144 lines
3.1 KiB
Matlab
144 lines
3.1 KiB
Matlab
function [ssc]=testObserver(mot)
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%http://ctms.engin.umich.edu/CTMS/index.php?example=Introduction§ion=ControlStateSpace
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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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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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Ap=A;Am=A;
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Bp=B;Bm=B;
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Cp=C;Cm=C;
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Dp=D;Dm=D;Dt=D;
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poles = eig(A);
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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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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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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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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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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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%discrete
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Ts=1/50; % 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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ss_tz=c2d(ss_t,Ts);
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figure();pzplot(ss_tz)
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[Atz,Btz,Ctz,Dtz]=ssdata(ss_tz);
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[Apz,Bpz,Cpz,Dpz]=ssdata(c2d(ss(Ap,Bp,Cp,Dp),Ts));
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[Amz,Bmz,Cmz,Dmz]=ssdata(c2d(ss(Am,Bm,Cm,Dm),Ts));
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Ao=Am-L*Cm;
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Bo=[Bm L];
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Co=K;
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Do=zeros(size(Co,1),size(Bo,2));
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[Aoz,Boz,Coz,Doz]=ssdata(c2d(ss(Ao,Bo,Co,Do),Ts));
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%state space controller
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ssc=struct();
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for k=["Ts","At","Bt","Ct","Dt","Atz","Btz","Ctz","Dtz","Ap","Bp","Cp","Dp","Am","Bm","Cm","Dm","Ao","Bo","Co","Do","Apz","Bpz","Cpz","Dpz","Aoz","Boz","Coz","Doz","V","K","L"]
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ssc=setfield(ssc,k,eval(k));
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end
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mdlName='testObserverSim';
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open(mdlName);
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end
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