#! /bin/sh
######################################
##### Model Transformation Tools #####
######################################
# Bourne shell script: sm2smo_r
# state matrices to cobserver form
# P.J.Gawthrop 12 Jan 1997
# Copyright (c) P.J.Gawthrop 1998
###############################################################
## Version control history
###############################################################
## $Id$
## $Log$
## Revision 1.3 2000/09/11 10:53:54 peterg
## Uses 1st io of mimo to create siso
##
## Revision 1.2 1998/01/22 13:25:22 peterg
## Added END;; to output file.
##
## Revision 1.1 1998/01/22 13:16:43 peterg
## Initial revision
##
###############################################################
Nu=`mtt_getsize $1 u`
Ny=`mtt_getsize $1 y`
if [ "$Nu" = "1" ]; then
if [ "$Ny" = "1" ]; then
blurb=' for this siso system'
else
blurb=" using first output of $Ny"
fi
else
if [ "$Ny" = "1" ]; then
blurb=" using first input of $Nu"
else
blurb=" using first input of $Nu and using first output of $Ny"
fi
fi
# Inform user
echo Creating $1_smo.r $blurb
# Remove the old log file
rm -f sm2smo_r.log
# Use reduce to accomplish the transformation
reduce >sm2smo_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 observibility matrix.
MATRIX MTTObs(MTTNx,MTTNX);
MTTCA := MTTC;
FOR i := 1:MTTNx DO
BEGIN
FOR j := 1:MTTNx DO
MTTObs(i,j) := MTTCA(1,j);
MTTCA := MTTCA*MTTA;
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 observer form
% MTTA_o matrix
matrix MTTA_o(MTTNx,MTTNx);
% First column is ai coefficients
for i := 1:MTTNx do
MTTA_o(i,1) := -part(ai,i);
% (MTTNx-1)x(MTTNx-1) unit matrix in upper right-hand corner (if n>1)
if MTTNx>1 then
for i := 1:MTTNx-1 do
MTTA_o(i,i+1) := 1;
% C_o vector;
matrix MTTC_o(1,MTTNx);
MTTC_o(1,1) := 1;
MTTC_o;
% B_o vector;
matrix MTTB_o(MTTNx,1);
for i := 1:MTTm+1 do
MTTB_o(i+MTTNx-MTTm-1,1) := part(bi,i);
% D_o
MTTD_o := MTTD;
%Observability matrix of observer form
MATRIX MTTObs_o(MTTNx,MTTNX);
MTTCA := MTTC_o;
FOR i := 1:MTTNx DO
BEGIN
FOR j := 1:MTTNx DO
MTTObs_o(i,j) := MTTCA(1,j);
MTTCA := MTTCA*MTTA_o;
END;
% Transformation matrix;
MTTT_o := MTTObs^(-1)*MTTObs_o;
%Create the output file
OUT "$1_smo.r";
%Write out the matrices.
% Observable form
MTT_Matrix := MTTA_o$
MTT_Matrix_name := "MTTA_o"$
MTT_Matrix_n := MTTNx$
MTT_Matrix_m := MTTNx$
Reduce_Matrix()$
MTT_Matrix := MTTB_o$
MTT_Matrix_name := "MTTB_o"$
MTT_Matrix_n := MTTNx$
MTT_Matrix_m := 1$
Reduce_Matrix()$
MTT_Matrix := MTTC_o$
MTT_Matrix_name := "MTTC_o"$
MTT_Matrix_n := 1$
MTT_Matrix_m := MTTNx$
Reduce_Matrix()$
MTT_Matrix := MTTD_o$
MTT_Matrix_name := "MTTD_o"$
MTT_Matrix_n := 1$
MTT_Matrix_m := 1$
Reduce_Matrix()$
write "% -Observability matrix";
MTT_Matrix := MTTObs$
MTT_Matrix_name := "MTTObs"$
MTT_Matrix_n := MTTNx$
MTT_Matrix_m := MTTNx$
Reduce_Matrix()$
write "% -Observability matrix - Observer form";
MTT_Matrix := MTTObs_o$
MTT_Matrix_name := "MTTObs_o"$
MTT_Matrix_n := MTTNx$
MTT_Matrix_m := MTTNx$
Reduce_Matrix()$
write "% - Transformation matrix - Observer form";
MTT_Matrix := MTTT_o$
MTT_Matrix_name := "MTTT_o"$
MTT_Matrix_n := MTTNx$
MTT_Matrix_m := MTTNx$
Reduce_Matrix()$
write "END;;";
SHUT "$1_smo.r";
quit;
EOF
# Now invoke the standard error handling.
mtt_error_r sm2smo_r.log