From ffe6b8ed4b491bfba4154f3313d599c0f6346174 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Mon, 20 Jan 2020 16:29:48 +0100 Subject: [PATCH] Add few study --- control-study.org | 244 ++++++++++++++++++++ dynamics-study.org | 285 ++++++++++++++++++++++++ figs/control_measure_rotating_2dof.png | Bin 0 -> 6174 bytes figs/cubic-configuration-definition.png | Bin 21652 -> 23912 bytes simscape-model.org | 4 +- src/initializeStrutDynamics.m | 2 +- 6 files changed, 533 insertions(+), 2 deletions(-) create mode 100644 control-study.org create mode 100644 dynamics-study.org create mode 100644 figs/control_measure_rotating_2dof.png diff --git a/control-study.org b/control-study.org new file mode 100644 index 0000000..26082da --- /dev/null +++ b/control-study.org @@ -0,0 +1,244 @@ +#+TITLE: Stewart Platform - Control Study +:DRAWER: +#+HTML_LINK_HOME: ./index.html +#+HTML_LINK_UP: ./index.html + +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: + +#+PROPERTY: header-args:matlab :session *MATLAB* +#+PROPERTY: header-args:matlab+ :comments org +#+PROPERTY: header-args:matlab+ :exports both +#+PROPERTY: header-args:matlab+ :results none +#+PROPERTY: header-args:matlab+ :eval no-export +#+PROPERTY: header-args:matlab+ :noweb yes +#+PROPERTY: header-args:matlab+ :mkdirp yes +#+PROPERTY: header-args:matlab+ :output-dir figs + +#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/}{config.tex}") +#+PROPERTY: header-args:latex+ :imagemagick t :fit yes +#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150 +#+PROPERTY: header-args:latex+ :imoutoptions -quality 100 +#+PROPERTY: header-args:latex+ :results file raw replace +#+PROPERTY: header-args:latex+ :buffer no +#+PROPERTY: header-args:latex+ :eval no-export +#+PROPERTY: header-args:latex+ :exports both +#+PROPERTY: header-args:latex+ :mkdirp yes +#+PROPERTY: header-args:latex+ :output-dir figs +#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png") +:END: + +* First Control Architecture +** Matlab Init :noexport: +#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) + <> +#+end_src + +#+begin_src matlab :exports none :results silent :noweb yes + <> +#+end_src + +#+begin_src matlab + addpath('./src/') +#+end_src + +** Control Schematic +#+begin_src latex :file control_measure_rotating_2dof.pdf + \begin{tikzpicture} + % Blocs + \node[block] (J) at (0, 0) {$J$}; + \node[addb={+}{}{}{}{-}, right=1 of J] (subr) {}; + \node[block, right=0.8 of subr] (K) {$K_{L}$}; + \node[block, right=1 of K] (G) {$G_{L}$}; + + % Connections and labels + \draw[<-] (J.west)node[above left]{$\bm{r}_{n}$} -- ++(-1, 0); + \draw[->] (J.east) -- (subr.west) node[above left]{$\bm{r}_{L}$}; + \draw[->] (subr.east) -- (K.west) node[above left]{$\bm{\epsilon}_{L}$}; + \draw[->] (K.east) -- (G.west) node[above left]{$\bm{\tau}$}; + \draw[->] (G.east) node[above right]{$\bm{L}$} -| ($(G.east)+(1, -1)$) -| (subr.south); + \end{tikzpicture} +#+end_src + +#+RESULTS: +[[file:figs/control_measure_rotating_2dof.png]] + +** Initialize the Stewart platform +#+begin_src matlab + stewart = initializeFramesPositions('H', 90e-3, 'MO_B', 45e-3); + stewart = generateCubicConfiguration(stewart, 'Hc', 60e-3, 'FOc', 45e-3, 'FHa', 5e-3, 'MHb', 5e-3); + stewart = computeJointsPose(stewart); + stewart = initializeStrutDynamics(stewart, 'Ki', 1e6*ones(6,1), 'Ci', 1e2*ones(6,1)); + stewart = computeJacobian(stewart); +#+end_src + +** Identification of the plant +Let's identify the transfer function from $\bm{\tau}}$ to $\bm{L}$. +#+begin_src matlab + %% Options for Linearized + options = linearizeOptions; + options.SampleTime = 0; + + %% Name of the Simulink File + mdl = 'stewart_platform_control'; + + %% Input/Output definition + clear io; io_i = 1; + io(io_i) = linio([mdl, '/tau'], 1, 'openinput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/L'], 1, 'openoutput'); io_i = io_i + 1; + + %% Run the linearization + G = linearize(mdl, io, options); + G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}; + G.OutputName = {'L1', 'L2', 'L3', 'L4', 'L5', 'L6'}; +#+end_src + +** Plant Analysis +Diagonal terms +#+begin_src matlab :exports none + freqs = logspace(1, 4, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + for i = 1:6 + plot(freqs, abs(squeeze(freqresp(G(i, i), freqs, 'Hz')))); + end + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + hold on; + for i = 1:6 + plot(freqs, 180/pi*angle(squeeze(freqresp(G(i, i), freqs, 'Hz')))); + end + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + + linkaxes([ax1,ax2],'x'); +#+end_src + +Compare to off-diagonal terms +#+begin_src matlab :exports none + freqs = logspace(1, 4, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + for i = 1:5 + for j = i+1:6 + plot(freqs, abs(squeeze(freqresp(G(i, j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2]); + end + end + set(gca,'ColorOrderIndex',1); + plot(freqs, abs(squeeze(freqresp(G(1, 1), freqs, 'Hz')))); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + hold on; + for i = 1:5 + for j = i+1:6 + plot(freqs, 180/pi*angle(squeeze(freqresp(G(i, j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2]); + end + end + set(gca,'ColorOrderIndex',1); + plot(freqs, 180/pi*angle(squeeze(freqresp(G(1, 1), freqs, 'Hz')))); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + + linkaxes([ax1,ax2],'x'); +#+end_src + +** Controller Design +One integrator should be present in the controller. + +A lead is added around the crossover frequency which is set to be around 500Hz. + +#+begin_src matlab + % wint = 2*pi*100; % Integrate until [rad] + % wlead = 2*pi*500; % Location of the lead [rad] + % hlead = 2; % Lead strengh + + % Kl = 1e6 * ... % Gain + % (s + wint)/(s) * ... % Integrator until 100Hz + % (1 + s/(wlead/hlead)/(1 + s/(wlead*hlead))); % Lead + + wc = 2*pi*100; + Kl = 1/abs(freqresp(G(1,1), wc)) * wc/s * 1/(1 + s/(3*wc)); + Kl = Kl * eye(6); +#+end_src + +#+begin_src matlab :exports none + freqs = logspace(1, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + plot(freqs, abs(squeeze(freqresp(Kl(1,1)*G(1, 1), freqs, 'Hz')))); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + hold on; + plot(freqs, 180/pi*angle(squeeze(freqresp(Kl(1,1)*G(1, 1), freqs, 'Hz')))); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + + linkaxes([ax1,ax2],'x'); +#+end_src + +#+begin_src matlab :exports none + freqs = logspace(1, 4, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + for i = 1:5 + for j = i+1:6 + plot(freqs, abs(squeeze(freqresp(Kl(i,i)*G(i, j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2]); + end + end + set(gca,'ColorOrderIndex',1); + plot(freqs, abs(squeeze(freqresp(Kl(1,1)*G(1, 1), freqs, 'Hz')))); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + hold on; + for i = 1:5 + for j = i+1:6 + plot(freqs, 180/pi*angle(squeeze(freqresp(Kl(i, i)*G(i, j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2]); + end + end + set(gca,'ColorOrderIndex',1); + plot(freqs, 180/pi*angle(squeeze(freqresp(Kl(1,1)*G(1, 1), freqs, 'Hz')))); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + + linkaxes([ax1,ax2],'x'); +#+end_src diff --git a/dynamics-study.org b/dynamics-study.org new file mode 100644 index 0000000..7870dcd --- /dev/null +++ b/dynamics-study.org @@ -0,0 +1,285 @@ +#+TITLE: Stewart Platform - Dynamics Study +:DRAWER: +#+HTML_LINK_HOME: ./index.html +#+HTML_LINK_UP: ./index.html + +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: + +#+PROPERTY: header-args:matlab :session *MATLAB* +#+PROPERTY: header-args:matlab+ :comments org +#+PROPERTY: header-args:matlab+ :exports both +#+PROPERTY: header-args:matlab+ :results none +#+PROPERTY: header-args:matlab+ :eval no-export +#+PROPERTY: header-args:matlab+ :noweb yes +#+PROPERTY: header-args:matlab+ :mkdirp yes +#+PROPERTY: header-args:matlab+ :output-dir figs +:END: + +* Some tests +** Matlab Init :noexport:ignore: +#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) + <> +#+end_src + +#+begin_src matlab :exports none :results silent :noweb yes + <> +#+end_src + +#+begin_src matlab + addpath('./src/') +#+end_src + +** Simscape Model +#+begin_src matlab + open('stewart_platform_dynamics.slx') +#+end_src + +** test +#+begin_src matlab + stewart = initializeFramesPositions('H', 90e-3, 'MO_B', 45e-3); + stewart = generateCubicConfiguration(stewart, 'Hc', 60e-3, 'FOc', 45e-3, 'FHa', 5e-3, 'MHb', 5e-3); + stewart = computeJointsPose(stewart); + stewart = initializeStrutDynamics(stewart, 'Ki', 1e6*ones(6,1), 'Ci', 1e2*ones(6,1)); + stewart = computeJacobian(stewart); +#+end_src + +Estimation of the transfer function from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}$: +#+begin_src matlab + %% Options for Linearized + options = linearizeOptions; + options.SampleTime = 0; + + %% Name of the Simulink File + mdl = 'stewart_platform_dynamics'; + + %% Input/Output definition + clear io; io_i = 1; + io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/X'], 1, 'openoutput'); io_i = io_i + 1; + + %% Run the linearization + G = linearize(mdl, io, options); + G.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'}; + G.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'}; +#+end_src + + +#+begin_src matlab + %% Options for Linearized + options = linearizeOptions; + options.SampleTime = 0; + + %% Name of the Simulink File + mdl = 'stewart_platform_dynamics'; + + %% Input/Output definition + clear io; io_i = 1; + io(io_i) = linio([mdl, '/J-T'], 1, 'openinput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/X'], 1, 'openoutput'); io_i = io_i + 1; + + %% Run the linearization + G = linearize(mdl, io, options); + G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}; + G.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'}; +#+end_src + +#+begin_src matlab + G_cart = minreal(G*inv(stewart.J')); + G_cart.InputName = {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz'}; +#+end_src + +#+begin_src matlab + figure; bode(G, G_cart) +#+end_src + +#+begin_src matlab + %% Options for Linearized + options = linearizeOptions; + options.SampleTime = 0; + + %% Name of the Simulink File + mdl = 'stewart_platform_dynamics'; + + %% Input/Output definition + clear io; io_i = 1; + io(io_i) = linio([mdl, '/Fext'], 1, 'openinput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/X'], 1, 'openoutput'); io_i = io_i + 1; + + %% Run the linearization + Gd = linearize(mdl, io, options); + Gd.InputName = {'Fex', 'Fey', 'Fez', 'Mex', 'Mey', 'Mez'}; + Gd.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'}; +#+end_src + +#+begin_src matlab + freqs = logspace(0, 3, 1000); + + figure; + bode(Gd, G) +#+end_src + +** Compare external forces and forces applied by the actuators +Initialization of the Stewart platform. +#+begin_src matlab + stewart = initializeFramesPositions('H', 90e-3, 'MO_B', 45e-3); + stewart = generateCubicConfiguration(stewart, 'Hc', 60e-3, 'FOc', 45e-3, 'FHa', 5e-3, 'MHb', 5e-3); + stewart = computeJointsPose(stewart); + stewart = initializeStrutDynamics(stewart, 'Ki', 1e6*ones(6,1), 'Ci', 1e2*ones(6,1)); + stewart = computeJacobian(stewart); +#+end_src + +Estimation of the transfer function from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}$: +#+begin_src matlab + %% Options for Linearized + options = linearizeOptions; + options.SampleTime = 0; + + %% Name of the Simulink File + mdl = 'stewart_platform_dynamics'; + + %% Input/Output definition + clear io; io_i = 1; + io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/X'], 1, 'openoutput'); io_i = io_i + 1; + + %% Run the linearization + G = linearize(mdl, io, options); + G.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'}; + G.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'}; +#+end_src + +Estimation of the transfer function from $\mathcal{\bm{F}}_{d}$ to $\mathcal{\bm{X}}$: +#+begin_src matlab + %% Options for Linearized + options = linearizeOptions; + options.SampleTime = 0; + + %% Name of the Simulink File + mdl = 'stewart_platform_dynamics'; + + %% Input/Output definition + clear io; io_i = 1; + io(io_i) = linio([mdl, '/Fext'], 1, 'openinput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/X'], 1, 'openoutput'); io_i = io_i + 1; + + %% Run the linearization + Gd = linearize(mdl, io, options); + Gd.InputName = {'Fex', 'Fey', 'Fez', 'Mex', 'Mey', 'Mez'}; + Gd.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'}; +#+end_src + +Comparison of the two transfer function matrices. +#+begin_src matlab + freqs = logspace(0, 4, 1000); + + figure; + bode(Gd, G, freqs) +#+end_src + +#+begin_important +Seems quite similar. +#+end_important + +** Comparison of the static transfer function and the Compliance matrix +Initialization of the Stewart platform. +#+begin_src matlab + stewart = initializeFramesPositions('H', 90e-3, 'MO_B', 45e-3); + stewart = generateCubicConfiguration(stewart, 'Hc', 60e-3, 'FOc', 45e-3, 'FHa', 5e-3, 'MHb', 5e-3); + stewart = computeJointsPose(stewart); + stewart = initializeStrutDynamics(stewart, 'Ki', 1e6*ones(6,1), 'Ci', 1e2*ones(6,1)); + stewart = computeJacobian(stewart); +#+end_src + +Estimation of the transfer function from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}$: +#+begin_src matlab + %% Options for Linearized + options = linearizeOptions; + options.SampleTime = 0; + + %% Name of the Simulink File + mdl = 'stewart_platform_dynamics'; + + %% Input/Output definition + clear io; io_i = 1; + io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/X'], 1, 'openoutput'); io_i = io_i + 1; + + %% Run the linearization + G = linearize(mdl, io, options); + G.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'}; + G.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'}; +#+end_src + +Let's first look at the low frequency transfer function matrix from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}$. +#+begin_src matlab :exports results :results value table replace :tangle no +data2orgtable(real(freqresp(G, 0.1)), {}, {}, ' %.1e '); +#+end_src + +#+RESULTS: +| 2.0e-06 | -9.1e-19 | -5.3e-12 | 7.3e-18 | 1.7e-05 | 1.3e-18 | +| -1.7e-18 | 2.0e-06 | 8.6e-19 | -1.7e-05 | -1.5e-17 | 6.7e-12 | +| 3.6e-13 | 3.2e-19 | 5.0e-07 | -2.5e-18 | 8.1e-12 | -1.5e-19 | +| 1.0e-17 | -1.7e-05 | -5.0e-18 | 1.9e-04 | 9.1e-17 | -3.5e-11 | +| 1.7e-05 | -6.9e-19 | -5.3e-11 | 6.9e-18 | 1.9e-04 | 4.8e-18 | +| -3.5e-18 | -4.5e-12 | 1.5e-18 | 7.1e-11 | -3.4e-17 | 4.6e-05 | + +And now at the Compliance matrix. +#+begin_src matlab :exports results :results value table replace :tangle no +data2orgtable(stewart.C, {}, {}, ' %.1e '); +#+end_src + +#+RESULTS: +| 2.0e-06 | 2.9e-22 | 2.8e-22 | -3.2e-21 | 1.7e-05 | 1.5e-37 | +| -2.1e-22 | 2.0e-06 | -1.8e-23 | -1.7e-05 | -2.3e-21 | 1.1e-22 | +| 3.1e-22 | -1.6e-23 | 5.0e-07 | 1.7e-22 | 2.2e-21 | -8.1e-39 | +| 2.1e-21 | -1.7e-05 | 2.0e-22 | 1.9e-04 | 2.3e-20 | -8.7e-21 | +| 1.7e-05 | 2.5e-21 | 2.0e-21 | -2.8e-20 | 1.9e-04 | 1.3e-36 | +| 3.7e-23 | 3.1e-22 | -6.0e-39 | -1.0e-20 | 3.1e-22 | 4.6e-05 | + +#+begin_important +The low frequency transfer function matrix from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}$ corresponds to the compliance matrix of the Stewart platform. +#+end_important + +** Transfer function from forces applied in the legs to the displacement of the legs +Initialization of the Stewart platform. +#+begin_src matlab + stewart = initializeFramesPositions('H', 90e-3, 'MO_B', 45e-3); + stewart = generateCubicConfiguration(stewart, 'Hc', 60e-3, 'FOc', 45e-3, 'FHa', 5e-3, 'MHb', 5e-3); + stewart = computeJointsPose(stewart); + stewart = initializeStrutDynamics(stewart, 'Ki', 1e6*ones(6,1), 'Ci', 1e2*ones(6,1)); + stewart = computeJacobian(stewart); +#+end_src + +Estimation of the transfer function from $\bm{\tau}$ to $\bm{L}$: +#+begin_src matlab + %% Options for Linearized + options = linearizeOptions; + options.SampleTime = 0; + + %% Name of the Simulink File + mdl = 'stewart_platform_dynamics'; + + %% Input/Output definition + clear io; io_i = 1; + io(io_i) = linio([mdl, '/J-T'], 1, 'openinput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/L'], 1, 'openoutput'); io_i = io_i + 1; + + %% Run the linearization + G = linearize(mdl, io, options); + G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}; + G.OutputName = {'L1', 'L2', 'L3', 'L4', 'L5', 'L6'}; +#+end_src + +#+begin_src matlab + freqs = logspace(1, 3, 1000); + figure; bode(G, 2*pi*freqs) +#+end_src + +#+begin_src matlab + bodeFig({G(1,1), G(1,2)}, freqs, struct('phase', true)); +#+end_src diff --git a/figs/control_measure_rotating_2dof.png b/figs/control_measure_rotating_2dof.png new file mode 100644 index 0000000000000000000000000000000000000000..fe6a5b5ba0226e89f5d455b70e12b2d2b6660418 GIT binary patch literal 6174 zcmbt&^I?(4o1UT8fhy-Rl&1Okz&swnA#KsX%0+WZay@SP(c z_5wJ7eRZEJfM*7HBY+bkFBM~75Qv)m_5&W|Jdy<#-Kt9R`a!dM=vP4$25tQqPXz@~ 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