257 lines
6.3 KiB
Matlab
257 lines
6.3 KiB
Matlab
function [ssc]=StateSpaceControlDesign(mot,motid)
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% !!! first it need to run: [mot1,mot2]=identifyFxFyStage() tobuild a motor object !!!
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%
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% builds a state space controller designed for the plant.
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% shows step answers of open and closed loop, also for the observer controller and the final discrete observer
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%
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% finally it opens a simulink observer file for testing
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%References:
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%http://ctms.engin.umich.edu/CTMS/index.php?example=Introduction§ion=ControlStateSpace
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%space state controller:
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% web(fullfile(docroot, 'simulink/examples.html'))
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% web(fullfile(docroot, 'simulink/examples/inverted-pendulum-with-animation.html'))
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% web(fullfile(docroot, 'simulink/examples/double-spring-mass-system.html'))
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%
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% https://www.youtube.com/watch?v=Lax3etc837U
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%ss_ol=mot.ssPlt;
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ss_ol_plt=mot.ssPlt; %real plant (model of real plant)
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ss_ol_plt.Name='open loop plant';
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ss_ol_mdl=mot.ssMdl;%ssMdl; %simplified model (observable,controlable) for observer
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ss_ol_mdl.Name='open loop model';
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[Ap,Bp,Cp,Dp]=ssdata(ss_ol_plt);
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[Am,Bm,Cm,Dm]=ssdata(ss_ol_mdl);
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%sys=ss(sys.A,sys.B,sys.C(3,:),0); % this would reduce the outputs to position only
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figure();h=bodeplot(ss_ol_plt,ss_ol_mdl);
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setoptions(h,'IOGrouping','all')
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% step answer on open loop:
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t = 0:1E-4:.5;
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u = ones(size(t));
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xp0 = zeros(1,length(Ap));
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xm0 = zeros(1,length(Am));
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[yp,t,x] = lsim(ss_ol_plt,u,t,xp0);
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[ym,t,x] = lsim(ss_ol_mdl,u,t,xm0);
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figure();plot(t,yp,t,ym,'--');title('step on open loop (plant and model)');
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legend('plt.iqMeas','plt.iqVolts','plt.actPos','mdl.iqMeas','mdl.iqVolts','mdl.actPos')
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poles = eig(Am);
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%w0=abs(poles);
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%ang=angle(-poles);
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%-------------------
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%p=w0.*exp(j.*ang)
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% *** space state controller ***
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%
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%place poles for the controller feedback
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if motid==1
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%2500rad/s = 397Hz -> locate poles here
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%6300rad/s = 1027Hz -> locate poles here
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if length(poles)==4
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p1=-6300+2800i;
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p2=-6200+1500i;
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P=[p1 p1' p2 p2'];
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else
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p1=-3300+2800i;
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p2=-2700+500i;
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p3=-2500+10i;
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%p1=-3300+2800i;
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%p2=-1500+500i;
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%p3=-1200+10i;
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P=[p1 p1' p2 p2' p3 p3'];
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end
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else
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%2500rad/s = 397Hz -> locate poles here
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%6300rad/s = 1027Hz -> locate poles here
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if length(poles)==4
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p1=-6300+2800i;
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p2=-6200+1500i;
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P=[p1 p1' p2 p2'];
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else
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p1=-3300+2800i;
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p2=-1900+130i;
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p3=-2900+80i;
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p4=-2300+450i;
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p5=-2000+20i;
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p6=-1500+10i;
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%p1=-3300+2800i;
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%p2=-1500+500i;
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%p3=-1200+10i;
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P=[p1 p1' p2 p2' p3 p3'];% p4 p4' p5 p5' p6 p6'];
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end
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end
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K = place(Am,Bm,P);
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%K = acker(Am,Bm,Pm);
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V=-1./(Cm*(Am-Bm*K)^-1*Bm); %(from Lineare Regelsysteme2 (Glattfelder) page:173 )
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%Nbar(2)=1; %the voltage stuff is crap for now
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if length(V)>1
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V=V(3); % only the position scaling needed
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end
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%prefilter to compensate non observable resonance frequencies
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numV=mot.prefilt.Numerator{1};
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denV=mot.prefilt.Denominator{1};
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% step answer on closed loop with space state controller:
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t = 0:1E-4:.5;
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ss_cl = ss(Am-Bm*K,Bm*V,Cm,0,'Name','space state controller','InputName',mot.ssMdl.InputName,'OutputName',mot.ssMdl.OutputName);
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[y,t,x]=lsim(ss_cl,V*u,t,xm0);
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figure();plot(t,y);title('step on closed loop');
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% *** observer controller ***
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%
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%observer poles-> 5 times farther left than system poles
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if motid==1
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op1=(p1*5);
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op2=(p2*5);
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if length(poles)>4
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op3=(p3*5);
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OP=[op1 op1' op2 op2' op3 op3'];
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else
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OP=[op1 op1' op2 op2'];
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end
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else
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op1=(p1*2);
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op2=(p2*2);
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if length(poles)>4
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op3=(p3*2);
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op4=(p4*2);
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op5=(p5*2);
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op6=(p6*2);
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OP=[op1 op1' op2 op2' op3 op3'];% op4 op4' op5 op5' op6 op6'];
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else
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OP=[op1 op1' op2 op2'];
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end
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end
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L=place(Am',Cm',OP)';
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%L=acker(A',C',OP)';
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At = [ Am-Bm*K Bm*K
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zeros(size(Am)) Am-L*Cm ];
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Bt = [ Bm*V
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zeros(size(Bm)) ];
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Ct = [ Cm zeros(size(Cm)) ];
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% step answer on closed loop with observer controller:
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ss_o = ss(At,Bt,Ct,0,'Name','observer controller','InputName',{'desPos'},'OutputName',mot.ssMdl.OutputName);
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figure();lsim(ss_o,ones(size(t)),t,[xm0 xm0]);title('step on closed loop with observer');
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% *** disctrete observer controller ***
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%
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Ts=1/5000; % 5kHz
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ss_od = c2d(ss_o,Ts);
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ss_od .Name='discrete obsvr ctrl';
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% step answer on closed loop with disctrete observer controller:
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t = 0:Ts:.05;
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figure();lsim(ss_od ,ones(size(t)),t,[xm0 xm0]);title('step on closed loop with observer discrete');
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%plot all bode diagrams of desPos->actPos
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figure();
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h=bodeplot(ss_cl(3),ss_o(3),ss_od(3));
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setoptions(h,'FreqUnits','Hz','Grid','on');legend('location','sw');
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figure();
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h=pzplot(ss_cl(3),ss_o(3),ss_od(3));
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setoptions(h,'FreqUnits','Hz','Grid','on');legend('location','sw');
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%calculate matrices for the simulink system
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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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mdlName='observer';
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open(mdlName);
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%state space controller
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ssc=struct();
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for k=["Ts","Ap","Bp","Cp","Dp","Ao","Bo","Co","Do","V","K","L","ss_cl","ss_o","ss_od","numV","denV"]
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ssc=setfield(ssc,k,eval(k));
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end
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end
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%code snipplets from an example on youtube (see reference at top)
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function SCRATCH()
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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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poles = eig(A)
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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,0);
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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;
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p2 = -10 - 10i;
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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;
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p2 = -20 - 20i;
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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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Nbar = rscale(sys,K)
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lsim(sys_cl,Nbar*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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end
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