screenshots added

labcontroltheory2b/lab_controltheory2b.m

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+clc;
+close all;
+clear all;
+
+Q0=3.7958e-5;
+C10=11.08e-5;
+C20=8.43e-5;
+C30=8.28e-5;
+H10=(Q0/C10)^2;
+H20=(Q0/C20)^2;
+H30=(Q0/C30)^2;
+s=0.25*0.035;
+
+A=[-C10*(1/(2*s*sqrt(H10))), 0, 0; C10*(1/(2*s*sqrt(H10))), -C20*(1/(2*s*sqrt(H20))), 0; 0, C20*(1/(2*s*sqrt(H20))), -C30*(1/(2*s*sqrt(H30)))];
+B=[-sqrt(H10)*(1/s), 0, 0; sqrt(H10)*(1/s), -sqrt(H20)*(1/s), 0; 0, sqrt(H20)*(1/s), -sqrt(H30)*(1/s)];
+C=[1,0,0;0,1,0;0,0,1];
+D=zeros(3, 3);
+A
+B
+C
+D
+I=[1 0 0; 0 1 0; 0 0 1];
+
+model=ss(A, B, C, D)
+[NUM1, den1]=ss2tf(A,B,C,D,1);
+[NUM2, den2]=ss2tf(A,B,C,D,2);
+[NUM3, den3]=ss2tf(A,B,C,D,3);
+
+TFM(1,1)=tf(NUM1(1,:),den1);
+TFM(2,1)=tf(NUM1(2,:),den1);
+TFM(3,1)=tf(NUM1(3,:),den1);
+TFM(1,2)=tf(NUM2(1,:),den2);
+TFM(2,2)=tf(NUM2(2,:),den2);
+TFM(3,2)=tf(NUM2(3,:),den2);
+TFM(1,3)=tf(NUM3(1,:),den3);
+TFM(2,3)=tf(NUM3(2,:),den3);
+TFM(3,3)=tf(NUM3(3,:),den3);
+TFM;
+
+if rank([B, B*A, B*A^2])==3
+    disp('is completely state controllable');
+end
+
+if rank([C*B, C*A*B, C*(A^2)*B, D])==3
+    disp('is completely output controllable');
+end
+
+if rank([C', A'*C',  ((A')^2)*C'])==3
+    disp('is completely observable');
+end
+
+% u is composed of C1 C2 C3
+% u = -k x(t) 
+% K = k11 k12 k13; k21 k22 k23..
+% X is H1-H10 ; H2-H20..
+P=eig(A);
+% p=[P(1,1); P(2,1); P(3,1)];
+% unstable pole should be stabilized 
+% real part of the pole should be negative time domain or in discrete pole should be in the unit circle
+p=[-14.5;-9.0;-23];
+K = place(A,B,p);
+eig(A-B*K)
+% q=[];
+% L = place(A',C',q).';

labcontroltheory2b/slprj/sim/varcache/lab_controltheory2b_2/tmwinternal/simulink_cache.xml

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