could be first stable observer of motor1
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@@ -63,6 +63,7 @@ function [ssc]=StateSpaceControlDesign(mot)
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p1=-6300+280i;
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p2=-6200+150i;
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P=[p1 p1' p2 p2'];
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P=[-4000 -4100 -1500+10j -1500-10j];
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else
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p1=-3300+2800i;
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p2=-2700+500i;
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@@ -1,19 +1,50 @@
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function [ssc]=testObserver(mot)
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%http://ctms.engin.umich.edu/CTMS/index.php?example=Introduction§ion=ControlStateSpace
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mdl=1; % 0:hovering ball 1:fast stage
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if mdl==0
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A = [ 0 1 0
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980 0 -2.8
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0 0 -100 ];
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A = [ 0 1 0
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980 0 -2.8
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0 0 -100 ];
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B = [ 0
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0
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100 ];
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B = [ 0
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0
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100 ];
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C = [ 1 0 0 ];
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D=0;
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else
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[A,B,C,D]=ssdata(mot.ssMdl);
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C=C(3,:);D=D(3);
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numc=(mot.mdl.numc);
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denc=(mot.mdl.denc);
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num1=(mot.mdl.num1);
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den1=(mot.mdl.den1);
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C = [ 1 0 0 ];
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D=0;
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%[A,B,C,D]=ssdata(mot.ssMdl)
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%C=C(3,:);D=D(3);
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g1=tf(numc,denc); % iqCmd->iqMeas
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s1=ss(g1);
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s1.C=[s1.C; 1E5* 2.4E-3 1E-3*s1.C(2)*8.8]; % add output iqVolts: iqVolts= i_meas*R+i_meas'*L 2.4mH 8.8Ohm (took random scaling values)
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g2=tf(num1,den1); %iqMeas->ActPos without resonance frequencies
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s2=ss(g2);
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s3=append(s1,s2);
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s3.A(3,2)=s3.C(1,2)*s3.B(3,2);
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%d=.77;w0=9100; %1.44kHz -> T0=6.9046e-04
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%numc=[w0^2];
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%denc=[1 d*2*w0 w0^2];
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%T0=6E-4; %w=1/1E-3=1E3 -> f=w/(2pi)=1000/6.2=159Hz
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%numc=[1];
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%denc=[T0^2 d*2*T0 1];
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%bode(numc,denc)
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num=conv(numc,num1);%num=1;
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den=conv(denc,den1);%den=[1 0 0];
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g4=tf(num,den); %iqMeas->ActPos
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s4=ss(g4);
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mot.ssMdl
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s3
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s4
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[A,B,C,D]=ssdata(s4);
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end
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Ap=A;Am=A;
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Bp=B;Bm=B;
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@@ -24,97 +55,133 @@ function [ssc]=testObserver(mot)
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disp(poles);
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t = 0:0.01:2;
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u = zeros(size(t));
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x0 = [0.01 0 0];
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%x0 = [0.1 0 0 0];
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if mdl==0
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t = 0:0.01:2;
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u = zeros(size(t));
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x0 = [0.01 0 0];
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sys = ss(A,B,C,D);
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sys = ss(A,B,C,D);
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[y,t,x] = lsim(sys,u,t,x0);
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plot(t,y)
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title('Open-Loop Response to Non-Zero Initial Condition')
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xlabel('Time (sec)')
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ylabel('Ball Position (m)')
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[y,t,x] = lsim(sys,u,t,x0);
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plot(t,y)
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title('Open-Loop Response to Non-Zero Initial Condition')
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xlabel('Time (sec)')
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ylabel('Ball Position (m)')
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p1 = -10 + 10i; p2 = -10 - 10i; p3 = -50;
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K = place(A,B,[p1 p2 p3]);
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sys_cl = ss(A-B*K,B,C,0);
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lsim(sys_cl,u,t,x0);
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xlabel('Time (sec)')
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ylabel('Ball Position (m)')
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p1 = -20 + 20i; p2 = -20 - 20i; p3 = -100;
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P=[p1 p2 p3];
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K = place(A,B,P);
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sys_cl = ss(A-B*K,B,C,0);
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lsim(sys_cl,u,t,x0);
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xlabel('Time (sec)')
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ylabel('Ball Position (m)')
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t = 0:0.01:2;
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u = 0.001*ones(size(t));
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sys_cl = ss(A-B*K,B,C,0);
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lsim(sys_cl,u,t);
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xlabel('Time (sec)')
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ylabel('Ball Position (m)')
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axis([0 2 -4E-6 0])
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V=-1./(Cm*(Am-Bm*K)^-1*Bm); %(from Lineare Regelsysteme2 (Glattfelder) page:173 )
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lsim(sys_cl,V*u,t)
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title('Linear Simulation Results (with Nbar)')
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xlabel('Time (sec)')
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ylabel('Ball Position (m)')
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axis([0 2 0 1.2*10^-3])
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else
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x0 = [0 0 0 0];
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p1=-63+2.80i;
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p2=-62+1.50i;
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P=[p1 p1' p2 p2'];
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P=[-4000 -4100 -500+10j -500-10j];
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K = place(A,B,P);
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Ts=1/5000
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t = 0:Ts:2;
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u = 0.001*ones(size(t));
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V=-1./(Cm*(Am-Bm*K)^-1*Bm); %(from Lineare Regelsysteme2 (Glattfelder) page:173 )
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sys_cl = ss(A-B*K,B*V,C,0);
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lsim(sys_cl,u,t,x0);
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xlabel('Time (sec)')
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ylabel('Motor Position (m)')
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axis([0 2 0 1.2E-3])
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end
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if mdl==0
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op1 = -100;
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op2 = -101;
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op3 = -102;
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OP=[op1,op2,op3];
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OP=P*2;
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L = place(A',C',OP)';
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At = [ A-B*K B*K
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zeros(size(A)) A-L*C ];
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Bt = [ B*V
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zeros(size(B)) ];
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Ct = [ C zeros(size(C)) ];
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sys = ss(At,Bt,Ct,0);
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%lsim(sys,zeros(size(t)),t,[x0 x0]);
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lsim(sys,u,t,[x0 x0]*0);
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title('Linear Simulation Results (with observer)')
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xlabel('Time (sec)')
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ylabel('Ball Position (m)')
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else
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OP=P*2;
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L = place(A',C',OP)';
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At = [ A-B*K B*K
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zeros(size(A)) A-L*C ];
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Bt = [ B*V
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zeros(size(B)) ];
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Ct = [ C zeros(size(C)) ];
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sys = ss(At,Bt,Ct,0);
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lsim(sys,u,t,[x0 x0]*0);
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title('Linear Simulation Results (with observer)')
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xlabel('Time (sec)')
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ylabel('Motor Position (m)')
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axis([0 2 0 1.2E-3])
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end
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p1 = -10 + 10i; p2 = -10 - 10i; p3 = -50;
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K = place(A,B,[p1 p2 p3]);
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sys_cl = ss(A-B*K,B,C,0);
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lsim(sys_cl,u,t,x0);
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xlabel('Time (sec)')
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ylabel('Ball Position (m)')
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if mdl==0
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t = 0:1E-6:0.1;
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x0 = [0.01 0.5 -5];
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[y,t,x] = lsim(sys,zeros(size(t)),t,[x0 x0]);
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p1 = -20 + 20i; p2 = -20 - 20i; p3 = -100;
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K = place(A,B,[p1 p2 p3]);
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sys_cl = ss(A-B*K,B,C,0);
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lsim(sys_cl,u,t,x0);
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xlabel('Time (sec)')
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ylabel('Ball Position (m)')
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n = 3;
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e = x(:,n+1:end);
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x = x(:,1:n);
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x_est = x - e;
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t = 0:0.01:2;
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u = 0.001*ones(size(t));
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sys_cl = ss(A-B*K,B,C,0);
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lsim(sys_cl,u,t);
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xlabel('Time (sec)')
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ylabel('Ball Position (m)')
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axis([0 2 -4E-6 0])
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V=-1./(Cm*(Am-Bm*K)^-1*Bm); %(from Lineare Regelsysteme2 (Glattfelder) page:173 )
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lsim(sys_cl,V*u,t)
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title('Linear Simulation Results (with Nbar)')
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xlabel('Time (sec)')
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ylabel('Ball Position (m)')
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axis([0 2 0 1.2*10^-3])
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op1 = -100;
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op2 = -101;
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op3 = -102;
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L = place(A',C',[op1 op2 op3])';
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At = [ A-B*K B*K
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zeros(size(A)) A-L*C ];
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Bt = [ B*V
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zeros(size(B)) ];
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Ct = [ C zeros(size(C)) ];
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sys = ss(At,Bt,Ct,0);
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lsim(sys,zeros(size(t)),t,[x0 x0]);
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title('Linear Simulation Results (with observer)')
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xlabel('Time (sec)')
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ylabel('Ball Position (m)')
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t = 0:1E-6:0.1;
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x0 = [0.01 0.5 -5];
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[y,t,x] = lsim(sys,zeros(size(t)),t,[x0 x0]);
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n = 3;
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e = x(:,n+1:end);
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x = x(:,1:n);
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x_est = x - e;
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% Save state variables explicitly to aid in plotting
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h = x(:,1); h_dot = x(:,2); i = x(:,3);
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h_est = x_est(:,1); h_dot_est = x_est(:,2); i_est = x_est(:,3);
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plot(t,h,'-r',t,h_est,':r',t,h_dot,'-b',t,h_dot_est,':b',t,i,'-g',t,i_est,':g')
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legend('h','h_{est}','hdot','hdot_{est}','i','i_{est}')
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xlabel('Time (sec)')
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% Save state variables explicitly to aid in plotting
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h = x(:,1); h_dot = x(:,2); i = x(:,3);
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h_est = x_est(:,1); h_dot_est = x_est(:,2); i_est = x_est(:,3);
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plot(t,h,'-r',t,h_est,':r',t,h_dot,'-b',t,h_dot_est,':b',t,i,'-g',t,i_est,':g')
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legend('h','h_{est}','hdot','hdot_{est}','i','i_{est}')
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xlabel('Time (sec)')
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end
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%discrete
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Ts=1/50; % deltatau std. frq. is 5kHz
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Ts=1/5000; % deltatau std. frq. is 5kHz
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%The discrete system works with sampling >100Hz,. the bigger the frequency the better the result
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%With sampling = 80Hz hte system already becomes instable.
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ss_t=ss(At,Bt,Ct,Dt);
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figure();pzplot(ss_t)
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%figure();pzplot(ss_t)
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ss_tz=c2d(ss_t,Ts);
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figure();pzplot(ss_tz)
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%figure();pzplot(ss_tz)
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[Atz,Btz,Ctz,Dtz]=ssdata(ss_tz);
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