function [ssc]=testObserver(mot) %http://ctms.engin.umich.edu/CTMS/index.php?example=Introduction§ion=ControlStateSpace mdl=1; % 0:hovering ball 1:fast stage if mdl==0 A = [ 0 1 0 980 0 -2.8 0 0 -100 ]; B = [ 0 0 100 ]; C = [ 1 0 0 ]; D=0; else [A,B,C,D]=ssdata(mot.ssMdl); C=C(3,:);D=D(3); numc=(mot.mdl.numc); denc=(mot.mdl.denc); num1=(mot.mdl.num1); den1=(mot.mdl.den1); g1=tf(numc,denc); % iqCmd->iqMeas s1=ss(g1); 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) g2=tf(num1,den1); %iqMeas->ActPos without resonance frequencies s2=ss(g2); s3=append(s1,s2); s3.A(3,2)=s3.C(1,2)*s3.B(3,2); %d=.77;w0=9100; %1.44kHz -> T0=6.9046e-04 %numc=[w0^2]; %denc=[1 d*2*w0 w0^2]; %T0=6E-4; %w=1/1E-3=1E3 -> f=w/(2pi)=1000/6.2=159Hz %numc=[1]; %denc=[T0^2 d*2*T0 1]; %bode(numc,denc) num=conv(numc,num1);%num=1; den=conv(denc,den1);%den=[1 0 0]; g4=tf(num,den); %iqMeas->ActPos s4=ss(g4); mot.ssMdl s3 s4 [A,B,C,D]=ssdata(s4); end Ap=A;Am=A; Bp=B;Bm=B; Cp=C;Cm=C; Dp=D;Dm=D;Dt=D; poles = eig(A); disp(poles); if mdl==0 t = 0:0.01:2; u = zeros(size(t)); x0 = [0.01 0 0]; sys = ss(A,B,C,D); [y,t,x] = lsim(sys,u,t,x0); plot(t,y) title('Open-Loop Response to Non-Zero Initial Condition') xlabel('Time (sec)') ylabel('Ball Position (m)') p1 = -10 + 10i; p2 = -10 - 10i; p3 = -50; K = place(A,B,[p1 p2 p3]); sys_cl = ss(A-B*K,B,C,0); lsim(sys_cl,u,t,x0); xlabel('Time (sec)') ylabel('Ball Position (m)') p1 = -20 + 20i; p2 = -20 - 20i; p3 = -100; P=[p1 p2 p3]; K = place(A,B,P); sys_cl = ss(A-B*K,B,C,0); lsim(sys_cl,u,t,x0); xlabel('Time (sec)') ylabel('Ball Position (m)') t = 0:0.01:2; u = 0.001*ones(size(t)); sys_cl = ss(A-B*K,B,C,0); lsim(sys_cl,u,t); xlabel('Time (sec)') ylabel('Ball Position (m)') axis([0 2 -4E-6 0]) V=-1./(Cm*(Am-Bm*K)^-1*Bm); %(from Lineare Regelsysteme2 (Glattfelder) page:173 ) lsim(sys_cl,V*u,t) title('Linear Simulation Results (with Nbar)') xlabel('Time (sec)') ylabel('Ball Position (m)') axis([0 2 0 1.2*10^-3]) else x0 = [0 0 0 0]; p1=-63+2.80i; p2=-62+1.50i; P=[p1 p1' p2 p2']; P=[-4000+100j -4000-100j -500+10j -500-10j]; K = place(A,B,P); Ts=1/5000 t = 0:Ts:2; u = 0.001*ones(size(t)); V=-1./(Cm*(Am-Bm*K)^-1*Bm); %(from Lineare Regelsysteme2 (Glattfelder) page:173 ) sys_cl = ss(A-B*K,B*V,C,0); lsim(sys_cl,u,t,x0); xlabel('Time (sec)') ylabel('Motor Position (m)') axis([0 2 0 1.2E-3]) end if mdl==0 op1 = -100; op2 = -101; op3 = -102; OP=[op1,op2,op3]; OP=P*2; L = place(A',C',OP)'; At = [ A-B*K B*K zeros(size(A)) A-L*C ]; Bt = [ B*V zeros(size(B)) ]; Ct = [ C zeros(size(C)) ]; sys = ss(At,Bt,Ct,0); %lsim(sys,zeros(size(t)),t,[x0 x0]); lsim(sys,u,t,[x0 x0]*0); title('Linear Simulation Results (with observer)') xlabel('Time (sec)') ylabel('Ball Position (m)') else OP=P*2; L = place(A',C',OP)'; At = [ A-B*K B*K zeros(size(A)) A-L*C ]; Bt = [ B*V zeros(size(B)) ]; Ct = [ C zeros(size(C)) ]; sys = ss(At,Bt,Ct,0); lsim(sys,u,t,[x0 x0]*0); title('Linear Simulation Results (with observer)') xlabel('Time (sec)') ylabel('Motor Position (m)') axis([0 2 0 1.2E-3]) end if mdl==0 t = 0:1E-6:0.1; x0 = [0.01 0.5 -5]; [y,t,x] = lsim(sys,zeros(size(t)),t,[x0 x0]); n = 3; e = x(:,n+1:end); x = x(:,1:n); x_est = x - e; % Save state variables explicitly to aid in plotting h = x(:,1); h_dot = x(:,2); i = x(:,3); h_est = x_est(:,1); h_dot_est = x_est(:,2); i_est = x_est(:,3); plot(t,h,'-r',t,h_est,':r',t,h_dot,'-b',t,h_dot_est,':b',t,i,'-g',t,i_est,':g') legend('h','h_{est}','hdot','hdot_{est}','i','i_{est}') xlabel('Time (sec)') end %discrete Ts=1/5000; % deltatau std. frq. is 5kHz %The discrete system works with sampling >100Hz,. the bigger the frequency the better the result %With sampling = 80Hz hte system already becomes instable. ss_t=ss(At,Bt,Ct,Dt); %figure();pzplot(ss_t) ss_tz=c2d(ss_t,Ts); %figure();pzplot(ss_tz) [Atz,Btz,Ctz,Dtz]=ssdata(ss_tz); [Apz,Bpz,Cpz,Dpz]=ssdata(c2d(ss(Ap,Bp,Cp,Dp),Ts)); [Amz,Bmz,Cmz,Dmz]=ssdata(c2d(ss(Am,Bm,Cm,Dm),Ts)); Ao=Am-L*Cm; Bo=[Bm L]; Co=K; Do=zeros(size(Co,1),size(Bo,2)); [Aoz,Boz,Coz,Doz]=ssdata(c2d(ss(Ao,Bo,Co,Do),Ts)); %state space controller ssc=struct(); 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"] ssc=setfield(ssc,k,eval(k)); end mdlName='testObserverSim'; open(mdlName); end