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towards simple prefilters

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zamofing_t
2019-02-08 16:46:38 +01:00
parent cc582d1bf8
commit af732b313e
4 changed files with 64 additions and 35 deletions
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45
MXfastStageDoc/MXfastStage.tex
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@@ -466,11 +466,11 @@ Figures \ref{fig:mot_chirp_sim} showed similar response as the real stages (Figu
\begin{figure}[h!] \begin{figure}[h!]
\center \center
\includegraphics[scale=.45]{../matlab/figures/sim_cl_DTGz.png} \includegraphics[scale=.45]{../matlab/figures/sim_cl_DTGz.png}\\
\includegraphics[scale=.65]{../matlab/figures/sim_cl_DTGz_1.eps} \includegraphics[scale=.45]{../matlab/figures/sim_cl_DTGz_1.eps}
\includegraphics[scale=.65]{../matlab/figures/sim_cl_DTGz_bode1.eps} \includegraphics[scale=.45]{../matlab/figures/sim_cl_DTGz_bode1.eps}\\
\includegraphics[scale=.65]{../matlab/figures/sim_cl_DTGz_2.eps} \includegraphics[scale=.45]{../matlab/figures/sim_cl_DTGz_2.eps}
\includegraphics[scale=.65]{../matlab/figures/sim_cl_DTGz_bode2.eps} \includegraphics[scale=.45]{../matlab/figures/sim_cl_DTGz_bode2.eps}
\caption{Motor 1 sim Motor 2 sim} \caption{Motor 1 sim Motor 2 sim}
\label{fig:mot_chirp_sim} \label{fig:mot_chirp_sim}
\end{figure} \end{figure}
@@ -562,27 +562,46 @@ end
\begin{figure}[h!] \begin{figure}[h!]
\center \center
\includegraphics[scale=.35]{../matlab/figures/sim_cl_observer.png}
\caption{Observer flow chart}
\label{fig:mot_observer_sim}
\end{figure}
\includegraphics[scale=.45]{../matlab/figures/sim_cl_observer.png}
\includegraphics[scale=.65]{../matlab/figures/sim_cl_observer_1.eps} \begin{figure}[h!]
\includegraphics[scale=.65]{../matlab/figures/sim_cl_observer_bode1.eps} \center
\includegraphics[scale=.65]{../matlab/figures/sim_cl_observer_2.eps} \includegraphics[scale=.45]{../matlab/figures/sim_cl_observer_1.eps}
\includegraphics[scale=.65]{../matlab/figures/sim_cl_observer_bode2.eps} \includegraphics[scale=.45]{../matlab/figures/sim_cl_observer_bode1.eps}\\
\caption{Motor 1 sim Motor 2 sim} \includegraphics[scale=.45]{../matlab/figures/sim_cl_observer_2.eps}
\label{fig:mot_chirp_sim} \includegraphics[scale=.45]{../matlab/figures/sim_cl_observer_bode2.eps}
\caption{Observer sim: Motor 1 Motor 2}
\label{fig:mot_observer_sim}
\end{figure} \end{figure}
Comparing figures \ref{fig:mot_chirp_sim} and \ref{fig:mot_observer_sim} shows the better behavious of the observer model.
With an additional prefilter resonance and reductions can be suppressed a bit.\\ With an additional prefilter resonance and reductions can be suppressed a bit.\\
\begin{figure}[h!]
\center
\includegraphics[scale=.45]{../matlab/figures/sim_cl_obs_pf_1.eps}
\includegraphics[scale=.45]{../matlab/figures/sim_cl_obs_pf_bode1.eps}\\
\includegraphics[scale=.45]{../matlab/figures/sim_cl_obs_pf_2.eps}
\includegraphics[scale=.45]{../matlab/figures/sim_cl_obs_pf_bode2.eps}
\caption{Observer with prefilter sim: Motor 1 Motor 2}
\label{fig:mot_observer_sim}
\end{figure}
The system was simulated with 5kHz servo loop frequency. The system was simulated with 5kHz servo loop frequency.
Higher servo loop frequency does not help, because a continious state space controller behaves not relevantly better than a sampled state space controller at 5kHz.\\ Higher servo loop frequency does not help, because a continious state space controller behaves not relevantly better than a sampled state space controller at 5kHz.\\
Now the controller must be implemented on deltatau to check the performance on the real stage. Now the controller must be implemented on deltatau to check the performance on the real stage.
\FloatBarrier
\subsection{Implementing state space controller on Deltatau} \subsection{Implementing state space controller on Deltatau}
In MATLAB the function \verb|StateSpaceControlDesign()| produces files \verb%/tmp/ssc[1|2].mat%.\\ In MATLAB the function \verb|StateSpaceControlDesign()| produces files \verb%/tmp/ssc[1|2].mat%.\\

40
matlab/StateSpaceControlDesign.m
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@@ -75,8 +75,6 @@ function [ssc]=StateSpaceControlDesign(mot)
end end
ss_mdl.Name='open loop model'; %model for observer ss_mdl.Name='open loop model'; %model for observer
[Ap,Bp,Cp,Dp]=ssdata(ss_plt);
[Am,Bm,Cm,Dm]=ssdata(ss_mdl); [Am,Bm,Cm,Dm]=ssdata(ss_mdl);
if bitand(mShow,1) if bitand(mShow,1)
@@ -84,7 +82,7 @@ function [ssc]=StateSpaceControlDesign(mot)
setoptions(h,'IOGrouping','all') setoptions(h,'IOGrouping','all')
end end
xp0 = zeros(1,length(Ap)); xp0 = zeros(1,length(ss_plt.A));
xm0 = zeros(1,length(Am)); xm0 = zeros(1,length(Am));
if bitand(mShow,2) if bitand(mShow,2)
@@ -142,6 +140,7 @@ function [ssc]=StateSpaceControlDesign(mot)
%p1=-6300+2800i; p2=-6200+1500i; %p1=-6300+2800i; p2=-6200+1500i;
%P=[p1 p1' p2 p2']; %P=[p1 p1' p2 p2'];
P=[-2500 -2800 -1500+10j -1500-10j]; P=[-2500 -2800 -1500+10j -1500-10j];
P=[-2500 -2800 -1100+10j -1100-10j];
case 2 case 2
%p1=-6300+2800i; p2=-6200+1500i; %p1=-6300+2800i; p2=-6200+1500i;
%P=[p1 p1' p2 p2']; %P=[p1 p1' p2 p2'];
@@ -235,21 +234,12 @@ function [ssc]=StateSpaceControlDesign(mot)
%discrete observer controller %discrete observer controller
ss_oz = c2d(ss_o,Ts); ss_oz = c2d(ss_o,Ts);
[Aoz,Boz,Coz,Doz]=ssdata(ss_oz);
%mdlName='observer';
%open(mdlName);
%prefilter to compensate non observable resonance frequencies %prefilter to compensate non observable resonance frequencies
prefilt=Prefilt(mot,mPrefilt); prefilt=Prefilt(mot,mPrefilt);
numV=prefilt.Numerator{1};
denV=prefilt.Denominator{1};
%discrete prefilter %discrete prefilter
prefiltz=c2d(prefilt,Ts); prefiltz=c2d(prefilt,Ts);
numVz=prefiltz.Numerator{1};
denVz=prefiltz.Denominator{1};
if bitand(mShow,64) if bitand(mShow,64)
h=bodeplot(prefilt,prefiltz); h=bodeplot(prefilt,prefiltz);
@@ -258,8 +248,6 @@ function [ssc]=StateSpaceControlDesign(mot)
%state space controller %state space controller
ssc=struct(); 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","ss_cl","ss_o","ss_oz","numV","denV","numVz","denVz"]
%for k=["Ts","Ap","Bp","Cp","Dp","Ao","Bo","Co","Do","Aoz","Boz","Coz","Doz","V","K","L","ss_cl","ss_o","ss_oz","numV","denV","numVz","denVz"]
for k=["Ts","ss_plt","ss_o","ss_oz","prefilt","prefiltz","V"] for k=["Ts","ss_plt","ss_o","ss_oz","prefilt","prefiltz","V"]
ssc=setfield(ssc,k,eval(k)); ssc=setfield(ssc,k,eval(k));
end end
@@ -287,14 +275,22 @@ function pf=Prefilt(mot,mode)
denV=den1; denV=den1;
pf=tf(numV,denV); pf=tf(numV,denV);
else else
f=277;w0=f*2*pi; num1=[1 20 w0^2]; den1=[1 500 w0^2];
f=138;w0=f*2*pi; num2=[1 300 w0^2]; den2=[1 100 w0^2]; %Lag
f=60;w0=f*2*pi; num3=[1 33 w0^2]; den3=[1 20 w0^2]; f=[100 200]; w=f*2*pi; T=1./w;
numV=conv(num1,num2); tf1=tf([T(1) 1],[T(2) 1]);
denV=conv(den1,den2); %bo = bodeoptions;
numV=conv(conv(num1,num2),num3); %bo.FreqUnits = 'Hz'; bo.MagUnits='abs'; bo.Grid='on';
denV=conv(conv(den1,den2),den3) ; %bode(tf1,bo)
pf=tf(numV,denV);
%k=1.2; aa=2; f=[40 60];w=f*2*pi; tf([1 33 w0^2]; den3=[1 20 w0^2];
%f=277;w0=f*2*pi; num1=[1 20 w0^2]; den1=[1 500 w0^2];
%f=138;w0=f*2*pi; num2=[1 300 w0^2]; den2=[1 100 w0^2];
%f=60;w0=f*2*pi; num3=[1 33 w0^2]; den3=[1 20 w0^2];
%numV=conv(conv(num1,num2),num3);
%denV=conv(conv(den1,den2),den3) ;
%pf=tf(numV,denV);
pf=tf1;
end end
end end
%controlSystemDesigner('bode',1,pf); % <<<<<<<<< This opens a transferfunction that can be edited %controlSystemDesigner('bode',1,pf); % <<<<<<<<< This opens a transferfunction that can be edited

14
matlab/documentFunctions.m
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@@ -26,6 +26,20 @@ for k =1:2
end end
disp('document figure generation done');close all; disp('document figure generation done');close all;
close all;disp('simulate observer with prefilter...');
for k =1:2
[ssc]=StateSpaceControlDesign(mot{k});sim('observer');
f=figure(); h=plot(desPos_actPos.Time,desPos_actPos.Data,'g');
set(h(1),'color','b'); set(h(2),'color',[0 0.5 0]);
print(f,sprintf('figures/sim_cl_obs_pf_%d',mot{k}.id),'-depsc');
f=bodeSamples(desPos_actPos);
print(f,sprintf('figures/sim_cl_obs_pf_bode%d',mot{k}.id),'-depsc');
end
disp('document figure generation done');close all;
function SCRATCH() function SCRATCH()
%plots bode of desPos_actPos %plots bode of desPos_actPos
[mot1,mot2]=identifyFxFyStage(); [mot1,mot2]=identifyFxFyStage();

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matlab/observer.slx
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