[Octave-bug-tracker] [bug #66651] control package, MIMO systems wrong created C matrix for state space representation using ss

[anonymous]

Follow-up Comment #3, bug #66651 (group octave):

i tried the provided code and it is still not working, i provide code with the
correct step response using manual transformation to MIMO so you can test and
make ss more robust





pkg load control
pkg load signal
clear

t=u1y1 =        tf([  4.74972290301299  0.0962858385264363
0.000679935548113776  3.72643701613439e-07  ],[  1  0.0207380329272262
0.000358651716393651  1.53426197558325e-06  1.60694141834117e-09  ]);
numu1y1_m1=t.num{1};
denu1y1_m1=t.den{1};


t=u1y2 =               tf([  -2.11493904790791e-05  -3.98828140784831e-07
-1.66475746406136e-08  -1.83748125520122e-10  -3.17372735779801e-12
-1.51387201191368e-14  -7.95515361277902e-18  ],[  1  0.0237440013869291
0.00093839286173024  1.36557230877558e-05  2.17818987171716e-07
1.82722920274503e-09  5.29889671308072e-12  4.97347909522557e-15  ]);
numu1y2_m1=t.num{1};
denu1y2_m1=t.den{1};


t=     u2y1=             tf([  0.0337260175091407  0.414338784602062
0.00343501567979344  0.00132279342826428  8.05249078940347e-06
1.39424444953855e-06  5.51151054539321e-09  5.10115766190411e-10
9.91853470677749e-13  2.88997553994485e-14  ],[  1  0.153889837566522
0.00677224375967168  0.000548671957421157  1.41722799246167e-05
6.85514842206994e-07  1.19614786183711e-08  3.46611370329274e-10
3.77280525883548e-12  5.76999094807308e-14  2.00325109640768e-16  ]);
numu2y1_m1=t.num{1};
denu2y1_m1=t.den{1};


t=   u2y2 =             tf([  -1.48787383837688e-06  -3.24705706205277e-08
-6.54751170609613e-10  -7.46171917997884e-12  ],[  1  0.0134226252067825
0.000316273404177729  2.74708154815059e-06  5.9854886873292e-09  ]);
numu2y2_m1=t.num{1};
denu2y2_m1=t.den{1};


t=u3y1 =        tf([  -8318.14771695403  -1005.17247836674  -69.388714502427
-2.13567218084595  -0.057214617650067  -0.00051673284923126
-5.21707731497307e-06  -3.10877494268659e-09  ],[  1  0.127298409756932
0.0105061762139007  0.000356618210494435  1.16880708107467e-05
1.51741412632152e-07  2.05485336227224e-09  2.72630351738011e-12  ]);
numu3y1_m1=t.num{1};
denu3y1_m1=t.den{1};


t=u3y2 =       tf([  6.58550303958022e-07  1.12032568300048e-06
4.84240826234966e-08  2.06589443851401e-09  3.25197618527417e-11
2.6086983962496e-14  ],[  1  0.0340866722611228  0.0019478738998518
3.09342222656595e-05  4.969573841421e-07  2.19170977290605e-09
2.86190017229284e-12  ]);
numu3y2_m1=t.num{1};
denu3y2_m1=t.den{1};

%tf matrix
sys=[u1y1 u2y1 u3y1 ;
u1y2 u2y2 u3y2];

sys_ss=ss(sys);%non working ss
A=sys_ss.a;
B=sys_ss.b;
C=sys_ss.c;
D=sys_ss.d;

%SISO ss
[A_u1y1,B_u1y1,C_u1y1,D_u1y1]=tf2ss(u1y1)
[A_u2y1,B_u2y1,C_u2y1,D_u2y1]=tf2ss(u2y1)
[A_u3y1,B_u3y1,C_u3y1,D_u3y1]=tf2ss(u3y1)
[A_u1y2,B_u1y2,C_u1y2,D_u1y2]=tf2ss(u1y2)
[A_u2y2,B_u2y2,C_u2y2,D_u2y2]=tf2ss(u2y2)
[A_u3y2,B_u3y2,C_u3y2,D_u3y2]=tf2ss(u3y2)

%manual transform to MIMO ss
A_ss = blkdiag(A_u1y1, A_u2y1, A_u3y1, A_u1y2, A_u2y2, A_u3y2)
B_ss = [ blkdiag(B_u1y1, B_u2y1, B_u3y1) ; blkdiag(B_u1y2, B_u2y2, B_u3y2) ]
C_ss = blkdiag([C_u1y1, C_u2y1, C_u3y1] , [C_u1y2, C_u2y2, C_u3y2])
D_ss = [D_u1y1, D_u2y1, D_u3y1 ; D_u1y2, D_u2y2, D_u3y2 ]

close all
s=ss(A_ss,B_ss,C_ss,D_ss)
step(s)%correct step response


%provided code

# Similarity trnasformation
[T, lambda] = eig (sys_ss.a);
A = inv(T)*sys_ss.a*T;
B = inv(T)*sys_ss.b;
C = sys_ss.c*T;
# Set very small values to 0 (finite
# numerical accuracy) for a nicer output
A(abs(A)<1e-12)= 0
B(abs(B)<1e-12)= 0
C(abs(C)<1e-12)= 0

figure
s=ss(A,B,C,D)
step(s)%incorrect step response


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