File mttroot/mtt/bin/trans/sm2smc_r artifact fd501bda09 part of check-in 080f1ef068

#! /bin/sh

     ###################################### 
     ##### Model Transformation Tools #####
     ######################################

# Bourne shell script: sm2smc_r
# state matrices to controller canonical form + related matrices
# P.J.Gawthrop  12 Jan 1997
# Copyright (c) P.J.Gawthrop 1997

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


# Inform user
echo Creating $1_smc.r -- NOTE this is for SISO systems only.

# Remove the old log file
rm -f sm2smc_r.log

# Use reduce to accomplish the transformation
reduce >sm2smc_r.log << EOF

in "$1_def.r";
in "$1_sm.r";
in "$1_tf.r";

%Read the formatting function
in "$MTTPATH/trans/reduce_matrix.r";


OFF Echo;
OFF Nat;

% Find the controllability matrix
MATRIX MTTCon(MTTNx,MTTNX);
MTTAB := MTTB;
FOR j := 1:MTTNx DO
  BEGIN
   FOR i := 1:MTTNx DO 
      MTTCon(i,j) := MTTAB(i,1);
   MTTAB := MTTA*MTTAB;
  END;


%Canonical forms:
% This statement makes Gs a scalar transfer function
Gs := MTTtf(1,1);

% Numerator and denominator polynomials
bs := num(gs);
as := den(gs);

% extract coeficients and divide by coeff of s^n
% reverse operator puts list with highest oder coeffs first
ai := reverse(coeff(as,s));
a0 := first(ai);
MTTn := length(ai) - 1;


% Normalised coeficients;
ai := reverse(coeff(as/a0,s));
bi := reverse(coeff(bs/a0,s));
MTTm := length(bi)-1;

% Zap the (unity) first element of ai list;
ai := rest(ai);

% System in controller form
% MTTA_c matrix
matrix MTTA_c(MTTn,MTTn);

% First row is ai coefficients
for i := 1:MTTn do
  MTTA_c(1,i) := -part(ai,i);

% (MTTn-1)x(MTTn-1) unit matrix in lower left-land corner (if n>1)
if MTTn>1 then
  for i := 1:MTTn-1 do
    MTTA_c(i+1,i) := 1;

% B_c vector;
matrix MTTB_c(MTTn,1);
MTTB_c(1,1) := 1;

% C_c vector;
matrix MTTC_c(1,MTTn);
for i := 1:MTTm+1 do
  MTTC_c(1,i+MTTn-MTTm-1) := part(bi,i);

% D_c
MTTD_c := MTTD;

%Controllability matrix of controllable form
MATRIX MTTCon_c(MTTNx,MTTNX);
MTTAB := MTTB_c;
FOR j := 1:MTTNx DO
  BEGIN
   FOR i := 1:MTTNx DO 
      MTTCon_c(i,j) := MTTAB(i,1);
   MTTAB := MTTA_c*MTTAB;
  END;

% Transformation matrix;
MTTT_c := MTTCon_c*MTTCon^(-1);



%Create the output file
OUT "$1_smc.r";

%Write out the matrices.

% Controllable form
write "%  - Controller form";
MTT_Matrix := MTTA_c$ 
MTT_Matrix_name := "MTTA_c"$
MTT_Matrix_n := MTTNx$
MTT_Matrix_m := MTTNx$
Reduce_Matrix()$

MTT_Matrix := MTTB_c$ 
MTT_Matrix_name := "MTTB_c"$
MTT_Matrix_n := MTTNx$
MTT_Matrix_m := MTTNu$
Reduce_Matrix()$

MTT_Matrix := MTTC_c$ 
MTT_Matrix_name := "MTTC_c"$
MTT_Matrix_n := MTTNy$
MTT_Matrix_m := MTTNx$
Reduce_Matrix()$

MTT_Matrix := MTTD_c$ 
MTT_Matrix_name := "MTTD_c"$
MTT_Matrix_n := MTTNy$
MTT_Matrix_m := MTTNu$
Reduce_Matrix()$


write "%  - Controllability matrix";
MTT_Matrix := MTTCon$ 
MTT_Matrix_name := "MTTCon"$
MTT_Matrix_n := MTTNx$
MTT_Matrix_m := MTTNx$
Reduce_Matrix()$


write "%  -Controllability matrix - controller form";
MTT_Matrix := MTTCon_c$ 
MTT_Matrix_name := "MTTCon_c"$
MTT_Matrix_n := MTTNx$
MTT_Matrix_m := MTTNx$
Reduce_Matrix()$

write "%  - Transformation matrix - controller form";
MTT_Matrix := MTTT_c$ 
MTT_Matrix_name := "MTTT_c"$
MTT_Matrix_n := MTTNx$
MTT_Matrix_m := MTTNx$
Reduce_Matrix()$

write "END;";

SHUT "$1_smc.r";
quit;

EOF

# Now invoke the standard error handling.
mtt_error_r sm2smc_r.log