From b0482babe6dcf88e577c5a2f82fc28a5d50de296 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Thu, 24 Jan 2019 17:52:32 +0100 Subject: [PATCH] Add some analysis on the coupling. Add uv_to_xy simulink blocs --- Figures/Gtvc_loop_gain.pdf | Bin 0 -> 44325 bytes Figures/Gtvc_loop_gain.png | Bin 0 -> 76126 bytes Figures/Gtvc_loop_gain.svg | Bin 0 -> 213139 bytes Figures/Gvc_loop_gain.pdf | Bin 0 -> 43289 bytes Figures/Gvc_loop_gain.png | Bin 0 -> 69084 bytes Figures/Gvc_loop_gain.svg | Bin 0 -> 204912 bytes Figures/Gvc_speed.pdf | Bin 0 -> 46770 bytes Figures/Gvc_speed.png | Bin 0 -> 70473 bytes Figures/Gvc_speed.svg | Bin 0 -> 330780 bytes ...avy.pdf => coupling_ratio_light_heavy.pdf} | Bin 67149 -> 67149 bytes ...avy.png => coupling_ratio_light_heavy.png} | Bin ...avy.svg => coupling_ratio_light_heavy.svg} | Bin Figures/coupling_ration_simscape_heavy.pdf | Bin 51769 -> 0 bytes Figures/coupling_ration_simscape_heavy.png | Bin 129201 -> 0 bytes Figures/coupling_ration_simscape_heavy.svg | Bin 264859 -> 0 bytes Figures/coupling_ration_simscape_light.pdf | Bin 49788 -> 0 bytes Figures/coupling_ration_simscape_light.png | Bin 116344 -> 0 bytes Figures/coupling_ration_simscape_light.svg | Bin 257132 -> 0 bytes rotating_frame.org | 224 +++++++++++++++--- rotating_frame.slx | Bin 30817 -> 34590 bytes 20 files changed, 193 insertions(+), 31 deletions(-) create mode 100644 Figures/Gtvc_loop_gain.pdf create mode 100644 Figures/Gtvc_loop_gain.png create mode 100644 Figures/Gtvc_loop_gain.svg create mode 100644 Figures/Gvc_loop_gain.pdf create mode 100644 Figures/Gvc_loop_gain.png create mode 100644 Figures/Gvc_loop_gain.svg create mode 100644 Figures/Gvc_speed.pdf create mode 100644 Figures/Gvc_speed.png create mode 100644 Figures/Gvc_speed.svg rename Figures/{coupling_ration_light_heavy.pdf => coupling_ratio_light_heavy.pdf} (98%) rename Figures/{coupling_ration_light_heavy.png => coupling_ratio_light_heavy.png} (100%) rename Figures/{coupling_ration_light_heavy.svg => coupling_ratio_light_heavy.svg} (100%) delete mode 100644 Figures/coupling_ration_simscape_heavy.pdf delete mode 100644 Figures/coupling_ration_simscape_heavy.png delete mode 100644 Figures/coupling_ration_simscape_heavy.svg delete mode 100644 Figures/coupling_ration_simscape_light.pdf delete mode 100644 Figures/coupling_ration_simscape_light.png delete mode 100644 Figures/coupling_ration_simscape_light.svg diff --git a/Figures/Gtvc_loop_gain.pdf b/Figures/Gtvc_loop_gain.pdf new file mode 100644 index 0000000000000000000000000000000000000000..981012ca0ccb3f5d63bbe7b045e672da5307ff8c GIT binary patch literal 44325 zcmYhCWmFqoxTq;E!QBZO+}#@7-L1GwaVeBSa19i9cXudI+}*v!wWY;c{G{JKYu)o_ z_T=@w=gpo;);tUvGIH$P9D?W!qZf%q==?NXG;WrT=wf1=DmJcmUiLHsFo_nYoP)EM zjRy^=l_gf0=_m55hYPzsL z)YrB9#jSr3Vt^%yOFNR^ULGHVpY7s|6se0#KF^0zai4VtEt#mvVFV1>51rG62l5!r z@yfXbF73F+Q3MQuOxy!+++i|lITwko%Q!&5i2cjAlvHxM$UJT(mzT30TG$DT{=>=d zk+H(aIJrmA?#x($U7TY!{@sfMmblf@kwJQZ)d4Jk_R|Ii9VCzYj5}y()5I7i;Sby* zw;rPt;8xkzcKcxnOYDA@w;AVsK$^|RKO2?AWv4zvBWIVO`K-NSL$|k z<9|sKZe4CD{l{!4cAmcg{6}ni1EmBdu*9wTTGhG)#|lM@gSiKp=Sa= z2ZAz<=LW+CSBb+L3L>+7Q;4Gt<_1sGC*{fioZ8I|a%a@n-%21O_ayY!$FJKlUVMCq 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We obtain the same result than the analytical case (figures [[fig:coupling_light]] and [[fig:coupling_heavy]]). #+begin_src matlab :results silent :exports none figure; @@ -892,18 +893,17 @@ We obtain the same result than the analytical case (figures [[fig:coupling_light #+end_src #+HEADER: :tangle no :exports results :results file :noweb yes -#+HEADER: :var filepath="Figures/coupling_ration_light_heavy.png" :var figsize="wide-tall" +#+HEADER: :var filepath="Figures/coupling_ratio_light_heavy.png" :var figsize="wide-tall" #+begin_src matlab <> #+end_src -#+NAME: fig:coupling_ration_light_heavy +#+NAME: fig:coupling_ratio_light_heavy #+RESULTS: -[[file:Figures/coupling_ration_light_heavy.png]] +[[file:Figures/coupling_ratio_light_heavy.png]] ** Plant Control - -The goal is the study control problems due to the coupling that appears because of the rotation. +The goal is to study the control problems due to the coupling that appears because of the rotation. #+begin_src matlab :exports none :results silent %% Options for Linearized @@ -923,44 +923,210 @@ The goal is the study control problems due to the coupling that appears because First, we identify the system when the rotation speed is null and then when the rotation speed is equal to 60rpm. -The actuators are voice coil with some damping. +The actuators are voice coil with some damping added. + +The bode plot of the system not rotating and rotating at 60rpm is shown figure [[fig:Gvc_speed]]. #+begin_src matlab :exports none :results silent w = 0; % Rotation speed [rad/s] m = mlight; % mass of the sample [kg] kTuv = kvc; - % cTuv = 0.1*sqrt(kTuv*m); - cTuv = 0; + cTuv = 0.1*sqrt(kTuv*m); - G = linearize(mdl, io, 0.1); - G.InputName = {'Fu', 'Fv'}; - G.OutputName = {'Du', 'Dv'}; + Gvc = linearize(mdl, io, 0.1); + Gvc.InputName = {'Fu', 'Fv'}; + Gvc.OutputName = {'Du', 'Dv'}; #+end_src #+begin_src matlab :exports none :results silent - w = 0.1; % Rotation speed [rad/s] + w = wlight; % Rotation speed [rad/s] m = mlight; % mass of the sample [kg] kTuv = kvc; - % cTuv = 0.1*sqrt(kTuv*m); - cTuv = 0; + cTuv = 0.1*sqrt(kTuv*m); - Gt = linearize(mdl, io, 0.1); - Gt.InputName = {'Fu', 'Fv'}; - Gt.OutputName = {'Du', 'Dv'}; + Gtvc = linearize(mdl, io, 0.1); + Gtvc.InputName = {'Fu', 'Fv'}; + Gtvc.OutputName = {'Du', 'Dv'}; #+end_src #+begin_src matlab :exports none :results silent figure; - bode(G, 'r-', Gt, 'b--') - legend({'G - w = 0', 'G - w = 60rpm'}, 'Location', 'southwest'); + bode(Gvc, Gtvc) + legend({'Gvc - $\omega = 0$', 'Gvc - $\omega = 60$rpm'}, 'Location', 'southwest'); #+end_src #+HEADER: :tangle no :exports results :results file :noweb yes -#+HEADER: :var filepath="Figures/coupling_ration_light_heavy.png" :var figsize="wide-tall" +#+HEADER: :var filepath="Figures/Gvc_speed.png" :var figsize="full-tall" #+begin_src matlab <> #+end_src +#+NAME: fig:Gvc_speed +#+CAPTION: Bode plot of the system not rotating and rotating at 60rmp - Voice coil and light sample +#+RESULTS: +[[file:Figures/Gvc_speed.png]] + +*** Controller design +We design a controller based on the identification when the system is not rotating. + +#+begin_src matlab :results none :exports code + sisotool(Gvc('Du', 'fu')) +#+end_src + +The controller is a lead-lag controller with the following transfer function. +#+begin_src matlab :results none :exports code + Kll = 2.0698e09*(s+40.45)*(s+1.181)/(s*(s+198.4)*(s+2790)); + K = [Kll 0; + 0 Kll]; +#+end_src + +The loop gain is displayed figure [[fig:Gvc_loop_gain]]. + +#+begin_src matlab :exports none :results silent + freqs = logspace(-2, 2, 1000); + + figure; + % Amplitude + ax1 = subaxis(2,1,1); + hold on; + plot(freqs, abs(squeeze(freqresp(Gvc('Du', 'fu')*Kll, freqs, 'Hz'))), '-'); + set(gca,'xscale','log'); set(gca,'yscale','log'); + ylabel('Amplitude [m/N]'); + set(gca, 'XTickLabel',[]); + hold off; + % Phase + ax2 = subaxis(2,1,2); + hold on; + plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Gvc('Du', 'fu')*Kll, freqs, 'Hz')))), '-'); + set(gca,'xscale','log'); + yticks(-180:180:180); + ylim([-180 180]); + xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); + hold off; + linkaxes([ax1,ax2],'x'); +#+end_src + +#+HEADER: :tangle no :exports results :results file :noweb yes +#+HEADER: :var filepath="Figures/Gvc_loop_gain.png" :var figsize="full-tall" +#+begin_src matlab + <> +#+end_src + +#+NAME: fig:Gvc_loop_gain +#+CAPTION: Loop gain obtained for a lead-lag controller on the system with a voice coil +#+RESULTS: +[[file:Figures/Gvc_loop_gain.png]] + +*** Controlling the rotating system +We here want to see if the system is robust with respect to the rotation speed. We then use the controller based on the non-rotating system, and see if the system is stable and its dynamics. + +We can then plot the same loop gain with the rotating system using the same controller (figure [[fig:Gtvc_loop_gain]]). The result obtained is unstable. + +#+begin_src matlab :exports none :results silent + freqs = logspace(-2, 2, 1000); + + figure; + % Amplitude + ax1 = subaxis(2,1,1); + hold on; + plot(freqs, abs(squeeze(freqresp(Gtvc('Du', 'fu')*Kll, freqs, 'Hz'))), '-'); + set(gca,'xscale','log'); set(gca,'yscale','log'); + ylabel('Amplitude [m/N]'); + set(gca, 'XTickLabel',[]); + hold off; + % Phase + ax2 = subaxis(2,1,2); + hold on; + plot(freqs, 180/pi*angle(squeeze(freqresp(Gtvc('Du', 'fu')*Kll, freqs, 'Hz'))), '-'); + set(gca,'xscale','log'); + yticks(-180:180:180); + ylim([-180 180]); + xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); + hold off; + linkaxes([ax1,ax2],'x'); +#+end_src + +#+HEADER: :tangle no :exports results :results file :noweb yes +#+HEADER: :var filepath="Figures/Gtvc_loop_gain.png" :var figsize="full-tall" +#+begin_src matlab + <> +#+end_src + +#+RESULTS: +[[file:Figures/Gtvc_loop_gain.png]] + +We can look at the poles of the system where we control only one direction ($u$ for instance). We obtain a pole with a positive real part. +#+begin_src matlab :results table :exports both + pole(feedback(Gtvc, blkdiag(Kll, 0))) +#+end_src + +#+RESULTS: +| -2798 | +| -58.906+94.246i | +| -58.906-94.246i | +| -71.654 | +| 3.1648 | +| -3.3031 | +| -1.1902 | + +However, when we look at the poles of the closed loop with a diagonal controller, all the poles have negative real part and the system is stable. +#+begin_src matlab :results table :exports both + pole(feedback(Gtvc, blkdiag(Kll, Kll))) +#+end_src + +#+RESULTS: +| -2798+0.035765i | +| -2798-0.035765i | +| -56.406+105.34i | +| -56.406-105.34i | +| -64.482+79.308i | +| -64.482-79.308i | +| -68.521+13.503i | +| -68.521-13.503i | +| -1.1837+0.0041777i | +| -1.1837-0.0041777i | + +*** + + + + + + + + + + + +#+begin_src matlab :results none :exports code + figure; + bode(Kll*Gvc('Du', 'fu')) +#+end_src + +#+begin_src matlab :results none :exports code + sisotool(Gtvc('Du', 'fu'), Kll) +#+end_src + +#+begin_src matlab :results none :exports code + figure; + bode(Kll*Gtvc('Du', 'fu')) +#+end_src + +#+begin_src matlab :results none :exports code + Gcl = feedback(Gvc, K); +#+end_src + +#+begin_src matlab :results none :exports code + Gtcl = feedback(Gtvc, K); +#+end_src + +#+begin_src matlab :results none :exports code + figure; + bode(Gcl, Gtcl) +#+end_src + + +** test #+begin_src matlab :exports none :results silent figure; @@ -1004,10 +1170,6 @@ The actuators are voice coil with some damping. linkaxes([ax1,ax2],'x'); #+end_src - - - - #+begin_src matlab :exports none :results silent figure; bode(Gpz_light, Gvc_light); @@ -1072,13 +1234,13 @@ Plot the ratio between the main transfer function and the coupling term: #+end_src #+HEADER: :tangle no :exports results :results file :noweb yes -#+HEADER: :var filepath="Figures/coupling_ration_simscape_light.png" :var figsize="wide-tall" +#+HEADER: :var filepath="Figures/coupling_ratio_simscape_light.png" :var figsize="wide-tall" #+begin_src matlab <> #+end_src #+RESULTS: -[[file:Figures/coupling_ration_simscape_light.png]] +[[file:Figures/coupling_ratio_simscape_light.png]] #+begin_src matlab :results silent :exports none freqs = logspace(-2, 3, 1000); @@ -1095,13 +1257,13 @@ Plot the ratio between the main transfer function and the coupling term: #+end_src #+HEADER: :tangle no :exports results :results file :noweb yes -#+HEADER: :var filepath="Figures/coupling_ration_simscape_heavy.png" :var figsize="wide-tall" +#+HEADER: :var filepath="Figures/coupling_ratio_simscape_heavy.png" :var figsize="wide-tall" #+begin_src matlab <> #+end_src #+RESULTS: -[[file:Figures/coupling_ration_simscape_heavy.png]] +[[file:Figures/coupling_ratio_simscape_heavy.png]] *** Low rotation speed and High rotation speed #+begin_src matlab :exports code :results silent diff --git a/rotating_frame.slx b/rotating_frame.slx index 276eeed5593a51955af48b4aeee5a8a321fc16a6..50e1bb80b081366d65ae64ee0352689d6e5ed225 100644 GIT binary patch delta 22658 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