 2 1 7 1 0 -1 0.000 0 0 0 0 0 5
	 10800 1125 12555 1125 12555 1350 10800 1350 10800 1125
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 9630 2745 9630 1170 6030 1170 6030 2745 9630 2745
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 8910 900 8145 900 8370 1125
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2790 3735 2115 3735 2340 3960
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4725 3960 3330 3960 3555 4185
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 6525 3960 5040 3960 5265 4185
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2700 8550 2025 8550 2250 8775
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4500 8775 3150 8775 3375 9000
2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 7200 8775 4905 8775 5130 9000
4 0 -1 0 0 0 20 0.0000 4 195 135 4863 4053 0\001
4 2 4 0 0 0 20 0.0000 4 255 1410 2702 6392 SS:[Joint_2]\001
4 0 -1 0 0 0 20 0.0000 4 195 135 4188 6393 1\001
4 1 -1 0 0 0 20 0.0000 4 255 810 6753 1623 SS:v_x\001
4 0 -1 0 0 0 20 0.0000 4 195 135 7833 6393 0\001
4 1 -1 0 0 0 20 0.0000 4 255 840 6758 11348 SS:F_x\001
4 1 -1 0 0 0 20 0.0000 4 255 840 7883 11348 SS:F_a\001
4 1 -1 0 0 0 20 0.0000 4 255 840 9053 11348 SS:F_y\001
4 0 1 1 0 3 20 0.0000 4 210 720 9945 4050 Link 1\001
4 0 1 1 0 3 20 0.0000 4 225 795 9900 6435 Joint 2\001
4 0 1 1 0 3 20 0.0000 4 210 720 9900 8865 Link 2\001
4 0 1 1 0 3 20 0.0000 4 270 375 9900 11160 Tip\001
4 0 1 1 0 3 20 0.0000 4 225 795 9900 1935 Joint 1\001
4 1 4 0 0 0 16 0.0000 4 225 900 7875 3645 [alpha_a]\001
4 1 4 0 0 0 16 0.0000 4 210 510 6750 4455 [x_b]\001
4 1 4 0 0 0 16 0.0000 4 225 915 7875 4455 [alpha_b]\001
4 1 4 0 0 0 16 0.0000 4 225 510 9000 4455 [y_b]\001
4 1 4 0 0 0 16 0.0000 4 225 495 9000 3645 [y_a]\001
4 1 4 0 0 0 16 0.0000 4 210 495 6755 8510 [x_a]\001
4 1 4 0 0 0 16 0.0000 4 225 900 7880 8510 [alpha_a]\001
4 1 4 0 0 0 16 0.0000 4 210 510 6757 9187 [x_b]\001
4 1 4 0 0 0 16 0.0000 4 225 915 7883 9188 [alpha_b]\001
4 1 -1 0 0 0 20 0.0000 4 255 810 9000 1620 SS:v_y\001
4 1 4 0 0 0 16 0.0000 4 210 495 6750 3645 [x_a]\001
4 0 -1 0 0 0 20 0.0000 4 195 135 7788 993 1\001
4 0 4 0 0 0 20 0.0000 4 255 1410 9046 991 SS:[Joint_1]\001
4 2 4 0 0 0 20 0.0000 4 255 1530 1892 3827 SS:[Theta_1]\001
4 1 4 0 0 0 16 0.0000 4 210 240 2700 3555 [s]\001
4 1 -1 0 0 0 20 1.5708 4 195 780 3154 3731 Sensor\001
4 1 4 0 0 0 16 0.0000 4 225 270 3420 3825 [p]\001
4 1 4 0 0 0 16 0.0000 4 210 270 3330 3195 [v]\001
4 1 -1 0 0 0 20 0.0000 4 195 1335 7879 4009 RODa:rod1\001
4 1 4 0 0 0 16 0.0000 4 225 675 6885 4005 [alpha]\001
4 1 4 0 0 0 16 0.0000 4 210 270 3375 8235 [v]\001
4 1 4 0 0 0 16 0.0000 4 210 240 2655 8460 [s]\001
4 1 -1 0 0 0 20 1.5708 4 195 780 3064 8546 Sensor\001
4 2 4 0 0 0 20 0.0000 4 255 1530 1937 8642 SS:[Theta_2]\001
4 1 4 0 0 0 16 0.0000 4 225 270 3375 8730 [p]\001
4 1 4 0 0 0 16 0.0000 4 225 495 8780 8510 [y_a]\001
4 1 4 0 0 0 16 0.0000 4 225 510 8739 9189 [y_b]\001
4 1 4 0 0 0 16 0.0000 4 225 675 7065 8820 [alpha]\001
4 1 -1 0 0 0 20 0.0000 4 195 1335 8061 8826 RODa:rod2\001
4 0 -1 0 0 0 20 0.0000 4 195 135 4593 8823 1\001

% Verbal description for system TwoLinkPS (TwoLinkPS_desc.tex)
% Generated by MTT on Fri Jun 13 16:30:23 BST 1997.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.1  1998/01/19 14:20:07  peterg
% %% Initial revision
% %%
% Revision 1.1  1997/08/15  13:31:00  peterg
% Initial revision
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   The acausal bond graph of system \textbf{TwoLinkPS} is
   displayed in Figure \Ref{TwoLinkPS_abg} and its label
   file is listed in Section \Ref{sec:TwoLinkPS_lbl}.
   The subsystems are listed in Section \Ref{sec:TwoLinkPS_sub}.

This is a heirachical version of the example from Section 10.5 of
"Metamodelling".  It uses the compound components: {\bf ROD}.  {\bf
ROD} is essentially as described in Figure 10.2.
There is no gravity included in this model.

This system has a number of dynamic elements (those corresponding to translation
motion) in derivative causality, thus the system is represnted as a
Differential-Algebraic Equation (Section
\Ref{sec:TwoLinkPS_dae.tex}). Hovever, this is of contrained-state form and
therfore can be written as a set of constrained-state equations (Section
\Ref{sec:TwoLinkPS_cse.tex}). The corresponding ordinary differential
equation is complicated due to the trig functions involved in
inverting the E matrix.

As well as the standard representation the ``robot-form'' equations
appear in Section  \Ref{sec:TwoLinkPS_rfe}. 

%%% Local Variables: 
%%% mode: plain-tex
%%% TeX-master: t
%%% End: 

%SUMMARY TwoLinkPS: two-link manipulator from Section 10.5 of "Metamodelling"
%DESCRIPTION This is a heirachical version of the 
%DESCRIPTION example from Section 10.5 of "Metamodelling".
%DESCRIPTION It uses two compound components: ROD and GRA
%DESCRIPTION ROD is essentially as described in Figure 10.2
%DESCRIPTION GRAV represents gravity by a vertical accelleration
%DESCRIPTION as in Section 10.9 of "Metamodelling"


%% Label (TwoLinkPS_lbl.txt)

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.2  1996/12/05  12:39:49  peterg
% %% Documentation
% %%
% %% Revision 1.1  1996/12/05 12:17:15  peterg
% %% Initial revision
% %%
% %% Revision 1.1  1996/11/14  10:48:42  peterg
% %% Initial revision
% %%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Each line should be of one of the following forms:
%	a comment (ie starting with %)
%	Component-name	CR_name	arg1,arg2,..argn
%	blank

%Rod parameters - uniform rods
rod1	none	l_r;l_r;j_r;m_r
rod2	none	l_r;l_r;j_r;m_r

%Zero velocity sources
v_x	SS     internal,0
v_y	SS     internal,0


%Zero force/torque sources
F_x	SS	   0,internal
F_a	SS	   0,internal
F_y	SS	   0,internal

%Named ports
[Joint_1]		SS	external,internal
[Joint_2]		SS	external,internal
[Theta_1]		SS	external,0
[Theta_2]		SS	external,0

%Torque/velocity at joints
%f_a1	SS	 external,external
%f_a2	SS	 external,external

%% Reduce  GPC observability function parameters for system TwoLinkPS (TwoLinkPS_obspar.r)

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

MTTGPCNy := 2;
MTTGPCNu := 0;
Matrix MTTdU(5,1);
MTTdU(1,1) := MTTdU1;
MTTdU(2,1) := MTTdU2;
MTTdU(3,1) := MTTdU3;
MTTdU(4,1) := MTTdU4;
MTTdU(5,1) := MTTdU5;
Matrix MTTUU(2,5);
MTTUU(1,1) := MTTu1;
MTTUU(1,2) := MTTu11;
MTTUU(1,3) := MTTu12;
MTTUU(1,4) := MTTu13;
MTTUU(1,5) := MTTu14;
MTTUU(2,1) := MTTu2;
MTTUU(2,2) := MTTu21;
MTTUU(2,3) := MTTu22;
MTTUU(2,4) := MTTu23;
MTTUU(2,5) := MTTu24;
END;

%% Reduce commands to simplify output for system TwoLinkP (TwoLinkP_simp.r)

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

LET cos(mttx2) = c_2;
LET sin(mttx2) = s_2;

LET cos(mttx4) = c_4;
LET sin(mttx4) = s_4;

LET cos(mttx2-mttx4) = c;
LET sin(mttx2-mttx4) = s;

END;

%% Reduce  substitution statements for system TwoLinkPSX (TwoLinkPSX_subs.r)

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.2  1998/03/22 20:13:25  peterg
% %% Trig simplification added
% %%
% %% Revision 1.1  1998/03/22 20:12:51  peterg
% %% Initial revision
% %%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

        trig1 := {cos(~x)*cos(~y) => (cos(x+y)+cos(x-y))/2,
                  cos(~x)*sin(~y) => (sin(x+y)-sin(x-y))/2,
                  sin(~x)*sin(~y) => (cos(x-y)-cos(x+y))/2,
                  cos(~x)^2       => (1+cos(2*x))/2,
                  sin(~x)^2       => (1-cos(2*x))/2};
       LET trig1;

END;

#FIG 3.1
Portrait
Center
Metric
1200 2
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3825 4050 4950 4050 4725 4275
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3600 4275 3600 5400 3825 5175
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2250 4050 3375 4050 3150 4275
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5400 4050 6525 4050 6300 4275
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5175 3825 5175 2700 5400 2925
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3600 3825 3600 2700 3825 2925
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 6975 4050 8100 4050 7875 4275
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 9000 4050 10125 4050 9900 4275
2 4 0 2 31 7 1 0 -1 0.000 0 0 7 0 0 5
	 11475 6975 11475 1125 1125 1125 1125 6975 11475 6975
4 1 -1 0 0 0 20 0.0000 4 195 135 3600 4185 1\001
4 2 4 0 0 0 20 0.0000 4 240 810 2160 4140 SS:[in]\001
4 1 -1 0 0 0 20 0.0000 4 255 480 3600 5715 I:j_s\001
4 1 1 1 0 0 20 0.0000 4 255 7035 4815 6345 Mass-spring-damper system (position output with extra lag)\001
4 1 -1 0 0 0 20 0.0000 4 195 135 5175 4140 0\001
4 1 -1 0 0 0 20 0.0000 4 255 615 3600 2565 R:r_s\001
4 1 -1 0 0 0 20 0.0000 4 255 630 5175 2565 C:c_s\001
4 1 -1 0 0 0 20 0.0000 4 195 390 6750 4140 AE\001
4 1 -1 0 0 0 20 0.0000 4 195 690 8550 4140 RC:rc\001
4 0 4 0 0 0 20 0.0000 4 240 960 10260 4140 SS:[out]\001

#FIG 3.1
Portrait
Center
Metric
1200 2
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3825 4050 4950 4050 4725 4275
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3600 4275 3600 5400 3825 5175
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2250 4050 3375 4050 3150 4275
2 4 0 2 31 7 1 0 -1 0.000 0 0 7 0 0 5
	 8325 6975 8325 1125 1125 1125 1125 6975 8325 6975
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5400 4050 6525 4050 6300 4275
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5175 3825 5175 2700 5400 2925
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3600 3825 3600 2700 3825 2925
4 1 -1 0 0 0 20 0.0000 4 195 135 3600 4185 1\001
4 2 4 0 0 0 20 0.0000 4 240 810 2160 4140 SS:[in]\001
4 1 -1 0 0 0 20 0.0000 4 255 480 3600 5715 I:j_s\001
4 1 1 1 0 0 20 0.0000 4 255 5355 4815 6345 Mass-spring-damper system (position output)\001
4 1 -1 0 0 0 20 0.0000 4 195 135 5175 4140 0\001
4 0 4 0 0 0 20 0.0000 4 240 960 6660 4140 SS:[out]\001
4 1 -1 0 0 0 20 0.0000 4 255 615 3600 2565 R:r_s\001
4 1 -1 0 0 0 20 0.0000 4 255 630 5175 2565 C:c_s\001

% Verbal description for system msdPS (msdPS_desc.tex)
% Generated by MTT on Thu Nov 13 09:38:17 GMT 1997.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   The acausal bond graph of system \textbf{msdPS} is
   displayed in Figure \Ref{msdPS_abg} and its label
   file is listed in Section \Ref{sec:msdPS_lbl}.
   The subsystems are listed in Section \Ref{sec:msdPS_sub}.


 \textbf{msdPS} is a simple Mass-Spring-Damper system with 
 force input and position output. It is set up to provide a specification system
 for each link of the two-link maipulator. This is appropriate because
 \begin{itemize}
 \item  it has compatible physical behaviour with the system itself,
 \item it specifies two decoupled systems,
 \item it has linear behaviour and
 \item it has a simple performance interpretation in terms of system
   rise-time and overshoot.
 \end{itemize}

%%% Local Variables: 
%%% mode: latex
%%% TeX-master: t
%%% End: 

%SUMMARY msdPS
%DESCRIPTION <Detailed description here>
%% Label file for system msdPS (msdPS_lbl.txt)

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Each line should be of one of the following forms:
%	a comment (ie starting with %)
%	Component-name	CR_name	arg1,arg2,..argn
%	blank



% Component type C
	c_s		lin	effort,c_s

% Component type I
	j_s		lin	flow,j_s

% Component type R
	r_s		lin	flow,r_s

% Component type RC
	rc		none	tau;1

% Component type SS
	[in]		SS	external,internal
	[out]		SS	external,0

#FIG 3.1
Portrait
Center
Metric
1200 2
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3825 4050 4950 4050 4725 4275
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3600 4275 3600 5400 3825 5175
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2250 4050 3375 4050 3150 4275
2 4 0 2 31 7 1 0 -1 0.000 0 0 7 0 0 5
	 8325 6975 8325 1125 1125 1125 1125 6975 8325 6975
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5400 4050 6525 4050 6300 4275
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 5175 3825 5175 2700 5400 2925
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3600 3825 3600 2700 3825 2925
4 1 -1 0 0 0 20 0.0000 4 195 135 3600 4185 1\001
4 2 4 0 0 0 20 0.0000 4 240 810 2160 4140 SS:[in]\001
4 1 -1 0 0 0 20 0.0000 4 255 480 3600 5715 I:j_s\001
4 1 1 1 0 0 20 0.0000 4 255 5355 4815 6345 Mass-spring-damper system (position output)\001
4 1 -1 0 0 0 20 0.0000 4 195 135 5175 4140 0\001
4 0 4 0 0 0 20 0.0000 4 240 960 6660 4140 SS:[out]\001
4 1 -1 0 0 0 20 0.0000 4 255 615 3600 2565 R:r_s\001
4 1 -1 0 0 0 20 0.0000 4 255 630 5175 2565 C:c_s\001

% Verbal description for system msdP (msdP_desc.tex)
% Generated by MTT on Thu Nov 13 09:38:17 GMT 1997.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   The acausal bond graph of system \textbf{msdP} is
   displayed in Figure \Ref{msdP_abg} and its label
   file is listed in Section \Ref{sec:msdP_lbl}.
   The subsystems are listed in Section \Ref{sec:msdP_sub}.


 \textbf{msdP} is a simple Mass-Spring-Damper system with 
 force input and position output. It is set up to provide a specification system
 for each link of the two-link maipulator. This is appropriate because
 \begin{itemize}
 \item  it has compatible physical behaviour with the system itself,
 \item it specifies two decoupled systems,
 \item it has linear behaviour and
 \item it has a simple performance interpretation in terms of system
   rise-time and overshoot.
 \end{itemize}

%%% Local Variables: 
%%% mode: latex
%%% TeX-master: t
%%% End: 

%SUMMARY msdP
%DESCRIPTION <Detailed description here>
%% Label file for system msdP (msdP_lbl.txt)

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Each line should be of one of the following forms:
%	a comment (ie starting with %)
%	Component-name	CR_name	arg1,arg2,..argn
%	blank



% Component type C
	c_s		lin	effort,c_s

% Component type I
	j_s		lin	flow,j_s

% Component type R
	r_s		lin	flow,r_s

% Component type SS
	[in]		SS	external,internal
	[out]		SS	external,0

#FIG 3.2
Portrait
Center
Metric
A4      
100.00
Single
-2
1200 2
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 4275 1800 5400 1800 5175 2025
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 4230 2700 5355 2700 5130 2925
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 5400 1575 5400 2025
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 5400 2475 5400 2925
4 0 0 100 0 18 20 0.0000 4 225 810 5625 1890 SS:z1\001
4 0 0 100 0 18 20 0.0000 4 240 810 5625 2790 SS:z2\001
4 2 4 100 0 18 20 0.0000 4 285 1305 4140 1890 SS:[y_in]\001
4 2 4 100 0 18 20 0.0000 4 285 1860 4140 2790 SS:[theta_in]\001

%% Label file for system Fixed (Fixed_lbl.txt)
%SUMMARY Fixed
%DESCRIPTION <Detailed description here>

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% Port aliases
%ALIAS	in	y_in,theta_in

% Argument aliases

%% 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 SS
	[theta_in]	SS		external,external
	[y_in]		SS		external,external
	z1		SS		internal,0
	z2		SS		internal,0

#FIG 3.2
Portrait
Center
Metric
A4      
100.00
Single
-2
1200 2
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 4275 1800 5400 1800 5175 2025
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 4230 2700 5355 2700 5130 2925
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 5400 1575 5400 2025
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 5400 2475 5400 2925
4 2 0 100 0 18 20 0.0000 4 225 810 4140 1890 SS:z1\001
4 2 0 100 0 18 20 0.0000 4 240 810 4140 2790 SS:z2\001
4 0 4 100 0 18 20 0.0000 4 285 1500 5490 1890 SS:[y_out]\001
4 0 4 100 0 18 20 0.0000 4 285 2055 5445 2790 SS:[theta_out]\001

%% Label file for system Free (Free_lbl.txt)
%SUMMARY Free
%DESCRIPTION <Detailed description here>

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% Port aliases
%ALIAS	out	y_out,theta_out

% Argument aliases

%% 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 SS
	[theta_out]	SS		external,external
	[y_out]		SS		external,external
	z1		SS		0,internal
	z2		SS		0,internal

#!/bin/sh
## Script file Make_figures.

ppp_1("PPPCantileverBeam",1:2,[1 2;1 3]); # 2 inputs; modes 1 2 and 1 and 3

#FIG 3.2
Portrait
Center
Metric
A4      
100.00
Single
-2
1200 2
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 1125 2700 2250 2700 2025 2925
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 8775 2700 9900 2700 9675 2925
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 2700 2700 3825 2700 3600 2925
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 4230 2700 5355 2700 5130 2925
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 4095 6300 4095 4500 4320 4725
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 3870 4500 4320 4500
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 5850 2700 6975 2700 6750 2925
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 7380 2700 8505 2700 8280 2925
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 7245 6300 7245 4500 7470 4725
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 7020 4500 7470 4500
4 1 0 100 0 18 20 1.5708 4 225 630 1035 2700 Free\001
4 1 0 100 0 18 20 1.5708 4 225 780 10260 2700 Fixed\001
4 1 0 100 0 18 20 1.5708 4 285 3690 8775 2700 BernoulliEuler:Chunk_3*3\001
4 1 0 100 0 18 20 1.5708 4 285 3690 2610 2700 BernoulliEuler:Chunk_1*3\001
4 1 0 100 0 18 20 1.5708 4 300 3480 4140 2700 pBernoulliEuler:Patch_1\001
4 1 4 100 0 18 16 0.0000 4 240 900 4095 4455 [torque]\001
4 1 0 100 0 18 20 0.0000 4 285 1275 4050 6660 SS:tau_1\001
4 1 0 100 0 18 20 1.5708 4 285 3690 5760 2700 BernoulliEuler:Chunk_2*8\001
4 1 0 100 0 18 20 1.5708 4 300 3480 7290 2700 pBernoulliEuler:Patch_2\001
4 1 4 100 0 18 16 0.0000 4 240 900 7245 4455 [torque]\001
4 1 0 100 0 18 20 0.0000 4 285 1275 7200 6660 SS:tau_2\001

% -*-latex-*- Put EMACS into LaTeX-mode
% Verbal description for system PPPCantileverBeam (PPPCantileverBeam_desc.tex)
% Generated by MTT on Mon Apr 19 07:04:54 BST 1999.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.1  1999/05/18 04:01:50  peterg
% %% Initial revision
% %%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

The acausal bond graph of system \textbf{PPPCantileverBeam} is displayed in
Figure \Ref{fig:PPPCantileverBeam_abg.ps} and its label file is listed in
Section \Ref{sec:PPPCantileverBeam_lbl}.  The subsystems are listed in Section
\Ref{sec:PPPCantileverBeam_sub}.
   
This example represents the dynamics of a uniform beam with one fixed
and one free end.  The beam is approximated by 16 equal lumps using
the Bernoulli-Euler approximation with damping. The ouputs are taken
to be the 16 lump velocities, the two inputs are taken to be torques
applied to lumps 3 away from each end; this approximates the effect of
two piezoelectric patches.

The system parameters are given in Section
\Ref{sec:PPPCantileverBeam_numpar.tex}.
The system has 32 states (16 modes of vibration), 2 inputs and 12
outputs.
The first 8 modal frequencies are given in Table \ref{tab:modes}.
\begin{table}[htbp]
  \begin{center}
    \begin{tabular}{||c|c||c|c||}
      \hline
      Mode & $\omega_i$ & Mode & $\omega_i$\\
      \hline
      \hline
      1 & 0.0079504 & 5 & 0.4352376\\
      2 & 0.0498140 & 6 & 0.6338899\\
      3 & 0.1386209 & 7 & 0.8573604\\
      4 & 0.2682835 & 8 & 1.0976942\\
      \hline
    \end{tabular}
    \caption{Modal frequencies}
    \label{tab:modes}
  \end{center}
\end{table}

Figure \Ref{fig:PPPCantileverBeam_lmfr.ps} shows the log modulus of the frequency
response and Figure \Ref{fig:PPPCantileverBeam_pppy0.ps} shows the system transient
reponse with no control and an initial unit twist.

Figure \Ref{fig:PPPCantileverBeam_pppy.ps} shows closed loop reponse when
controlled by a PPP controller attempting to damp modes 1 and 2 from
input 1 and modes 1 and three from input 2. Figure
\Ref{fig:PPPCantileverBeam_pppy.ps} shows the corresponding control signals.

# -*-octave-*- Put Emacs into octave-mode
# Input specification (PPPCantileverBeam_input.txt)
# Generated by MTT at Thu Apr 22 00:12:54 BST 1999
###############################################################
## Version control history
###############################################################
## $Id$
## $Log$
###############################################################

# Set the inputs
mttu(1) = exp(-t/0.1); 	# tau (PPPCantileverBeam)

# Set the switches

%% Label file for system PPPCantileverBeam (PPPCantileverBeam_lbl.txt)
%SUMMARY PPPCantileverBeam
%DESCRIPTION <Detailed description here>

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Declare some variables
%VAR Area
%VAR AreaMoment
%VAR BeamLength
%VAR BeamThickness
%VAR BeamWidth
%VAR Density
%VAR N
%VAR Youngs
%VAR EI
%VAR rhoA

% Port aliases

% Argument aliases

%% 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 BenoulliEuler
  Chunk_1
  Patch_1
  Chunk_2
  Patch_2
  Chunk_3


% Component type SS
	tau_1	SS		external,external
	tau_2	SS		external,external

# -*-octave-*- Put Emacs into octave-mode
# Numerical parameter file (PPPCantileverBeam_numpar.txt)
# Generated by MTT at Mon Apr 19 06:24:08 BST 1999

# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% Version control history
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% $Id$
# %% $Log$
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

# Parameters
N = 16;
BeamLength = 0.58;
BeamWidth = 0.05;
BeamThickness = 0.005;
Youngs = 1e6;
Density = 1e5;
Area = BeamWidth*BeamThickness;
AreaMoment = (BeamThickness*BeamWidth^2)/12;


EI= 58.6957			# from Reza
rhoA= 0.7989			# from Reza
 
dz = BeamLength/N;		# Incremental length
dm = rhoA*dz;			# Incremental mass
dk = EI/dz;			# Incremental stiffness
dr = 1e-2;			# Damping

## -*-octave-*- Put Emacs into octave-mode
## Outline report file for system PPPCantileverBeam (PPPCantileverBeam_rep.txt)
## Generated by MTT on" Mon Apr 19 06:43:08 BST 1999.

###############################################################
## Version control history
###############################################################
## $Id$
## $Log$
###############################################################

mtt PPPCantileverBeam abg tex			# The system description
## mtt PPPCantileverBeam cbg ps 		        # The causal bond graph
## Uncomment the following lines or add others
mtt PPPCantileverBeam struc tex	        # The system structure
## mtt PPPCantileverBeam dae tex	        # The system dae
## mtt PPPCantileverBeam ode tex	        # The system ode 
## mtt PPPCantileverBeam sspar tex		# Steady-state parameters
## mtt PPPCantileverBeam ss tex 		# Steady state
## mtt PPPCantileverBeam dm tex		# Descriptor matrices (of linearised system)
## mtt PPPCantileverBeam sm tex		# State matrices (of linearised system)
## mtt PPPCantileverBeam tf tex		# Transfer function (of linearised system)
mtt PPPCantileverBeam simpar tex		# Simulation parameters
mtt PPPCantileverBeam numpar tex		# Numerical simulation parameters
## mtt PPPCantileverBeam input tex		# Simulation input
## mtt PPPCantileverBeam odeso ps		# Simulation output
mtt PPPCantileverBeam lmfr ps		# log modulus of frequency response (of linearised system)

mtt PPPCantileverBeam pppy ps		# PPP output
mtt PPPCantileverBeam pppu ps		# PPP input
mtt PPPCantileverBeam pppy0 ps		# PPP open-loop op

# -*-octave-*- Put Emacs into octave-mode
# Simulation parameters for system PPPCantileverBeam (PPPCantileverBeam_simpar.txt)
# Generated by MTT on Mon Apr 19 06:32:42 BST 1999.
###############################################################
## Version control history
###############################################################
## $Id$
## $Log$
###############################################################


LAST        = 1.0;       # Last time in simulation
DT          = 0.01;        # Print interval
STEPFACTOR  = 10;          # Integration steps per print interval
WMIN        = 1;         # Minimum frequency = 10^WMIN
WMAX        = 4;          # Maximum frequency = 10^WMAX
WSTEPS      = 500;        # Number of frequency steps
INPUT       = 1;          # Index of the input

# -*-octave-*- Put Emacs into octave-mode
# Simulation parameters for system PPPCantileverBeam (PPPCantileverBeam_simpar.txt)
# Generated by MTT on Mon Apr 19 06:32:42 BST 1999.
###############################################################
## Version control history
###############################################################
## $Id$
## $Log$
###############################################################


LAST        = 1.0;       # Last time in simulation
DT          = 0.01;        # Print interval
STEPFACTOR  = 10;          # Integration steps per print interval
METHOD      = Implicit;   # Integration method
WMIN        = 1;         # Minimum frequency = 10^WMIN
WMAX        = 4;          # Maximum frequency = 10^WMAX
WSTEPS      = 500;        # Number of frequency steps
INPUT       = 1;          # Index of the input

function  ppp_1(Name,Inputs,Modes);

# Name = "CantileverBeam"
# Inputs = 1:2
# Modes = [1 2;1 3]

  path(path,"~/Research/CGPC/PPP");  
  
  Name,Inputs,Modes

  ## System
  system(sprintf("mtt -q %s numpar m", Name));
  system(sprintf("mtt -q %s sm m", Name));
  par = eval(sprintf("%s_numpar;",Name));
  eval(sprintf("[A,B,C,D]=%s_sm(par);",Name));
  [n_x,n_u,n_y] = abcddim(A,B,C,D)


  ## Change B
  B = B(:,Inputs);
  [junk,n_u]=size(B);
  n_u

  ## Redo C and D to reveal ALL velocities
   n_y = n_x/2
   C = zeros(n_y,n_x);
   for i = 1:n_y
     C(i,2*i-1) = 1;
   endfor

  ## Sort out D
  D = zeros(n_y,n_u);

  e = eig(A);			# Eigenvalues
  N = length(e);
  frequencies = sort(imag(e));
  frequencies = frequencies(N/2+1:N); # Modal frequencies

  ## Controller
  ## Controller design parameters
  t = [0.9:0.01:1.0];		# Optimisation horizon

  ## Specify input basis functions 
  ##  - damped sinusoids with same frequencies as beam
  damping_ratio = [0.1 0.1];		# Damping ratio of inputs
  A_u=[];
#   Modes = [1  3  
# 	   1  2];		# Choose modes to be controlled by each input 
  if n_u == 1			# Put all modes on each input
    Modes = [Modes; Modes];
  endif
  
  Modes

  for i=Inputs
    A_ui = damped_matrix(frequencies(Modes(i,:)),damping_ratio(i)*ones(size(Modes(i,:))));
    A_u = [A_u;A_ui];
    u_0 = ones(n_x,1);		# Initial conditions
  endfor
  

  A_w = 0;			# Setpoint
  Q = ones(n_y,1);		# Output weighting

  ## Design 
  disp("Control design - unconstrained");
  [k_x,k_w,K_x,K_w,Us0,J_uu,J_ux,J_uw] = ppp_lin  (A,B,C,D,A_u,A_w,t); # Unconstrained design

  ## Organise some plots
   dt = 0.002;		# Time increment
#   T =  0:dt:t(length(t));	# Time starting at zero but past horizon
   T =  0:dt:1.0;		# Time 

  ## Set up an "typical" initial condition
  x_0 = zeros(n_x,1);
  x_0(2:2:n_x) = ones(1,n_x/2);	# Set initial twist to 1.
#  disp("Computing OL response");
#  [Ys,Us] = ppp_transient (T,A_u,-(K_x*x_0)',u_0,A,B,C,D,x_0); # Compute open-loop control
  
  
  disp("Computing OL response (no control)");
  [Y_0] = ppp_sm2sr(A, B, C, D, T, zeros(n_u,1), x_0); # Compute Closed-loop control
  title("Y (no control)");
  xlabel("Time")
  grid; 
  plot(T,Y_0);
  psfig(sprintf("%s_pppy0",Name));

  disp("Computing Unconstrained CL response");
  [y_u,X_u] = ppp_sm2sr(A-B*k_x, B, C, D, T, zeros(n_u,1), x_0);
  u_u = -k_x*X_u';


  title("Unconstrained closed-loop control - y");
  xlabel("Time")
  grid; 
  plot(T,y_u);
  psfig(sprintf("%s_pppy",Name));

  title("Unconstrained closed-loop control - u");
  xlabel("Time")
  grid; 
  plot(T,u_u);
  psfig(sprintf("%s_pppu",Name));

#   ## Constrained version
  
#   ## Constraints - u
#   Tau_u = [0:0.01:1];
#   one = ones(size(Tau_u));
#   limit = 1e10;
#   Min_u = -limit*one;
#   Max_u =  limit*one;
#   Order_u = 0*one;

#   ## Constraints - y
#   Tau_y = [];
#   one = ones(size(Tau_y));
#   limit = 1e5; 
#   Min_y = -limit*one;
#   Max_y =  limit*one;
#   Order_y = 0*one;

#   ## Simulation

#   ## Constrained - open-loop
#   Gamma = [];
#   gamma = [];
#   for i=1:n_u			# Put same constraints on each input
#     [Gamma_i,gamma_i] = ppp_input_constraint (A_u,Tau_u,Min_u,Max_u,Order_u,i,n_u);
#     Gamma = [Gamma; Gamma_i];
#     gamma = [gamma; gamma_i];
#   endfor


#   disp("Open-loop simulations...");
#   ## Constrained OL simulation
#   W = zeros(n_y,1);
#   [u,U] = ppp_qp (x_0,W,J_uu,J_ux,J_uw,Us0,Gamma,gamma);
#   T = [0:t(2)-t(1):t(length(t))];
#   [ys,us] = ppp_ystar (A,B,C,D,x_0,A_u,U,T);

#   title("Constrained y*");
#   xlabel("t");
#   grid;
#   plot(T,ys)

#   ## Unconstrained OL simulation
#   [uu,Uu] = ppp_qp (x_0,W,J_uu,J_ux,J_uw,Us0,[],[]); 
#   [ysu,usu] = ppp_ystar (A,B,C,D,x_0,A_u,Uu,T);

#   title("Unconstrained y*");
#   xlabel("t");
#   grid;
#   plot(T,ysu)

#   ## Non-linear - closed-loop
#   disp("Closed-loop simulation");
#   Tc = [0:4e-4:1.0];	
#   Delta_ol = 1.0;
#   [yc,uc,J] = ppp_qp_sim (A,B,C,D,A_u,A_w,t,Q, T, Tau_u,Min_u,Max_u,Order_u, Tau_y,Min_y,Max_y,Order_y,W,x_0,Delta_ol);

#   title("y,y*,u and u*");
#   xlabel("t");
#   grid;
#   plot(T1,y,T,ys,T1,u,T,us);

endfunction

## Make file for the ppp output rep
## Symlinked to:
##	pppy
##	pppy0
##	pppu

all: $(SYS)_pppy.ps $(SYS)_pppy0.ps $(SYS)_pppu.ps

$(SYS)_pppy.ps: Make_figures.m ppp_1.m $(SYS)_sm.m $(SYS)_numpar.m
	octave Make_figures.m
$(SYS)_pppy0.ps: $(SYS)_pppy.ps
	touch $(SYS)_pppy0.ps
$(SYS)_pppu.ps: $(SYS)_pppy.ps
	touch $(SYS)_pppu.ps

$(SYS)_sm.m: 
	mtt $(SYS) sm m

$(SYS)_numpar.m: 
	mtt $(SYS) numpar m

## Make file for the ppp output rep
## Symlinked to:
##	pppy
##	pppy0
##	pppu

all: $(SYS)_pppy.ps $(SYS)_pppy0.ps $(SYS)_pppu.ps

$(SYS)_pppy.ps: Make_figures.m ppp_1.m $(SYS)_sm.m $(SYS)_numpar.m
	octave Make_figures.m
$(SYS)_pppy0.ps: $(SYS)_pppy.ps
	touch $(SYS)_pppy0.ps
$(SYS)_pppu.ps: $(SYS)_pppy.ps
	touch $(SYS)_pppu.ps

$(SYS)_sm.m: 
	mtt $(SYS) sm m

$(SYS)_numpar.m: 
	mtt $(SYS) numpar m

## Make file for the ppp output rep
## Symlinked to:
##	pppy
##	pppy0
##	pppu

all: $(SYS)_pppy.ps $(SYS)_pppy0.ps $(SYS)_pppu.ps

$(SYS)_pppy.ps: Make_figures.m ppp_1.m $(SYS)_sm.m $(SYS)_numpar.m
	octave Make_figures.m
$(SYS)_pppy0.ps: $(SYS)_pppy.ps
	touch $(SYS)_pppy0.ps
$(SYS)_pppu.ps: $(SYS)_pppy.ps
	touch $(SYS)_pppu.ps

$(SYS)_sm.m: 
	mtt $(SYS) sm m

$(SYS)_numpar.m: 
	mtt $(SYS) numpar m

#FIG 3.2
Portrait
Center
Metric
A4      
100.00
Single
-2
1200 2
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 4747 5175 6097 5175 5872 5400
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 7447 5175 8797 5175 8572 5400
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 2677 5175 4027 5175 3802 5400
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 6772 3375 6772 4725 6997 4500
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 6750 6750 6750 5400 6975 5625
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 6750 8550 6750 7200 6975 7425
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 6750 1575 6750 2925 6975 2700
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 9472 5175 10822 5175 10597 5400
4 1 0 100 0 18 20 0.0000 4 225 405 6750 3240 AE\001
4 1 0 100 0 18 20 0.0000 4 225 405 6750 7110 AE\001
4 1 0 100 0 18 20 0.0000 4 225 405 4365 5265 AE\001
4 1 4 100 0 18 20 0.0000 4 285 975 2115 5265 SS:[in]\001
4 1 4 100 0 18 20 0.0000 4 285 1335 6795 1485 SS:[mod]\001
4 1 4 100 0 18 20 0.0000 4 285 1500 6705 8820 SS:[smod]\001
4 1 0 100 0 18 30 0.0000 4 330 660 6750 5265 R:r\001
4 1 4 100 0 18 14 0.0000 4 210 270 5985 4995 [1]\001
4 1 4 100 0 18 14 0.0000 4 210 270 7560 4995 [2]\001
4 1 4 100 0 18 14 0.0000 4 210 270 6570 4590 [3]\001
4 1 4 100 0 18 14 0.0000 4 210 270 6570 5625 [4]\001
4 1 0 100 0 18 20 0.0000 4 225 405 9135 5265 AE\001
4 1 4 100 0 18 20 0.0000 4 285 1170 11475 5265 SS:[out]\001

%% Label file for system AE3 (AE3_lbl.txt)
%SUMMARY AE3
%DESCRIPTION <Detailed description here>

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% Port aliases
%ALIAS	in	in
%ALIAS	mod	mod
%ALIAS	out	out
%ALIAS	smod	smod

% Argument aliases
%ALIAS	$1	l

% CR aliases
%ALIAS	$1	slsin


%% 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 R
	r		slsin	-1*l

% Component type SS
	[in]	SS		external,external
	[mod]	SS		external,external
	[out]	SS		external,external
	[smod]	SS		external,external

#FIG 3.2
Portrait
Center
Metric
A4      
100.00
Single
-2
1200 2
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 4747 5175 6097 5175 5872 5400
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 7447 5175 8797 5175 8572 5400
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 2677 5175 4027 5175 3802 5400
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 6772 3375 6772 4725 6997 4500
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 6750 6750 6750 5400 6975 5625
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 6750 8550 6750 7200 6975 7425
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 6750 1575 6750 2925 6975 2700
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 9472 5175 10822 5175 10597 5400
4 1 0 100 0 18 20 0.0000 4 225 405 6750 3240 AE\001
4 1 0 100 0 18 20 0.0000 4 225 405 6750 7110 AE\001
4 1 4 100 0 18 20 0.0000 4 285 975 2115 5265 SS:[in]\001
4 1 4 100 0 18 20 0.0000 4 285 1335 6795 1485 SS:[mod]\001
4 1 4 100 0 18 20 0.0000 4 285 1500 6705 8820 SS:[smod]\001
4 1 0 100 0 18 30 0.0000 4 330 660 6750 5265 R:r\001
4 1 4 100 0 18 14 0.0000 4 210 270 5985 4995 [1]\001
4 1 4 100 0 18 14 0.0000 4 210 270 7560 4995 [2]\001
4 1 4 100 0 18 14 0.0000 4 210 270 6570 4590 [3]\001
4 1 4 100 0 18 14 0.0000 4 210 270 6570 5625 [4]\001
4 1 0 100 0 18 20 0.0000 4 225 390 4365 5310 AF\001
4 1 0 100 0 18 20 0.0000 4 225 390 9135 5265 AF\001
4 1 4 100 0 18 20 0.0000 4 285 1170 11610 5265 SS:[out]\001

%% Label file for system AE3 (AE3_lbl.txt)
%SUMMARY AE3
%DESCRIPTION <Detailed description here>

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% Port aliases
%ALIAS	in	in
%ALIAS	mod	mod
%ALIAS	out	out
%ALIAS	smod	smod

% Argument aliases
%ALIAS	$1	l

% CR aliases
%ALIAS	$1	slsin


%% 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 R
	r		slsin	l

% Component type SS
	[in]	SS		external,external
	[mod]	SS		external,external
	[out]	SS		external,external
	[smod]	SS		external,external

#FIG 3.2
Portrait
Center
Metric
A4      
100.00
Single
-2
1200 2
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 3600 4275 4950 4275 4725 4500
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 4950 5400 3600 5400 3825 5625
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 4950 5175 4950 5625
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 3015 3150 4365 3150 4140 3375
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 4815 3150 6165 3150 5940 3375
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 4590 2925 4590 1575 4815 1800
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 4815 1575 4365 1575
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 4793 2934 6153 1574 6153 1893
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 4387 2947 3027 1587 3346 1587
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 7650 3150 9000 3150 8775 3375
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 3600 4050 3600 4500
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 5400 5400 6750 5400 6525 5625
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 6750 5175 6750 5625
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 5400 4275 6750 4275 6525 4500
4 2 0 100 0 18 18 0.0000 4 270 2130 3510 4365 Sf:zero_velocity\001
4 1 1 101 0 3 18 0.0000 4 255 1125 5310 4725 y-velocity\001
4 1 1 101 0 3 18 0.0000 4 255 1155 5265 3735 x-velocity\001
4 1 1 101 0 3 18 0.0000 4 255 1905 5175 5940 angular-velocity\001
4 2 0 100 0 18 18 0.0000 4 270 720 3555 5490 R:r_p\001
4 1 0 100 0 18 18 0.0000 4 195 150 4590 3240 1\001
4 1 4 100 0 18 18 0.0000 4 270 765 6390 1440 SS:[x]\001
4 1 0 100 0 18 18 0.0000 4 270 870 4635 1440 IS:m_c\001
4 1 0 100 0 18 18 0.0000 4 270 690 2880 1440 R:r_c\001
4 1 4 100 0 18 18 0.0000 4 270 1290 2250 3240 SS:[drive]\001
4 0 0 100 0 18 18 0.0000 4 210 1560 9090 3240 De:Position\001
4 1 0 100 0 18 18 0.0000 4 210 1035 6975 3240 INTFS:x\001
4 1 0 100 0 18 18 0.0000 4 195 150 5175 5490 1\001
4 1 4 100 0 18 18 0.0000 4 270 780 7245 5490 SS:[a]\001
4 1 0 100 0 18 18 0.0000 4 195 150 5175 4365 1\001
4 1 4 100 0 18 18 0.0000 4 270 765 7245 4365 SS:[y]\001

%% Label file for system Cart (Cart_lbl.txt)
%SUMMARY Cart
%DESCRIPTION <Detailed description here>

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% Port aliases
%ALIAS	in	drive
%ALIAS	pendulum|out	x,y,a

% Argument aliases
%ALIAS	$1	m_c
%ALIAS	$2	r_c
%ALIAS	$3	r_p

%% 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 IS
	m_c		lin	flow,m_c;v_0

% Component type R
	r_c		lin	flow,r_c
	r_p		lin	flow,r_p

% Component type INTFS
	x               none    x_0

% Component type SS
	[a]	SS		internal,0
	[drive]	SS		external,internal
	[x]	SS		0,internal
	[y]	SS		0,internal

% Component type De
	Position		SS	external

% Component type Sf
	zero_velocity		SS	0

#FIG 3.2
Portrait
Center
Metric
A4      
100.00
Single
-2
1200 2
6 3330 1305 3870 1395
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 3375 1350 3825 1350
-6
6 7965 2475 8505 2565
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 8010 2520 8460 2520
-6
6 3330 2475 3420 3015
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 3375 2520 3375 2970
-6
6 9810 2475 9900 3015
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 9855 2520 9855 2970
-6
6 7965 2430 8055 2970
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 8010 2475 8010 2925
-6
6 3735 2430 3825 2970
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 3780 2475 3780 2925
-6
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 4860 4730 4860 494 2293 494 2293 4730 4860 4730
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 2036 2724 3371 2724 3063 2947
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3576 2501 3576 1342 3833 1609
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3782 2724 5116 2724 4808 2947
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3576 2947 3576 4106 3833 3839
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 6656 2724 7991 2724 7683 2947
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 8196 2947 8196 4106 8453 3839
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 8453 2724 9788 2724 9480 2947
2 4 0 1 1 7 1 0 -1 0.000 0 0 7 0 0 5
	 9480 4730 9480 494 6913 494 6913 4730 9480 4730
2 4 0 1 31 7 1 0 -1 0.000 0 0 7 0 0 5
	 12150 5175 45 5175 45 316 12150 316 12150 5175
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 8190 2501 8190 1341 8447 1609
4 2 4 0 0 0 18 0.0000 4 240 1605 1980 2790 SS:[Electrical]\001
4 1 -1 0 0 0 18 0.0000 4 195 135 3525 2858 1\001
4 1 -1 0 0 0 18 0.0000 4 255 945 5938 2813 GY:k_m\001
4 1 -1 0 0 0 18 0.0000 4 195 135 8196 2813 1\001
4 1 -1 0 0 0 18 0.0000 4 255 630 3525 1252 IS:l_a\001
4 1 -1 0 0 0 18 0.0000 4 255 600 3628 4463 R:r_a\001
4 1 -1 0 0 0 18 0.0000 4 255 735 8248 4463 R:b_m\001
4 1 1 1 0 0 18 0.0000 4 195 1065 3576 5043 Electrical\001
4 1 1 1 0 0 18 0.0000 4 195 1290 8196 5043 Mechanical\001
4 1 1 1 0 0 18 0.0000 4 195 600 10404 3170 Shaft\001
4 1 1 1 0 0 18 0.0000 4 195 1155 1472 3170 Terminals\001
4 0 4 0 0 0 18 0.0000 4 240 1830 9945 2835 SS:[Mechanical]\001
4 1 -1 0 0 0 18 0.0000 4 255 585 8235 1215 I:j_m\001

%SUMMARY DCS: DCS motor 
%DESCRIPTION A special for the inverted pendulum system
%DESCRIPTION Derivative causality on the  shaft
%DESCRIPTION No aliased parameters
%DESCRIPTION Built in causality - speeds things up
%DESCRIPTION Only the armature state and shaft resistance are variable

%ALIAS in	Electrical
%ALIAS out	Mechanical


%% Label file for system DCS (DCS_lbl.txt)


%% Each line should be of one of the following forms:
%	a comment (ie starting with %)
%	Component-name	CR_name	arg1,arg2,..argn
%	blank

%Motor gain
k_m	lin		flow,k_m

% Electrical components
%Inductance
l_a	lin		flow,l_a;i_0

%Resistance
r_a	lin		flow,r_a

% Mechanical components
%Inertia
j_m	lin		flow,j_m

%Friction
b_m	lin		flow,b_m

% Ports
	[Electrical]	SS	external,external
	[Mechanical]	SS	external,external

#FIG 3.2
Portrait
Center
Metric
A4      
100.00
Single
-2
1200 2
6 3555 4005 3645 4545
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 3600 4050 3600 4500
-6
6 6255 4005 6345 4545
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 6300 4050 6300 4500
-6
2 4 0 2 1 7 101 0 -1 0.000 0 0 7 0 0 5
	 7650 4725 5850 4725 5850 3825 7650 3825 7650 4725
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 2250 4275 3600 4275 3375 4500
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 4950 4275 6300 4275 6075 4500
2 4 0 2 1 7 101 0 -1 0.000 0 0 7 0 0 5
	 5175 4725 3375 4725 3375 3825 5175 3825 5175 4725
2 4 0 2 1 7 101 0 -1 0.000 0 0 7 0 0 5
	 2610 4725 585 4725 585 3825 2610 3825 2610 4725
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 7425 4275 8775 4275 8550 4500
2 4 0 2 31 7 101 0 -1 0.000 0 0 7 0 0 5
	 10125 4950 10125 2025 225 2025 225 4950 10125 4950
4 1 0 100 0 18 20 0.0000 4 360 1815 1620 4410 OpenLoop\001
4 1 0 100 0 18 20 0.0000 4 285 960 4320 4410 Drive\001
4 1 0 100 0 18 20 0.0000 4 285 765 6795 4410 Cart\001
4 1 0 100 0 18 20 0.0000 4 285 810 9225 4410 Zero\001

# -*-octave-*- Put Emacs into octave-mode
# Input specification (DriveCart_input.txt)
# Generated by MTT at Thu Aug  5 09:17:30 BST 1999
###############################################################
## Version control history
###############################################################
## $Id$
## $Log$
###############################################################

# Set the inputs
#mttu(1) = 1.0*(t<1) -1.0*((t>=1)&&(t<2)); 	# u (DriveCart_F)
mttu(1) = 1;
mttu(2) = 0;
mttu(3) = 0;
mttu(4) = 0;

# Set the switches

%% Label file for system DriveCart (DriveCart_lbl.txt)
%SUMMARY DriveCart
%DESCRIPTION 

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%VAR l_p		#Pendulum length

% Port aliases

% Argument aliases

%% 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 ----

# -*-octave-*- Put Emacs into octave-mode
# Numerical parameter file (DriveCart_numpar.txt)
# Generated by MTT at Wed Aug 25 22:57:05 BST 1999

# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% Version control history
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% $Id$
# %% $Log$
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

# Parameters
j_m = 	3.87e-7;		# Motor inertia
k_m = 	0.00767;		# Motor constant
r_a = 	2.6;			# Armature resistance
l_a = 	0.18e-3;		# Armature inductance

k_g = 	1/3.7;			# Internal gear ratio 
r = 	0.635e-2;		# Motor gear radius

m_c = 	0.455;			# Cart mass

b_m = 	0.0;			# Motor friction
r_c = 	1.5;			# Cart friction

# l_p =   0.61;			# Pendulum length
# m_p =   0.210;			# Pendulum mass
# r_p = 	0.0;			# Pendulum friction

# j_p = m_p*(l_p*l_p)/12;		# Pendulum inertia about cm.

# g = 9.81;			# Gravity


## Sensitivity parameters
# m_cs = 0;			# Cart mass
# b_ms = 0;			# Motor friction 
# r_cs = 0;			# Cart friction
# r_ps = 0;			# Pendulum friction


## Control parameters
k_1 = 1;
k_2 = 0;
k_3 = 0;

## States
i_0 = 0;			# Initial armature current
v_0 = 0;			# Initial cart velocity
x_0 = 0;			# Initial cart position

# omega_0 = 0;			# Initial pendulum velocity
# theta_0 = 0;			# Initial pendulum angle

## Control sensitivity parameters
# k_1s = 0;
# k_2s = 0;
# k_3s = 0;

# ## Argument list
# if (mtt_n_parameters>1)
#   r_cs= mtt_parameters(1);
#   r_c = mtt_parameters(2);
# endif;

# if (mtt_n_parameters>3)
#   m_cs= mtt_parameters(3);
#   m_c = mtt_parameters(4);
# endif;

# if (mtt_n_parameters>5)
#   k_1s= mtt_parameters(5);
#   k_1 = mtt_parameters(6);
# endif;

# if (mtt_n_parameters>7)
#   k_2s= mtt_parameters(7);
#   k_2 = mtt_parameters(8);
# endif;

# if (mtt_n_parameters>9)
#   k_3s= mtt_parameters(9);
#   k_3 = mtt_parameters(10);
# endif;

## -*-octave-*- Put Emacs into octave-mode
## Outline report file for system DriveCart (DriveCart_rep.txt)
## Generated by MTT on" Fri Oct 22 09:03:14 EST 1999.

###############################################################
## Version control history
###############################################################
## $Id$
## $Log$
###############################################################

mtt DriveCart abg tex			# The system description
mtt DriveCart cbg ps 		        # The causal bond graph
## Uncomment the following lines or add others
mtt DriveCart struc tex	        # The system structure
mtt DriveCart dae tex	        # The system dae
## mtt DriveCart ode tex	        # The system ode 
## mtt DriveCart sspar tex		# Steady-state parameters
## mtt DriveCart ss tex 		# Steady state
## mtt DriveCart dm tex		# Descriptor matrices (of linearised system)
mtt DriveCart sm tex		# State matrices (of linearised system)
## mtt DriveCart tf tex		# Transfer function (of linearised system)
## mtt DriveCart lmfr ps		# log modulus of frequency response (of linearised system)
mtt DriveCart simpar tex		# Simulation parameters
mtt DriveCart numpar tex		# Numerical simulation parameters
mtt DriveCart input tex		# Simulation input
mtt -c DriveCart odeso ps		# Simulation output

# -*-octave-*- Put Emacs into octave-mode
# Simulation parameters for system DriveCart (DriveCart_simpar.txt)
# Generated by MTT on Thu Aug 5 09:17:05 BST 1999.
###############################################################
## Version control history
###############################################################
## $Id$
## $Log$
###############################################################


LAST        = 10.0;      # Last time in simulation
DT          = 0.1;        # Print interval
STEPFACTOR  = 1000;		# Integration steps per print interval
WMIN        = -1;         # Minimum frequency = 10^WMIN
WMAX        = 2;          # Maximum frequency = 10^WMAX
WSTEPS      = 100;        # Number of frequency steps
INPUT       = 1;          # Index of the input

#FIG 3.2
Portrait
Center
Metric
A4      
100.00
Single
-2
1200 2
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 3825 2475 3825 2925
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 2475 2700 3825 2700 3600 2925
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 5625 2700 6975 2700 6750 2925
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 8325 2700 9675 2700 9450 2925
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 10575 2700 11925 2700 11700 2925
2 4 0 2 31 7 101 0 -1 0.000 0 0 7 0 0 5
	 14400 4725 14400 675 225 675 225 4725 14400 4725
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 6975 2475 6975 2925
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 11925 2475 11925 2925
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 9675 2475 9675 2925
4 1 1 101 0 3 20 0.0000 4 255 1530 4590 3330 DC motor\001
4 1 1 101 0 3 20 0.0000 4 330 2745 2205 3330 Power supply unit\001
4 2 4 100 0 18 18 0.0000 4 270 1845 2430 2790 SS:[Electrical]\001
4 1 0 100 0 18 18 0.0000 4 210 1470 4725 2790 DCS:motor\001
4 1 0 100 0 18 18 0.0000 4 270 915 7695 2790 TF:k_g\001
4 1 0 100 0 18 18 0.0000 4 210 540 10125 2790 TF:r\001
4 0 4 100 0 18 18 0.0000 4 270 2115 12015 2790 SS:[Mechanical]\001
4 1 1 101 0 3 20 0.0000 4 330 2010 7515 3330 Internal gear\001
4 1 1 101 0 3 20 0.0000 4 330 1710 10080 3330 Motor gear\001

%% Label file for system Drive (Drive_lbl.txt)
%SUMMARY Drive
%DESCRIPTION <Detailed description here>

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% Port aliases
%ALIAS	in	Electrical
%ALIAS	out	Mechanical

%% 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 DC
	motor

% Component type SS
	[Electrical]	SS		external,external
	[Mechanical]	SS		external,external

% Component type TF
	k_g		lin	flow,k_g
	r		lin	flow,r

#FIG 3.2
Portrait
Center
Metric
A4      
100.00
Single
-2
1200 2
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 3376 3151 4276 3151 4051 3376
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4501 2926 4501 2026 4726 2251
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 4726 3151 5626 3151 5401 3376
2 4 0 2 31 7 1 0 -1 0.000 0 0 7 0 0 5
	 10575 4950 45 4950 45 1350 10575 1350 10575 4950
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 1575 3150 2475 3150 2250 3375
2 1 0 2 -1 7 0 0 -1 0.000 0 0 -1 0 0 3
	 6526 3150 7426 3150 7201 3375
4 1 -1 0 0 0 20 0.0000 4 255 180 4501 3241 0\001
4 1 -1 0 0 0 20 0.0000 4 255 1110 4501 1891 CS:unit\001
4 2 4 0 0 0 20 0.0000 4 315 1455 1530 3240 SS:[Flow]\001
4 1 -1 0 0 0 20 0.0000 4 255 825 2925 3240 AF:af\001
4 1 -1 0 0 0 20 0.0000 4 255 900 6075 3240 AE:ae\001
4 0 4 0 0 0 20 0.0000 4 330 3045 7470 3240 SS:[Integrated_flow]\001

%% Label file for system INTFS (INTFS_lbl.txt)
%SUMMARY	INTFS: flow integrator
%DESCRIPTION	Port [in]:	Flow to be integrated
%DESCRIPTION	Port [out]:	Effort = integral of flow on port [in]


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.3  1998/07/16 07:35:10  peterg
% %% Aliased version
% %%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% Port aliases
%ALIAS	in	Flow
%ALIAS	out	Integrated_flow

% Argument aliases
%ALIAS	$1 x_0	

%% 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 CS
	unit			lin		effort,1;x_0

% Component type AE
	ae			lin		1

% Component type AF
	af			lin		1

% Component type SS
	[Flow]			SS		external,external
	[Integrated_flow]	SS		external,external

#FIG 3.2
Portrait
Center
Metric
A4      
100.00
Single
-2
1200 2
6 2340 3915 2610 4185
4 1 0 100 0 18 20 0.0000 4 270 195 2475 4185 0\001
-6
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 2475 3825 2475 2475 2700 2700
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 2475 5625 2475 4275 2700 4500
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 2700 4050 4050 4050 3825 4275
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 4050 3825 4050 4275
4 1 0 100 0 18 20 0.0000 4 285 315 2475 2295 I:i\001
4 0 0 100 0 18 20 0.0000 4 360 1035 4185 4185 Sf:f_0\001
4 1 4 100 0 18 20 0.0000 4 360 1185 2475 6030 SS:[in]\001

%% Label file for system IS (IS_lbl.txt)
%SUMMARY IS I component with initial state


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% Port aliases
%ALIAS	in	in

% Argument aliases
%ALIAS	$1	flow,i
%ALIAS	$2	f_0

%% 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 I
	i		lin	flow,i

% Component type SS
	[in]	 SS	external,external

% Component type Sf
	f_0		SS	f_0

#FIG 3.2
Portrait
Center
Metric
A4      
100.00
Single
-2
1200 2
6 3555 4005 3645 4545
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 3600 4050 3600 4500
-6
6 6255 4005 6345 4545
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 6300 4050 6300 4500
-6
2 4 0 2 1 7 101 0 -1 0.000 0 0 7 0 0 5
	 7650 4725 5850 4725 5850 3825 7650 3825 7650 4725
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 2250 4275 3600 4275 3375 4500
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 4950 4275 6300 4275 6075 4500
2 4 0 2 1 7 101 0 -1 0.000 0 0 7 0 0 5
	 5175 4725 3375 4725 3375 3825 5175 3825 5175 4725
2 4 0 2 1 7 101 0 -1 0.000 0 0 7 0 0 5
	 2610 4725 585 4725 585 3825 2610 3825 2610 4725
2 4 0 2 31 7 101 0 -1 0.000 0 0 7 0 0 5
	 9675 4950 9675 2025 225 2025 225 4950 9675 4950
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 6750 3825 7705 2870 7705 3189
2 1 0 2 1 7 101 0 -1 0.000 0 0 -1 0 0 5
	 6952 3487 8347 2092 8527 2272 7177 3622 6997 3442
4 1 0 100 0 18 20 0.0000 4 360 1815 1620 4410 OpenLoop\001
4 1 0 100 0 18 20 0.0000 4 285 960 4320 4410 Drive\001
4 1 0 100 0 18 20 0.0000 4 285 3255 7830 2835 InvertedPendulum\001
4 1 0 100 0 18 20 0.0000 4 285 765 6795 4410 Cart\001

% -*-latex-*- Put EMACS into LaTeX-mode
% Verbal description for system InvertedPendulumOnCart (InvertedPendulumOnCart_desc.tex)
% Generated by MTT on Thu Aug 5 10:38:16 BST 1999.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   The acausal bond graph of system \textbf{InvertedPendulumOnCart} is
   displayed in Figure \Ref{fig:InvertedPendulumOnCart_abg.ps} and its label
   file is listed in Section \Ref{sec:InvertedPendulumOnCart_lbl}.
   The subsystems are listed in Section \Ref{sec:InvertedPendulumOnCart_sub}.

This is a one input, two output nonlinear system comprising an
inverted pendulum attached by a hinge to a cart constrained to move in
the horizontal direction. The input is the horizontal force acting on
the cart, and the two outputs are the horizontal position and the
pendulum angle respectively.

The bond graph in Figure \Ref{InvertedPendulumOnCartPPP_abg} is augmented with the {\em
open-loop\/} controller comprising
\begin{itemize}
\item two effort source \textbf{Se} components ``u1'' and ``u2''
\item two effort amplifier \textbf{AE} components ``ppp\_1'' and `ppp\_2''
\end{itemize}

This is a \emph{nonlinear} system and it is used to illustate
\emph{nonlinear} PPP control. Section
\Ref{sec:InvertedPendulumOnCartPPP_nppp.ps} shows the cart position
$x$ and the pendulum angle $\theta$  when the pendulum starts from the
initial condition of  $\theta = \frac{\pi}{2}$ (ie the pendulum is
horizontal).
 

# -*-octave-*- Put Emacs into octave-mode
# Input specification (InvertedPendulumOnCartPPP_input.txt)
# Generated by MTT at Thu Aug  5 09:17:30 BST 1999
###############################################################
## Version control history
###############################################################
## $Id$
## $Log$
###############################################################

# Set the inputs
#mttu(1) = 1.0*(t<1) -1.0*((t>=1)&&(t<2)); 	# u (InvertedPendulumOnCartPPP_F)
mttu(1) = 1;
mttu(2) = 0;
mttu(3) = 0;
mttu(4) = 0;

# Set the switches

%% Label file for system InvertedPendulumOnCartPPP (InvertedPendulumOnCartPPP_lbl.txt)
%SUMMARY InvertedPendulumOnCartPPP
%DESCRIPTION 

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%VAR l_p		#Pendulum length

% Port aliases

% Argument aliases

%% 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 ----

## Figures.m
## Makes figures for the InvertedPendulumOnCart_PPP exasmple.
## $Log$
## Revision 1.4  2000/08/17 12:34:58  peterg
## *** empty log message ***
##
## Revision 1.3  2000/08/11 16:01:27  peterg
## Fixed documentation error
##
## Revision 1.2  2000/05/21 06:39:40  peterg
## Parameterised _sm
##
## Revision 1.1  2000/05/20 11:30:41  peterg
## Initial revision
##
## Revision 1.2  2000/05/17 16:59:57  peterg
## Revised for Inverted pendulum - it works !!!!
##
## Revision 1.1  2000/05/17 14:07:53  peterg
## Initial revision
##
## Revision 1.1  2000/05/17 09:14:37  peterg
## Initial revision
##
system_name = "InvertedPendulumOnCartPPP";

## Uncomment the following the first time
## (Or do ./Make InvertedPendulumOnCartPPP in this directory)

## MTT stuff for the system simulation
##system("Make InvertedPendulumOnCartPPP");

t_s=1.0*[0:0.1:10];
u = [ones(4,length(t_s))];
x_0 = InvertedPendulumOnCartPPP_state;
par  = InvertedPendulumOnCartPPP_numpar;

## Simulate the system
tick=time;
[y,x] = InvertedPendulumOnCartPPP_sim(x_0,u,t_s,par);
Elapsed = time-tick
plot(t_s,y, t_s,x);

## Simulate the system to give just the final few points
t_s1 = 10*[9:0.1:10];
tick=time;
[y,x] = InvertedPendulumOnCartPPP_sim(x_0,u,t_s1,par);
Elapsed = time-tick
plot(t_s1,y,t_s1,x);

## Sensitivity system simulation parameters
x_0s = sInvertedPendulumOnCartPPP_state;
pars  = sInvertedPendulumOnCartPPP_numpar;
sympars  = sInvertedPendulumOnCartPPP_sympar;

## Simulate the sensitivity system
sensitivities = [sympars.ppp_1s,sympars.ppp_2s,sympars.r_cs]
tick=time;
[y,ys] = sInvertedPendulumOnCartPPP_sim(x_0s,u,t_s,pars,sensitivities);
Elapsed = time-tick
plot(t_s,y,t_s,ys);

### PPP parameters
A_w = [0;0];
A_u = laguerre_matrix(4,20); # Specify basis functions: constant &
			     # exp(-5t)
tau = 0.5*[0.9:0.01:1];             # Optimisation interval
t_ol =0.5*[0:0.01:0.2];            # Open-loop interval
N = 20;                          # Number of open-loop intervals in simulation
w = [0;0];                         # Setpoint

## Linear system
## Linear system
[A,B,C,D] = InvertedPendulumOnCartPPP_sm(par);
Q = [1;1];
ppp_lin_plot (A,B(:,1),C,D(:,1),A_u,A_w,tau,Q,w,x_0);
psfig("InvertedPendulumOnCartPPP_lin");

## Simulate non-linear PPP (on this nonlinear system)
extras.U_initial = "zero";
extras.U_next = "continuation";
extras.criterion = 1e-5;
extras.max_iterations = 10;
extras.v = 0;
extras.verbose = 0;

# ##  -- with no optimisation using linear PPP with continuation
# extras.U_initial = "linear";
# extras.U_next = "continuation";
# extras.criterion = 1e-5;
# extras.max_iterations = 0;
# [y_c,x,u_c,t,U,U_c,U_l] = ppp_nlin_sim (system_name,A_u,tau,t_ol,N,w,extras);

# ##  -- with no optimisation using linear PPP at each step
# extras.U_initial = "linear";
# extras.U_next = "linear";
# extras.criterion = 1e-5;
# extras.max_iterations = 0;
# [y_l,x,u_l,t,U,U_c,U_l] = ppp_nlin_sim (system_name,A_u,tau,t_ol,N,w,extras);

##  -- with optimisation using nonlinear PPP with continuation
extras.U_initial = "zero";
extras.U_next = "continuation";
extras.criterion = 1e-4;
extras.max_iterations = 100;
extras.v = 1e-3;
extras.verbose = 0;
[y,x,u,t,U,U_c,U_l] = ppp_nlin_sim (system_name,A_u,tau,t_ol,N,w,extras);


## Plots
title("");

## U, U_c and U_l
I = 1:N;
IU1 = [I' U(1,:)'];
IU1_c = [I' U_c(1,:)'];
IU1_l = [I' U_l(1,:)'];
gset grid; xlabel "Interval"
gplot IU1 title "U_1", IU1_c title "U_c1", IU1_l title "U_l1"
psfig("InvertedPendulumOnCartPPP_U1");

IU2 = [I' U(2,:)'];
IU2_c = [I' U_c(2,:)'];
IU2_l = [I' U_l(2,:)'];
gset grid; xlabel "Interval "
gplot IU2 title "U_2", IU2_c title "U_c2", IU2_l title "U_l2"
psfig("InvertedPendulumOnCartPPP_U2");

## y & u
gset grid; xlabel "Time (sec)"
tu =  [t' u']; 
gplot tu title "Output"
psfig("InvertedPendulumOnCartPPP_u");

gset grid; xlabel "Time (sec)"
ty_th = [t' y(1,:)'] ;
ty_x = [t' y(2,:)'] ;
gplot ty_th title "Theta",ty_x title "x"
psfig("InvertedPendulumOnCartPPP_nppp");

# -*-octave-*- Put Emacs into octave-mode
# Numerical parameter file (sInvertedPendulumOnCart_numpar.txt)
# Generated by MTT at Tue Apr 18 18:07:52 BST 2000

# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% Version control history
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% $Id$
# %% $Log$
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

## Default parameters
b_m = 	0.0; # sDCS
c = 	0.0; # sC,sC,sCS,sCS
e_0 = 	0.0; # sCS,sCS
e_s = 	0.0; # Se,Se,Se,sSe,sSe,sSe
f_0 = 	0.0; # sIS,sIS,sIS
f_s = 	0.0; # Sf,Sf,Sf,sSf,sSf,sSf
g = 	0.0; # AFe,AFe,sInvertedPendulum,sROD
i = 	0.0; # sI,sI,sI,sI,sI,sI,sIS,sIS,sIS
i_0 = 	0.0; # sDCS
j_m = 	0.0; # sDCS,sROD
j_p = 	0.0; # sInvertedPendulum
ppp_1 = 	1.0; # sOpenLoop
ppp_2 = 	0.0; # sOpenLoop
ppp_3 = 	0.0; # sOpenLoop
ppp_4 = 	0.0; # sOpenLoop
k_g = 	0.0; # sDrive
k_m = 	0.0; # sDCS
l_a = 	0.0; # sDCS,sROD
l_b = 	0.0; # sROD
l_p = 	0.0; # sInvertedPendulum,sInvertedPendulumOnCart
m = 	0.0; # sROD
m_c = 	0.0; # sCart
m_p = 	0.0; # sInvertedPendulum
m_t = 	0.0; # sInvertedPendulum
omega_0 = 	0.0; # sInvertedPendulum,sROD
r = 	0.0; # sDrive,sR,sR
r_a = 	0.0; # sDCS
r_c = 	0.0; # sCart
r_p = 	0.0; # sCart
theta_0 = 	0.0; # sInvertedPendulum,sROD
v_0 = 	0.0; # sCart
x_0 = 	0.0; # sCart,sINTFS,sINTFS


## Pysical Parameters
j_m = 	3.87e-7;		# Motor inertia
k_m = 	0.00767;		# Motor constant
r_a = 	2.6;			# Armature resistance
l_a = 	0.18e-3;		# Armature inductance

k_g = 	1/3.7;			# Internal gear ratio 
r = 	0.635e-2;		# Motor gear radius

m_c = 	0.455;			# Cart mass

b_m = 	0.0;			# Motor friction
r_c = 	1.5;			# Cart friction

l_p =   0.61;			# Pendulum length
m_p =   0.210;			# Pendulum mass
r_p = 	0.0;			# Pendulum friction

j_p = m_p*(l_p*l_p)/12;		# Pendulum inertia about cm.

g = 9.81;			# Gravity

## -*-octave-*- Put Emacs into octave-mode
## Outline report file for system InvertedPendulumOnCartPPP (InvertedPendulumOnCartPPP_rep.txt)
## Generated by MTT on" Fri Oct 22 09:03:14 EST 1999.

###############################################################
## Version control history
###############################################################
## $Id$
## $Log$
## Revision 1.3  2000/08/29 13:57:23  peterg
## Zapped some steps which prevent ppp from working ????
##
## Revision 1.2  2000/05/20 17:45:38  peterg
## Tidied
##
## Revision 1.1  2000/05/20 17:43:40  peterg
## Initial revision
##
###############################################################

mtt InvertedPendulumOnCartPPP abg tex # The system description
mtt InvertedPendulumOnCartPPP cbg ps # The causal bond graph
mtt InvertedPendulumOnCartPPP struc tex	# The system structure
mtt InvertedPendulumOnCartPPP dae tex # The system dae
# mtt InvertedPendulumOnCartPPP sm tex # State matrices (of linearised system)

# mtt InvertedPendulumOnCartPPP simpar tex # Simulation parameters
# mtt InvertedPendulumOnCartPPP numpar tex # Numerical simulation parameters
# mtt InvertedPendulumOnCartPPP input tex	# Simulation input
# mtt -c InvertedPendulumOnCartPPP odeso ps # Simulation output

mtt InvertedPendulumOnCartPPP nppp m # How its done
mtt InvertedPendulumOnCartPPP nppp ps # The PPP output

mtt InvertedPendulumOnCartPPP rep txt # The report outline