From db8640997a2389cd9ab561d7c999dfb24d0523a3 Mon Sep 17 00:00:00 2001 From: Thierry Zamofing Date: Mon, 18 Feb 2019 10:51:31 +0100 Subject: [PATCH] toward optimized cotroller parameters --- MXfastStageDoc/MXfastStage.tex | 17 ++++++++++++++++- matlab/identifyFxFyStage.m | 23 +++++++++++++++++++++++ matlab/libESB_MX.slx | Bin 38483 -> 39031 bytes matlab/sample.slx | Bin 27215 -> 28004 bytes matlab/simFxFyStage.m | 11 ++++++++++- matlab/stage_closed_loop.slx | Bin 35124 -> 35490 bytes python/MXTuning.py | 4 ++-- 7 files changed, 51 insertions(+), 4 deletions(-) diff --git a/MXfastStageDoc/MXfastStage.tex b/MXfastStageDoc/MXfastStage.tex index 7896b3f..613092b 100644 --- a/MXfastStageDoc/MXfastStage.tex +++ b/MXfastStageDoc/MXfastStage.tex @@ -782,9 +782,24 @@ Motor[1].Ctrl =UserAlgo.ServoCtrlAddr[1] \subsection{The reality of the state space controller} The state space controller assumes that the system is observable and controlable. The bode plot shows a flat amplitude at low frequencies, which makes the feeling, that the system is observable and controlable. But in fact the reason of that flat amplitude is friction (section \ref{sec:friction}). The viscode damping is also negligable.\\ -This results to the fact that $F=m \cdot \ddot{x}$ consists of really 2 integrators. But an integrator $\frac{1}{s}$ is neighter observable and controlable. Therefore we have to check, how to implement an optimal controller for such a system. +This results to the fact that $F=m \cdot \ddot{x}$ consists of really 2 integrators. But an integrator $\frac{1}{s}$ is neighter observable and controlable. Therefore we have to check, how to implement an optimal controller for such a system.\\ +A controller consists in a feed forward and a feed back transfer function. +The overall transfer functions y/u and y/e are: ... Setting H(s)=s results in a overall transfer function of y/u=... and y/e=... .\\ +Simulating all this in MATLAB results in unstable system because of the derivate, but with a discrete differentiator it becomes stable again.\\ +The optimal loop would be Kaff=(bode value of integrator), Kvff=Kvfb=Kafb=0. +Kp values is the speed to attenuate error values.\\ +This is stable as long as Kp=0. With a Kp value, the system starts to osscilate instable. Stability can be achived again with e.g. Kvff=Kvfb=...\\ +Looking at the Standard Delta Tau controller, one sees, that it has exactly the feed forward and feedback loop. So after all the measurements, we can calculate the optimal Kfff and Kaff values. +Kp and Ki values will attenuate the errors. Kvff=Kvfb makes the system stable at hither Kp values. +% Motor 1: 19.8Hz 0dB +% K=(19.8*2*np.pi)**2 +% Ts=5kHz=.2ms +% Kaff = 1/(Ts*Ts*K) = 1/((19.8*2*np.pi)**2/5000/5000) = 1615.2877200403302 + +% Motor 2:11.84Hz 0dB +% Kaff = 1/((11.84*2*np.pi)**2/5000/5000) = 4517.278506241804 \vspace{1pc} diff --git a/matlab/identifyFxFyStage.m b/matlab/identifyFxFyStage.m index d4d3236..9b10473 100644 --- a/matlab/identifyFxFyStage.m +++ b/matlab/identifyFxFyStage.m @@ -270,6 +270,29 @@ function motCell=identifyFxFyStage(mode) mot.ss_q.Name='simplified mechanics, no current loop, no resonance'; chkCtrlObsv(mot.ss_q,'ss_q fyStage'); + % TESTS + % u +-----------+ y + %iqCmd------->|1 1|-------> iqMeas + % | 2|-------> actVel + % | 3|-------> actPos + % +-----------+ + s=tfq.InputName{1};tfq.InputName{1}='iqMeas'; + mot.ss_cq=connect(tfc,tfq,'iqCmd',{'iqMeas','actVel','actPos'}); + mot.ss_cq.Name='simplified mechanics, current loop, no resonance'; + tfq.InputName{1}=s;%restore + + % TESTS + % u +-----------+ y + %iqCmd------->|1 1|-------> actVel + % | 2|-------> actPos + % +-----------+ + s=tf1.InputName{1};tf1.InputName{1}='iqCmd'; + mot.ss_qr=connect(tfq,tf1,'iqCmd',{'actVel','actPos'}); + mot.ss_qr.Name='simplified mechanics, no current loop, resonance'; + tfp.InputName{1}=s;%restore + + + %h=bodeplot(mot.meas,'r',mot.tf4_2,'b',mot.tf6_4,'g'); %h=bodeplot(mot.meas,'r',mot.tf2_0,'b',mot.tf_mdl,'g',mot.w); plotBode(mot) diff --git a/matlab/libESB_MX.slx b/matlab/libESB_MX.slx index 149fbc4e5c3d754b05d33f5d8a02084a654ed262..f12acc804824d69932542acd68aae8cbce8f9ccb 100644 GIT binary patch delta 23193 zcmV({K+?a{tOED20vk|E0|XQR000O8>Q*;OL`L-cWdQ&H!~y^S87^HU{u|Na3T7SK?+v=u^Z*b1x+{3*$n}5nG*n+V_ zs~I9ui~>+x7ebXY^tf7t6BJm-RKY5(V1`<-D46FNuPN6C?u@R%H~}{BM#@rN&(OxX znqqAE1|+kQS13=ewUNyEtA8nR&GJ18x zp#llYSxh2=f3#A#wuZAW4&;&AfsyvCxMv3Crxk;$X_}}>d!5fu@bmKaq5o*Eg#L%9EIk!)KU;NxF)s^zwox zZC9NF9e;WSP*q*LFG`1ifPjL4fC3*Jx*Md9lz^mkHzFa8fJk>sNq2W1>CPi1 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z(5Xb}h`{O0KtuTL{JAR-pH`x<*V78Sz$1PdNsimhvjB@1ZX`I_g}!dD|bHue9wgaHjGdIqT{&yl+6g z5by7w@RIE>hME7V3tmAUdh~$vlmMbX0|E3+d$z&*^*9|X)=`0CGG(u9%~2DKV??RE z_rC%efi0qr;h5pH;hh=n!C4qx$W1ip zWD17-t>Aw721H~o42}shG^Zl?zh8VXFuea0@t?BdKa(H;m6(e_pmKv4w6H*s z7W5E1YX7+eAUO+ah&Xl7t`-R>^FP;L6Etce2BD_~s?ntZ@miu0{7*UmL!tctvB1Fo zHzvI{2+*SjC0J5JVCaB)ETtfdbU-Lpk`R)*AWbVi2xNUwh7~(RgaN3-m>l$GMGf&~ T2x2g$0LfUR!8{rLe^~zu8>|h6 diff --git a/matlab/simFxFyStage.m b/matlab/simFxFyStage.m index b5d8f21..d9af8a6 100644 --- a/matlab/simFxFyStage.m +++ b/matlab/simFxFyStage.m @@ -13,12 +13,20 @@ function [pb]=simFxFyStage(mot) if mot.id==1 %!motor_servo(mot=1,ctrl='ServoCtrl',Kp=25,Kvfb=400,Ki=0.02,Kvff=350,Kaff=5000,MaxInt=1000) %!motor(mot=1,dirCur=0,contCur=800,peakCur=2400,timeAtPeak=1,IiGain=5,IpfGain=8,IpbGain=8,JogSpeed=10.,numPhase=3,invDir=True,servo=None,PhasePosSf=1./81250,PhaseFindingDac=100,PhaseFindingTime=50,SlipGain=0,AdvGain=0,PwmSf=10000,FatalFeLimit=200,WarnFeLimit=100,InPosBand=2,homing='enc-index') - pb.Kp=25;pb.Kvfb=400;pb.Ki=0.02;pb.Kvff=350;pb.Kaff=5000;pb.MaxInt=1000; + %pb.Kp=25;pb.Kvfb=400;pb.Ki=0.02;pb.Kvff=350;pb.Kaff=5000;pb.MaxInt=1000; + pb.Kp=25;pb.Kvfb=350;pb.Ki=0.02;pb.Kvff=350;pb.Kaff=1/(1.548e04*(pb.Ts^2));pb.MaxInt=1000; + %19.8Hz 0dB K=(19.8*2*np.pi)**2=15477.1 Ts=5kHz=.2ms + %Kaff = 1/(Ts*Ts*K) = 1/((19.8*2*np.pi)**2/5000**2) = 1615.2877200403302 + %Kfff=100 else %!motor_servo(mot=2,ctrl='ServoCtrl',Kp=22,Kvfb=350,Ki=0.02,Kvff=240,Kaff=1500,MaxInt=1000) %!motor(mot=2,dirCur=0,contCur=800,peakCur=2400,timeAtPeak=1,IiGain=5,IpfGain=8,IpbGain=8,JogSpeed=10.,numPhase=3,invDir=True,servo=None,PhasePosSf=1./81250,PhaseFindingDac=100,PhaseFindingTime=50,SlipGain=0,AdvGain=0,PwmSf=10000,FatalFeLimit=200,WarnFeLimit=100,InPosBand=2,homing='enc-index') %Kp=22;Kvfb=350;Ki=0.02;Kvff=240;Kaff=1500;MaxInt=1000; pb.Kp=22;pb.Kvfb=350;pb.Ki=0.02;pb.Kvff=240;pb.Kaff=3500;pb.MaxInt=1000; + %11.84Hz 0dB K=(11.84*2*np.pi)**2=5534.3 Ts=5kHz=.2ms + %Kaff = 1/(Ts*Ts*K) = 1/((11.84*2*np.pi)**2/5000**2) = 4517.278506241803 + %Kfff=100 + end pb.ss_plt=mot.ss_plt; pb.sel={3,[3]}; %pb.ss_plt=mot.ss_plt0; pb.sel={3,[3]}; @@ -26,6 +34,7 @@ function [pb]=simFxFyStage(mot) %pb.ss_plt=mot.ss_d1; pb.sel={3,[3]}; %pb.ss_plt=mot.ss_1; pb.sel={2,[2]}; %pb.ss_plt=mot.ss_p; pb.sel={2,[2]}; + %pb.ss_plt=mot.ss_q; pb.sel={2,[2]}; %mdlName='stage_closed_loop'; %open(mdlName) diff --git a/matlab/stage_closed_loop.slx b/matlab/stage_closed_loop.slx index 1be8e990ce4d280a892ed1d521144f861130d296..6089ee50e8c0bd5b07af8d12da9a7c03734f30da 100644 GIT binary patch delta 13905 zcmaibbC4!H@aEXIZS2^#%^lme-?9Df?ASJTY}>YWY#X=V)m{DS{<@?psp|BTbX6*; z?oOV@WUzu1Fnnb>a0m<#5D*v;J7E)rHm`;n6HpM4elQRad|+P)5x`${PH}()<1;1v z8Ow@|OJ;-8=IH>fkPXieA>UKiGziLR>%+&oV_5-vXE$r0EyCB4cV~ibHK@K=6Sn|W z1e7K}M%AA6p;IT64MTfGqmRCtL=3u)ChfSqEPWP=D7L1r70qrp?w5JN^z3q5hOylc z7DY>v7L8I(Q_|*ZC17ngBL=w}lmOi&jFQ{HX~fwUXStA^R|m_au}Vl`2^RxQ3=-|v zpEOB~Z!7atBn~}4mPBeBXvy`M{dn9IU)}hM66*r0Q#V1Oq1uV}(yL12@^wvEVShkt 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zZQT(wxk01OL`$H>*%0O$mKUW)%f;|Sj-D0PTCw2}Tq1H8Da8+2UF~;-m{cxR;vMev zM>W*NwkxOrBLB7T=Qseo5zQYA8uI^GeUflP4L~!KJVWKcGQpC(Lh+NfLkaQ!Un>d- z$bXKM|4+CjVTXx>(c&fPh0zlH{{_GQJL^C1(0>s{@}K-C3HHjDbn;*Nx^@y{xHy=D zd(xW+K~iiu9T=@gQb)Kvn2uKxbc75Tw|A0i1poiDPYDs2pioIF5g19G5u#wlzW+_3 zC!t32g7NtMA7~iK1Gedxlo2TmRs%6cOg diff --git a/python/MXTuning.py b/python/MXTuning.py index ee889e2..6cd0830 100755 --- a/python/MXTuning.py +++ b/python/MXTuning.py @@ -206,8 +206,8 @@ class MXTuning(Tuning): denq=np.poly1d([1,0,0]) #force->velocity (simplified) - #reiner integrator: 19.8Hz=0dB -> k=frq*2*pi - numv=np.poly1d([19.8*2*np.pi]) + #reiner integrator: 11.84Hz=0dB -> k=frq*2*pi + numv=np.poly1d([11.84*2*np.pi]) denv=np.poly1d([1,0])