267 lines
9.8 KiB
Org Mode
267 lines
9.8 KiB
Org Mode
#+TITLE: Identification of the Stewart Platform using Simscape
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:DRAWER:
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#+HTML_LINK_HOME: ./index.html
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#+HTML_LINK_UP: ./index.html
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
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#+HTML_HEAD: <script src="./js/jquery.min.js"></script>
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#+HTML_HEAD: <script src="./js/bootstrap.min.js"></script>
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#+HTML_HEAD: <script src="./js/jquery.stickytableheaders.min.js"></script>
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#+HTML_HEAD: <script src="./js/readtheorg.js"></script>
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#+PROPERTY: header-args:matlab :session *MATLAB*
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#+PROPERTY: header-args:matlab+ :tangle matlab/identification.m
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#+PROPERTY: header-args:matlab+ :comments org
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#+PROPERTY: header-args:matlab+ :exports both
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#+PROPERTY: header-args:matlab+ :results none
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#+PROPERTY: header-args:matlab+ :eval no-export
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#+PROPERTY: header-args:matlab+ :noweb yes
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#+PROPERTY: header-args:matlab+ :mkdirp yes
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#+PROPERTY: header-args:matlab+ :output-dir figs
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:END:
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* Identification
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#+begin_src matlab :results none :exports none :noweb yes
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<<matlab-init>>
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addpath('src');
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addpath('library');
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#+end_src
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#+begin_src matlab :results none :exports none
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open stewart
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#+end_src
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The hexapod structure and Sample structure are initialized.
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#+begin_src matlab :results none
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stewart = initializeGeneralConfiguration();
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stewart = computeGeometricalProperties(stewart);
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stewart = initializeMechanicalElements(stewart);
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save('./mat/stewart.mat', 'stewart');
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initializeSample();
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#+end_src
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#+begin_src matlab :results none
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G = identifyPlant();
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#+end_src
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#+begin_src matlab :results none
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freqs = logspace(2, 4, 1000);
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#+end_src
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* Cartesian Plot
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From a force applied in the Cartesian frame to a displacement in the Cartesian frame.
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(freqs, abs(squeeze(freqresp(G.G_cart(1, 1), freqs, 'Hz'))));
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plot(freqs, abs(squeeze(freqresp(G.G_cart(2, 1), freqs, 'Hz'))));
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plot(freqs, abs(squeeze(freqresp(G.G_cart(3, 1), freqs, 'Hz'))));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Amplitude');
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#+end_src
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#+begin_src matlab :results none
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figure;
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bode(G.G_cart, freqs);
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#+end_src
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* From a force to force sensor
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(freqs, abs(squeeze(freqresp(G.G_forc(1, 1), freqs, 'Hz'))), 'k-', 'DisplayName', '$F_{m_i}/F_{i}$');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Amplitude [N/N]');
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legend('location', 'southeast');
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#+end_src
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(freqs, abs(squeeze(freqresp(G.G_forc(1, 1), freqs, 'Hz'))), 'k-', 'DisplayName', '$F_{m_i}/F_{i}$');
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plot(freqs, abs(squeeze(freqresp(G.G_forc(2, 1), freqs, 'Hz'))), 'k--', 'DisplayName', '$F_{m_j}/F_{i}$');
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plot(freqs, abs(squeeze(freqresp(G.G_forc(3, 1), freqs, 'Hz'))), 'k--', 'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(G.G_forc(4, 1), freqs, 'Hz'))), 'k--', 'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(G.G_forc(5, 1), freqs, 'Hz'))), 'k--', 'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(G.G_forc(6, 1), freqs, 'Hz'))), 'k--', 'HandleVisibility', 'off');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Amplitude [N/N]');
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legend('location', 'southeast');
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#+end_src
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* From a force applied in the leg to the displacement of the leg
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(freqs, abs(squeeze(freqresp(G.G_legs(1, 1), freqs, 'Hz'))), 'k-', 'DisplayName', '$D_{i}/F_{i}$');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
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#+end_src
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(freqs, abs(squeeze(freqresp(G.G_legs(1, 1), freqs, 'Hz'))), 'k-', 'DisplayName', '$D_{i}/F_{i}$');
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plot(freqs, abs(squeeze(freqresp(G.G_legs(2, 1), freqs, 'Hz'))), 'k--', 'DisplayName', '$D_{j}/F_{i}$');
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plot(freqs, abs(squeeze(freqresp(G.G_legs(3, 1), freqs, 'Hz'))), 'k--', 'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(G.G_legs(4, 1), freqs, 'Hz'))), 'k--', 'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(G.G_legs(5, 1), freqs, 'Hz'))), 'k--', 'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(G.G_legs(6, 1), freqs, 'Hz'))), 'k--', 'HandleVisibility', 'off');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
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legend('location', 'northeast');
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#+end_src
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* Transmissibility
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(freqs, abs(squeeze(freqresp(G.G_tran(1, 1), freqs, 'Hz'))));
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plot(freqs, abs(squeeze(freqresp(G.G_tran(2, 2), freqs, 'Hz'))));
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plot(freqs, abs(squeeze(freqresp(G.G_tran(3, 3), freqs, 'Hz'))));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Amplitude [m/m]');
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#+end_src
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(freqs, abs(squeeze(freqresp(G.G_tran(4, 4), freqs, 'Hz'))));
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plot(freqs, abs(squeeze(freqresp(G.G_tran(5, 5), freqs, 'Hz'))));
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plot(freqs, abs(squeeze(freqresp(G.G_tran(6, 6), freqs, 'Hz'))));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Amplitude [$\frac{rad/s}{rad/s}$]');
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#+end_src
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(freqs, abs(squeeze(freqresp(G.G_tran(1, 1), freqs, 'Hz'))));
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plot(freqs, abs(squeeze(freqresp(G.G_tran(1, 2), freqs, 'Hz'))));
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plot(freqs, abs(squeeze(freqresp(G.G_tran(1, 3), freqs, 'Hz'))));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Amplitude [m/m]');
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#+end_src
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* Compliance
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From a force applied in the Cartesian frame to a relative displacement of the mobile platform with respect to the base.
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(freqs, abs(squeeze(freqresp(G.G_comp(1, 1), freqs, 'Hz'))));
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plot(freqs, abs(squeeze(freqresp(G.G_comp(2, 2), freqs, 'Hz'))));
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plot(freqs, abs(squeeze(freqresp(G.G_comp(3, 3), freqs, 'Hz'))));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
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#+end_src
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* Inertial
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From a force applied on the Cartesian frame to the absolute displacement of the mobile platform.
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(freqs, abs(squeeze(freqresp(G.G_iner(1, 1), freqs, 'Hz'))));
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plot(freqs, abs(squeeze(freqresp(G.G_iner(2, 2), freqs, 'Hz'))));
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plot(freqs, abs(squeeze(freqresp(G.G_iner(3, 3), freqs, 'Hz'))));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
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#+end_src
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* identifyPlant
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:PROPERTIES:
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:HEADER-ARGS:matlab+: :exports code
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:HEADER-ARGS:matlab+: :comments yes
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:HEADER-ARGS:matlab+: :eval no
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:HEADER-ARGS:matlab+: :tangle src/identifyPlant.m
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:END:
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#+begin_src matlab
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function [sys] = identifyPlant(opts_param)
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#+end_src
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We use this code block to pass optional parameters.
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#+begin_src matlab
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%% Default values for opts
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opts = struct();
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%% Populate opts with input parameters
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if exist('opts_param','var')
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for opt = fieldnames(opts_param)'
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opts.(opt{1}) = opts_param.(opt{1});
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end
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end
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#+end_src
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We defined the options for the =linearize= command.
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Here, we just identify the system at time $t = 0$.
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#+begin_src matlab
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options = linearizeOptions;
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options.SampleTime = 0;
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#+end_src
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We define the name of the Simulink File used to identification.
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#+begin_src matlab
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mdl = 'stewart';
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#+end_src
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Then we defined the input/output of the transfer function we want to identify.
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#+begin_src matlab
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%% Inputs
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io(1) = linio([mdl, '/F'], 1, 'input'); % Cartesian forces
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io(2) = linio([mdl, '/Fl'], 1, 'input'); % Leg forces
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io(3) = linio([mdl, '/Fd'], 1, 'input'); % Direct forces
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io(4) = linio([mdl, '/Dw'], 1, 'input'); % Base motion
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%% Outputs
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io(5) = linio([mdl, '/Dm'], 1, 'output'); % Relative Motion
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io(6) = linio([mdl, '/Dlm'], 1, 'output'); % Displacement of each leg
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io(7) = linio([mdl, '/Flm'], 1, 'output'); % Force sensor in each leg
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io(8) = linio([mdl, '/Xm'], 1, 'output'); % Absolute motion of platform
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#+end_src
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The linearization is run.
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#+begin_src matlab
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G = linearize(mdl, io, 0);
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#+end_src
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We defined all the Input/Output names of the identified transfer function.
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#+begin_src matlab
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G.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz', ...
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'F1', 'F2', 'F3', 'F4', 'F5', 'F6', ...
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'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz', ...
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'Dwx', 'Dwy', 'Dwz', 'Rwx', 'Rwy', 'Rwz'};
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G.OutputName = {'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm', ...
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'D1m', 'D2m', 'D3m', 'D4m', 'D5m', 'D6m', ...
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'F1m', 'F2m', 'F3m', 'F4m', 'F5m', 'F6m', ...
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'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'};
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#+end_src
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We split the transfer function into sub transfer functions and we compute their minimum realization.
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#+begin_src matlab
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sys.G_cart = minreal(G({'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'}, {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'}));
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sys.G_forc = minreal(G({'F1m', 'F2m', 'F3m', 'F4m', 'F5m', 'F6m'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}));
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sys.G_legs = minreal(G({'D1m', 'D2m', 'D3m', 'D4m', 'D5m', 'D6m'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}));
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sys.G_tran = minreal(G({'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'}, {'Dwx', 'Dwy', 'Dwz', 'Rwx', 'Rwy', 'Rwz'}));
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sys.G_comp = minreal(G({'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'}, {'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'}));
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sys.G_iner = minreal(G({'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'}, {'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'}));
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% sys.G_all = minreal(G);
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#+end_src
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#+begin_src matlab
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end
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#+end_src
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