From ba2944e05741e40f99950beb3743fde1f071d162 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Mon, 28 Jan 2019 11:22:15 +0100 Subject: [PATCH] Add rotation speed analysis --- Figures/Guu_ws.pdf | Bin 0 -> 100557 bytes Figures/Guu_ws.png | Bin 0 -> 105636 bytes Figures/Guu_ws.svg | Bin 0 -> 404825 bytes Figures/Guv_ws.pdf | Bin 0 -> 98887 bytes Figures/Guv_ws.png | Bin 0 -> 113589 bytes Figures/Guv_ws.svg | Bin 0 -> 397718 bytes rotating_frame.org | 151 +++++++++++++++++++++++++++++++++++---------- 7 files changed, 120 insertions(+), 31 deletions(-) create mode 100644 Figures/Guu_ws.pdf create mode 100644 Figures/Guu_ws.png create mode 100644 Figures/Guu_ws.svg create mode 100644 Figures/Guv_ws.pdf create mode 100644 Figures/Guv_ws.png create mode 100644 Figures/Guv_ws.svg diff --git a/Figures/Guu_ws.pdf b/Figures/Guu_ws.pdf new file mode 100644 index 0000000000000000000000000000000000000000..70bc23ff543ca1428ec58dd95de7d82d7f736ed0 GIT binary patch literal 100557 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+:DRAWER: +#+STARTUP: overview + #+HTML_HEAD: #+HTML_HEAD: #+HTML_HEAD: #+HTML_HEAD: #+HTML_HEAD: #+HTML_HEAD: + #+LATEX_CLASS: cleanreport #+LaTeX_CLASS_OPTIONS: [tocnp, secbreak, minted] -#+STARTUP: overview #+LaTeX_HEADER: \usepackage{svg} #+LaTeX_HEADER: \newcommand{\authorFirstName}{Thomas} #+LaTeX_HEADER: \newcommand{\authorLastName}{Dehaeze} #+LaTeX_HEADER: \newcommand{\authorEmail}{dehaeze.thomas@gmail.com} + #+PROPERTY: header-args:matlab :session *MATLAB* #+PROPERTY: header-args:matlab+ :comments org #+PROPERTY: header-args:matlab+ :exports both #+PROPERTY: header-args:matlab+ :eval no-export #+PROPERTY: header-args:matlab+ :output-dir Figures +:END: * Introduction The objective of this note it to highlight some control problems that arises when controlling the position of an object using actuators that are rotating with respect to a fixed reference frame. @@ -902,7 +907,8 @@ We obtain the same result than the analytical case (figures [[fig:coupling_light #+RESULTS: [[file:Figures/coupling_ratio_light_heavy.png]] -** Plant Control +** Plant Control - SISO approach +*** Plant identification 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 @@ -1086,45 +1092,128 @@ However, when we look at the poles of the closed loop with a diagonal controller | -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 - +*** TODO Close loop performance +First we compute the close loop transfer functions. #+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 +*** Effect of rotation speed +We first identify the system (voice coil and light mass) for multiple rotation speed. +Then we compute the bode plot of the diagonal element (figure [[fig:Guu_ws]]) and of the coupling element (figure [[fig:Guv_ws]]). + +As the rotation frequency increases: +- one pole goes to lower frequencies while the other goes to higher frequencies +- one zero appears between the two poles +- the zero disappears when $\omega > \sqrt{\frac{k}{m}}$ and the low frequency pole becomes unstable (positive real part) + +To stabilize the unstable pole, we need a control bandwidth of at least twice of frequency of the unstable pole. + +#+begin_src matlab :exports none :results silent + ws = linspace(0, 2*pi, 5); % Rotation speed vector [rad/s] + m = mlight; % mass of the sample [kg] + + kTuv = kvc; + cTuv = 0.1*sqrt(kTuv*m); + + Gs = {zeros(1, length(ws))}; + + for i = 1:length(ws) + w = ws(i); + Gs{i} = linearize(mdl, io, 0.1); + end +#+end_src + +#+begin_src matlab :exports none :results silent + freqs = logspace(-2, 2, 1000); + + figure; + ax1 = subaxis(2,1,1); + hold on; + for i = 1:length(ws) + plot(freqs, abs(squeeze(freqresp(Gs{i}(1, 1), freqs, 'Hz')))); + end + hold off; + xlim([freqs(1), freqs(end)]); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + set(gca, 'XTickLabel',[]); + ylabel('Magnitude [m/N]'); + + ax2 = subaxis(2,1,2); + hold on; + for i = 1:length(ws) + plot(freqs, 180/pi*angle(squeeze(freqresp(Gs{i}(1, 1), freqs, 'Hz'))), 'DisplayName', sprintf('w = %.0f [rpm]', ws(i)*60/2/pi)); + end + hold off; + yticks(-180:90:180); + ylim([-180 180]); + xlim([freqs(1), freqs(end)]); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); + legend('Location', 'northeast'); + linkaxes([ax1,ax2],'x'); +#+end_src + +#+HEADER: :tangle no :exports results :results file :noweb yes +#+HEADER: :var filepath="Figures/Guu_ws.png" :var figsize="full-tall" +#+begin_src matlab + <> +#+end_src + +#+NAME: fig:Guu_ws +#+CAPTION: Diagonal term as a function of the rotation frequency +#+RESULTS: +[[file:Figures/Guu_ws.png]] + +#+begin_src matlab :exports none :results silent + freqs = logspace(-2, 2, 1000); + + figure; + ax1 = subaxis(2,1,1); + hold on; + for i = 1:length(ws) + plot(freqs, abs(squeeze(freqresp(Gs{i}(1, 2), freqs, 'Hz')))); + end + hold off; + xlim([freqs(1), freqs(end)]); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + set(gca, 'XTickLabel',[]); + ylabel('Magnitude [m/N]'); + + ax2 = subaxis(2,1,2); + hold on; + for i = 1:length(ws) + plot(freqs, 180/pi*angle(squeeze(freqresp(Gs{i}(1, 2), freqs, 'Hz'))), 'DisplayName', sprintf('w = %.0f [rpm]', ws(i)*60/2/pi)); + end + hold off; + yticks(-180:90:180); + ylim([-180 180]); + xlim([freqs(1), freqs(end)]); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); + legend('Location', 'northeast'); + linkaxes([ax1,ax2],'x'); +#+end_src + +#+HEADER: :tangle no :exports results :results file :noweb yes +#+HEADER: :var filepath="Figures/Guv_ws.png" :var figsize="full-tall" +#+begin_src matlab + <> +#+end_src + +#+NAME: fig:Guv_ws +#+CAPTION: Couplin term as a function of the rotation frequency +#+RESULTS: +[[file:Figures/Guv_ws.png]] + +** TODO Plant Control - MIMO approach ** test

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