From fca54e3d888818b2585b03d05f3b67d239775ceb Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Mon, 10 Feb 2025 17:35:49 +0100 Subject: [PATCH] Add figures to explain the multi-body model --- figs/nhexa_actuator_model.pdf | Bin 0 -> 21426 bytes figs/nhexa_actuator_model.png | Bin 0 -> 16651 bytes figs/nhexa_actuator_model.svg | 1017 ++++++ figs/nhexa_simscape_screenshot.jpg | Bin 0 -> 44014 bytes figs/nhexa_simscape_screenshot.png | Bin 0 -> 24609 bytes figs/nhexa_stewart_loop_closure.svg | 2434 ------------- figs/nhexa_stewart_model_def.pdf | Bin 0 -> 19403 bytes figs/nhexa_stewart_model_def.png | Bin 0 -> 50291 bytes figs/nhexa_stewart_model_def.svg | 3211 ++++++++++++++++++ figs/nhexa_stewart_model_input_outputs.pdf | Bin 0 -> 11312 bytes figs/nhexa_stewart_model_input_outputs.png | Bin 0 -> 28734 bytes figs/nhexa_stewart_model_input_outputs.svg | 2910 ++++++++++++++++ matlab/nano_hexapod_model.slx | Bin 73412 -> 73426 bytes matlab/src/initializeSimplifiedNanoHexapod.m | 6 +- simscape-nano-hexapod.bib | 12 + simscape-nano-hexapod.org | 163 +- simscape-nano-hexapod.pdf | Bin 446796 -> 547371 bytes simscape-nano-hexapod.tex | 161 +- 18 files changed, 7412 insertions(+), 2502 deletions(-) create mode 100644 figs/nhexa_actuator_model.pdf create mode 100644 figs/nhexa_actuator_model.png create mode 100644 figs/nhexa_actuator_model.svg create mode 100644 figs/nhexa_simscape_screenshot.jpg create mode 100644 figs/nhexa_simscape_screenshot.png delete mode 100644 figs/nhexa_stewart_loop_closure.svg create mode 100644 figs/nhexa_stewart_model_def.pdf create mode 100644 figs/nhexa_stewart_model_def.png create mode 100644 figs/nhexa_stewart_model_def.svg create mode 100644 figs/nhexa_stewart_model_input_outputs.pdf create mode 100644 figs/nhexa_stewart_model_input_outputs.png create mode 100644 figs/nhexa_stewart_model_input_outputs.svg diff --git a/figs/nhexa_actuator_model.pdf b/figs/nhexa_actuator_model.pdf new file mode 100644 index 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zU@jRufd+$yrsI^Hu=e3m3If5V4s=g)$!QAD$P9n_{Q#am(xQXcYlhw4`bIz}M;|E! zim?rNUZ}i1MoIz5XuV7%y$y$AZQyWVaxDGUp&5Ays9a&*!LQTlckrX#_ocL@w&XZK zAsFwip6vF)V^v$@`Rf8czb=&6k|U+AxTK-7v)HPeH~p3mJi=#l_=m4Nc9pI1C28!G zA&jYy@PbCUAc691wbtGdtzep*KK@qGik0NS;Oh2{rHV6fERiqo5E&XBO!&k0eg6HX zi<^y%OO9c2Ls$?2BF}q3)gX{Y9T-%k{tw}cxJL&XsMeuPnAe6Aophku#6lhDmumfA zY)|MDM|7a4)tdHw8WT45!HB1Hq2^EqF-R9`rvEpwYFn*U69PE|`KLku?j*!gUFbRJ zG?AwZ{Z4J*9D#T45Yc--RNLThVvq&|LfifSYwmnUDEUsm@yUKDf9L> -- [ ] Make schematic with inputs and outputs (maybe add frames {F} and {M} to connect to outside world) -- [ ] Screenshot of the obtained multi-body model ? - - If all is perfect (mass-less struts, perfect joints, etc...), maybe compare analytical model with simscape model? - Say something about the model order Model order is 12, and that we can compute modes from matrices M and K, compare with the Simscape model @@ -926,6 +938,22 @@ During the conceptual design: Actuators = 1DoF + Encoder (mass-less) - Compare with analytical formulas (see number of states) - [ ] Effect of parallel on IFF plant? +#+attr_latex: :options [b]{0.6\linewidth} +#+begin_minipage +#+name: fig:nhexa_stewart_model_input_outputs +#+caption: Nano-Hexapod plant with inputs and outputs. Frames $\{F\}$ and $\{M\}$ can be connected to other elements in the multi-body models. +#+attr_latex: :scale 1 :float nil +[[file:figs/nhexa_stewart_model_input_outputs.png]] +#+end_minipage +\hfill +#+attr_latex: :options [b]{0.35\linewidth} +#+begin_minipage +#+name: fig:nhexa_simscape_screenshot +#+caption: 3D representation of the multi-body model +#+attr_latex: :width 0.90\linewidth :float nil +[[file:figs/nhexa_simscape_screenshot.jpg]] +#+end_minipage + #+begin_src matlab %% Plant using Analytical Equations % Stewart platform definition @@ -1088,6 +1116,105 @@ xlim([freqs(1), freqs(end)]); #+begin_src matlab initializeSimplifiedNanoHexapod(); +initializeSample('type', 'cylindrical', 'm', 50); +initializeLoggingConfiguration('log', 'none'); +initializeController('type', 'open-loop'); +#+end_src + +#+begin_src matlab +% Input/Output definition +clear io; io_i = 1; +io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Inputs [N] +io(io_i) = linio([mdl, '/plant'], 2, 'openoutput', [], 'dL'); io_i = io_i + 1; % Encoders [m] +io(io_i) = linio([mdl, '/plant'], 2, 'openoutput', [], 'fn'); io_i = io_i + 1; % Force Sensors [N] + +% With no payload +G = linearize(mdl, io); +G.InputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'}; +G.OutputName = {'dL1', 'dL2', 'dL3', 'dL4', 'dL5', 'dL6', ... + 'fn1', 'fn2', 'fn3', 'fn4', 'fn5', 'fn6'}; +#+end_src + +#+begin_src matlab :exports none +%% Diagonal elements of the FRF matrix from u to de +figure; +tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +plot(freqs, abs(squeeze(freqresp(G(1,1), freqs, 'Hz'))), 'color', colors(2,:), ... + 'DisplayName', '$d_{ei}/u_i$ - Model') +for i = 2:6 + plot(freqs, abs(squeeze(freqresp(G(i,i), freqs, 'Hz'))), 'color', colors(2,:), ... + 'HandleVisibility', 'off'); +end +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], ... + 'HandleVisibility', 'off'); + end +end +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); +ylim([1e-9, 1e-4]); +leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1); +leg.ItemTokenSize(1) = 15; + +ax2 = nexttile; +hold on; +for i = 1:6 + plot(freqs, 180/pi*angle(squeeze(freqresp(G(i,i), freqs, 'Hz'))), 'color', [colors(2,:),0.5]); +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'); +xlim([freqs(1), freqs(end)]); +#+end_src + +#+begin_src matlab :exports none +%% Diagonal elements of the FRF matrix from u to de +figure; +tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None'); + +ax1 = nexttile([2,1]); +hold on; +plot(freqs, abs(squeeze(freqresp(G(6+1,1), freqs, 'Hz'))), 'color', colors(2,:), ... + 'DisplayName', '$d_{ei}/u_i$ - Model') +for i = 2:6 + plot(freqs, abs(squeeze(freqresp(G(6+i,i), freqs, 'Hz'))), 'color', colors(2,:), ... + 'HandleVisibility', 'off'); +end +for i = 1:5 + for j = i+1:6 + plot(freqs, abs(squeeze(freqresp(G(6+i,j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ... + 'HandleVisibility', 'off'); + end +end +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); +ylim([1e-5, 1e2]); +leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1); +leg.ItemTokenSize(1) = 15; + +ax2 = nexttile; +hold on; +for i = 1:6 + plot(freqs, 180/pi*angle(squeeze(freqresp(G(6+i,i), freqs, 'Hz'))), 'color', [colors(2,:),0.5]); +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'); +xlim([freqs(1), freqs(end)]); #+end_src ** Conclusion @@ -1447,11 +1574,11 @@ function [nano_hexapod] = initializeSimplifiedNanoHexapod(args) args.MTh (6,1) double {mustBeNumeric} = [255, 285, 15, 45, 135, 165]*(pi/180) % Angles of fixed joints [rad] %% Actuators args.actuator_type char {mustBeMember(args.actuator_type,{'1dof', '2dof', 'flexible'})} = '1dof' - args.actuator_k (1,1) double {mustBeNumeric, mustBePositive} = 380000 - args.actuator_kp (1,1) double {mustBeNumeric, mustBeNonnegative} = 0 + args.actuator_k (1,1) double {mustBeNumeric, mustBePositive} = 1e6 + args.actuator_kp (1,1) double {mustBeNumeric, mustBeNonnegative} = 5e4 args.actuator_ke (1,1) double {mustBeNumeric, mustBePositive} = 4952605 args.actuator_ka (1,1) double {mustBeNumeric, mustBePositive} = 2476302 - args.actuator_c (1,1) double {mustBeNumeric, mustBePositive} = 5 + args.actuator_c (1,1) double {mustBeNumeric, mustBePositive} = 50 args.actuator_cp (1,1) double {mustBeNumeric, mustBeNonnegative} = 0 args.actuator_ce (1,1) double {mustBeNumeric, mustBePositive} = 100 args.actuator_ca (1,1) double {mustBeNumeric, mustBePositive} = 50 diff --git 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