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475
C3-test-bench-struts/test_struts_3_simscape_model.m
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475
C3-test-bench-struts/test_struts_3_simscape_model.m
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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%% Path for functions, data and scripts
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addpath('./mat/'); % Path for data
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addpath('./src/'); % Path for functions
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addpath('./STEPS/'); % Path for Simscape Model
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%% Linearization options
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opts = linearizeOptions;
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opts.SampleTime = 0;
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%% Open Simscape Model
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mdl = 'test_struts_simscape'; % Name of the Simulink File
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open(mdl); % Open Simscape Model
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%% Colors for the figures
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colors = colororder;
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%% Input/Output definition of the Model
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clear io; io_i = 1;
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io(io_i) = linio([mdl, '/u'], 1, 'openinput'); io_i = io_i + 1; % DAC Voltage
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io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; % Sensor Voltage
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io(io_i) = linio([mdl, '/de'], 1, 'openoutput'); io_i = io_i + 1; % Encoder
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io(io_i) = linio([mdl, '/da'], 1, 'openoutput'); io_i = io_i + 1; % Interferometer
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%% Frequency vector [Hz]
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freqs = logspace(1, log10(2000), 1000);
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%% Load measured FRF for comparison
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load('meas_struts_frf.mat', 'f', 'enc_frf', 'int_frf', 'iff_frf', 'strut_nums');
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%% Initialize strut with 2DoF model for the APA300ML and identify the dynamics
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n_hexapod = struct();
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n_hexapod.flex_bot = initializeBotFlexibleJoint('type', '4dof');
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n_hexapod.flex_top = initializeTopFlexibleJoint('type', '4dof');
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n_hexapod.actuator = initializeAPA('type', '2dof');
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c_granite = 0; % Do not take into account damping added by the air bearing
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% Run the linearization
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Gs_2dof = exp(-s*1e-4)*linearize(mdl, io, 0.0, opts);
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Gs_2dof.InputName = {'u'};
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Gs_2dof.OutputName = {'Vs', 'de', 'da'};
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%% Initialize strut with "flexible" model for the APA300ML and identify the dynamics
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n_hexapod = struct();
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n_hexapod.flex_bot = initializeBotFlexibleJoint('type', '4dof');
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n_hexapod.flex_top = initializeTopFlexibleJoint('type', '4dof');
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n_hexapod.actuator = initializeAPA('type', 'flexible');
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c_granite = 100; % Do not take into account damping added by the air bearing
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% Run the linearization
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Gs_flex = exp(-s*1e-4)*linearize(mdl, io, 0.0, opts);
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Gs_flex.InputName = {'u'};
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Gs_flex.OutputName = {'Vs', 'de', 'da'};
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%% Compare the FRF and identified dynamics from u to Vs and da
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figure;
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tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
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ax1a = nexttile([2,1]);
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hold on;
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plot(f, abs(int_frf(:, 1)), 'color', [0,0,0,0.2], ...
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'DisplayName', 'FRF');
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for i = 2:length(strut_nums)
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plot(f, abs(int_frf(:, i)), 'color', [0,0,0,0.2], ...
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'HandleVisibility', 'off');
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end
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plot(freqs, abs(squeeze(freqresp(Gs_2dof('da', 'u'), freqs, 'Hz'))), '-', ...
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'color', colors(1,:), 'DisplayName', '2DoF Model')
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plot(freqs, abs(squeeze(freqresp(Gs_flex('da', 'u'), freqs, 'Hz'))), '-', ...
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'color', colors(2,:), 'DisplayName', 'Flex. Model')
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude $d_a/u$ [m/V]'); set(gca, 'XTickLabel',[]);
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hold off;
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ylim([1e-8, 1e-3]);
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leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
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leg.ItemTokenSize(1) = 15;
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ax2a = nexttile;
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hold on;
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for i = 1:length(strut_nums)
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plot(f, 180/pi*angle(int_frf(:, i)), 'color', [0,0,0,0.2]);
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end
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gs_2dof('da', 'u'), freqs, 'Hz'))), '-', 'color', colors(1,:))
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gs_flex('da', 'u'), freqs, 'Hz'))), '-', 'color', colors(2,:))
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
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hold off;
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yticks(-360:90:360); ylim([-180, 180]);
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linkaxes([ax1a,ax2a],'x');
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xlim([10, 2e3]);
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xticks([1e1, 1e2, 1e3]);
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%% Compare the FRF and identified dynamics from u to Vs and da
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figure;
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tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
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ax1a = nexttile([2,1]);
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hold on;
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plot(f, abs(enc_frf(:, 1)), 'color', [0,0,0,0.2], ...
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'DisplayName', 'FRF');
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for i = 2:length(strut_nums)
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plot(f, abs(enc_frf(:, i)), 'color', [0,0,0,0.2], ...
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'HandleVisibility', 'off');
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end
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plot(freqs, abs(squeeze(freqresp(Gs_2dof('de', 'u'), freqs, 'Hz'))), '-', ...
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'color', colors(1,:), 'DisplayName', '2DoF Model')
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plot(freqs, abs(squeeze(freqresp(Gs_flex('de', 'u'), freqs, 'Hz'))), '-', ...
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'color', colors(2,:), 'DisplayName', 'Flex. Model')
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude $d_e/u$ [m/V]'); set(gca, 'XTickLabel',[]);
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hold off;
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ylim([1e-8, 1e-3]);
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leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
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leg.ItemTokenSize(1) = 15;
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ax2a = nexttile;
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hold on;
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for i = 1:length(strut_nums)
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plot(f, 180/pi*angle(enc_frf(:, i)), 'color', [0,0,0,0.2]);
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end
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gs_2dof('de', 'u'), freqs, 'Hz'))), '-', 'color', colors(1,:))
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gs_flex('de', 'u'), freqs, 'Hz'))), '-', 'color', colors(2,:))
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
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hold off;
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yticks(-360:90:360); ylim([-180, 180]);
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linkaxes([ax1a,ax2a],'x');
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xlim([10, 2e3]);
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xticks([1e1, 1e2, 1e3]);
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%% Compare the FRF and identified dynamics from u to Vs and da
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figure;
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tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
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ax1a = nexttile([2,1]);
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hold on;
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plot(f, abs(iff_frf(:, i)), 'color', [0,0,0,0.2], ...
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'DisplayName', 'FRF');
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for i = 1:length(strut_nums)
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plot(f, abs(iff_frf(:, i)), 'color', [0,0,0,0.2], ...
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'HandleVisibility', 'off');
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end
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plot(freqs, abs(squeeze(freqresp(Gs_2dof('Vs', 'u'), freqs, 'Hz'))), '-', ...
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'color', colors(1,:), 'DisplayName', '2DoF Model')
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plot(freqs, abs(squeeze(freqresp(Gs_flex('Vs', 'u'), freqs, 'Hz'))), '-', ...
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'color', colors(2,:), 'DisplayName', 'Flex. Model')
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude $V_s/u$ [V/V]'); set(gca, 'XTickLabel',[]);
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hold off;
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ylim([1e-2, 1e2]);
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leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
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leg.ItemTokenSize(1) = 15;
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ax2a = nexttile;
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hold on;
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for i = 1:length(strut_nums)
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plot(f, 180/pi*angle(iff_frf(:, i)), 'color', [0,0,0,0.2]);
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end
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set(gca,'ColorOrderIndex',1);
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gs_2dof('Vs', 'u'), freqs, 'Hz'))), '-', 'color', colors(1,:))
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gs_flex('Vs', 'u'), freqs, 'Hz'))), '-', 'color', colors(2,:))
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
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hold off;
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yticks(-360:90:360); ylim([-180, 180]);
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linkaxes([ax1a,ax2a],'x');
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xlim([10, 2e3]);
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xticks([1e1, 1e2, 1e3]);
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%% Effect of a misalignment in Y-Direction
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% Considered misalignment in the Y direction
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dy_aligns = [-0.5, -0.1, 0.1, 0.5]*1e-3; % [m]
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% Transfer functions from u to de for all the misalignment in y direction
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Gs_dy_align = {zeros(length(dy_aligns), 1)};
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for i = 1:length(dy_aligns)
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n_hexapod.actuator = initializeAPA('type', 'flexible', 'd_align_bot', [0; dy_aligns(i); 0], 'd_align_top', [0; dy_aligns(i); 0]);
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G = exp(-s*1e-4)*linearize(mdl, io, 0.0, opts);
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G.InputName = {'u'};
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G.OutputName = {'Vs', 'de', 'da'};
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Gs_dy_align(i) = {G};
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end
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%% Effect of a misalignment in X-Direction
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% Considered misalignment in the X direction
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dx_aligns = [-0.1, -0.05, 0.05, 0.1]*1e-3; % [m]
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% Transfer functions from u to de for all the misalignment in x direction
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Gs_dx_align = {zeros(length(dx_aligns), 1)};
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for i = 1:length(dx_aligns)
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n_hexapod.actuator = initializeAPA('type', 'flexible', 'd_align_bot', [dx_aligns(i); 0; 0], 'd_align_top', [dx_aligns(i); 0; 0]);
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G = exp(-s*1e-4)*linearize(mdl, io, 0.0, opts);
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G.InputName = {'u'};
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G.OutputName = {'Vs', 'de', 'da'};
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Gs_dx_align(i) = {G};
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end
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%% Transfer function from Vs to de - effect of x-misalignment
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figure;
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tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
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ax1 = nexttile([2,1]);
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hold on;
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for i = 1:length(dy_aligns)
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plot(freqs, abs(squeeze(freqresp(Gs_dy_align{i}('de', 'u'), freqs, 'Hz'))), ...
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'DisplayName', sprintf('$d_y = %.1f$ [mm]', 1e3*dy_aligns(i)));
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end
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plot(freqs, abs(squeeze(freqresp(Gs_flex('de', 'u'), freqs, 'Hz'))), 'k-', ...
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'DisplayName', 'aligned');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude $d_e/u$ [m/V]'); set(gca, 'XTickLabel',[]);
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hold off;
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ylim([1e-8, 1e-3]);
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leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
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leg.ItemTokenSize(1) = 15;
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ax2 = nexttile;
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hold on;
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for i = 1:length(dy_aligns)
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gs_dy_align{i}('de', 'u'), freqs, 'Hz'))));
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end
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gs_flex('de', 'u'), freqs, 'Hz'))), 'k-');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
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hold off;
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yticks(-360:90:360); ylim([-180, 180]);
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linkaxes([ax1,ax2],'x');
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xlim([10, 2e3]);
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xticks([1e1, 1e2, 1e3]);
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%% Transfer function from Vs to de - effect of x-misalignment
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figure;
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tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
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ax1 = nexttile([2,1]);
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hold on;
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for i = 1:length(dx_aligns)
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plot(freqs, abs(squeeze(freqresp(Gs_dx_align{i}('de', 'u'), freqs, 'Hz'))), ...
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'DisplayName', sprintf('$d_x = %.1f$ [mm]', 1e3*dx_aligns(i)));
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end
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plot(freqs, abs(squeeze(freqresp(Gs_flex('de', 'u'), freqs, 'Hz'))), 'k-', ...
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'DisplayName', 'aligned');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude $d_e/u$ [m/V]'); set(gca, 'XTickLabel',[]);
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hold off;
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ylim([1e-8, 1e-3]);
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leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
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leg.ItemTokenSize(1) = 15;
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ax2 = nexttile;
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hold on;
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for i = 1:length(dx_aligns)
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gs_dx_align{i}('de', 'u'), freqs, 'Hz'))));
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end
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gs_flex('de', 'u'), freqs, 'Hz'))), 'k-');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
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hold off;
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yticks(-360:90:360); ylim([-180, 180]);
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linkaxes([ax1,ax2],'x');
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xlim([10, 2e3]);
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xticks([1e1, 1e2, 1e3]);
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%% Measurement of the y misalignment between the APA and the flexible joints
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% Mesured struts
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strut_nums = [1, 2, 3, 4, 5];
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% Measured height differences in [mm]
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% R ("red" side), B ("black" side)
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% R Top B Top R Bot B Bot
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strut_align = [[-0.40, -0.60, -0.16, -0.82] % Strut 1
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[-0.67, -0.30, -0.34, -0.63] % Strut 2
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[-0.07, -0.88, -0.16, -0.79] % Strut 3
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[-0.48, -0.46, 0.07, -1.00] % Strut 4
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[-0.33, -0.64, -0.48, -0.52]]; % Strut 5
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||||
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% Verification that the thickness difference between the APA shell and the flexible joints is 1mm
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thichness_diff_top = strut_align(:,1) + strut_align(:,2); % [mm]
|
||||
thichness_diff_bot = strut_align(:,1) + strut_align(:,2); % [mm]
|
||||
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% Estimation of the dy misalignment
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||||
dy_bot = (strut_align(:,1) - strut_align(:,2))/2; % [mm]
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dy_top = (strut_align(:,3) - strut_align(:,4))/2; % [mm]
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||||
%% Idenfity the dynamics from u to de - misalignement estimated from measurement
|
||||
Gs_y_align = {zeros(size(strut_align,1), 1)};
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% Measured dy alignment
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strut_align = 1e-3*[[-0.60, -0.82, -0.40, -0.16]
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[-0.30, -0.63, -0.67, -0.34]
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[-0.88, -0.79, -0.07, -0.16]
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[-0.48, 0.07, -0.46, -1.00]
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[-0.33, -0.48, -0.64, -0.52]
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[-0.34, -0.42, -0.63, -0.57]];
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for i = 1:size(strut_align,1)
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n_hexapod.actuator = initializeAPA('type', 'flexible', ...
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'd_align_bot', [0; strut_align(i, 2) - strut_align(i, 4); 0], ...
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'd_align_top', [0; strut_align(i, 1) - strut_align(i, 3); 0]);
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G = exp(-s*1e-4)*linearize(mdl, io, 0.0, opts);
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G.InputName = {'u'};
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G.OutputName = {'Vs', 'de', 'da'};
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||||
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Gs_y_align(i) = {G};
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end
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||||
%% Idenfity the dynamics from u to de - misalignement tuned to have the best match
|
||||
d_aligns = [[-0.05, -0.3, 0];
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[ 0, 0.5, 0];
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[-0.1, -0.3, 0];
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[ 0, 0.3, 0];
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[-0.05, 0.05, 0]]'*1e-3;
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||||
% Idenfity the transfer function from actuator to encoder for all cases
|
||||
Gs_xy_align = {zeros(size(d_aligns,2), 1)};
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||||
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||||
for i = 1:5
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n_hexapod.actuator = initializeAPA('type', 'flexible', 'd_align_top', d_aligns(:,i), 'd_align_bot', d_aligns(:,i));
|
||||
|
||||
G = exp(-s*1e-4)*linearize(mdl, io, 0.0, opts);
|
||||
G.InputName = {'u'};
|
||||
G.OutputName = {'Vs', 'de', 'da'};
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||||
|
||||
Gs_xy_align(i) = {G};
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||||
end
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||||
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||||
%% Comparison of the plants (encoder output) when tuning the misalignment
|
||||
figure;
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||||
tiledlayout(1, 3, 'TileSpacing', 'Compact', 'Padding', 'None');
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||||
|
||||
ax1 = nexttile();
|
||||
hold on;
|
||||
plot(f, abs(enc_frf(:, 1)), 'DisplayName', 'Measurement');
|
||||
plot(freqs, abs(squeeze(freqresp(Gs_y_align{1}('de', 'u'), freqs, 'Hz'))), ...
|
||||
'DisplayName', '$d_y$ from meas');
|
||||
plot(freqs, abs(squeeze(freqresp(Gs_xy_align{1}('de', 'u'), freqs, 'Hz'))), ...
|
||||
'DisplayName', 'Tuned $d_x$, $d_y$');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude [m/V]');
|
||||
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
title('Strut 1');
|
||||
xticks([1e1, 1e2, 1e3]);
|
||||
|
||||
ax2 = nexttile();
|
||||
hold on;
|
||||
plot(f, abs(enc_frf(:, 2)), 'DisplayName', 'Measurement');
|
||||
plot(freqs, abs(squeeze(freqresp(Gs_y_align{2}('de', 'u'), freqs, 'Hz'))), ...
|
||||
'DisplayName', '$d_y$ from meas');
|
||||
plot(freqs, abs(squeeze(freqresp(Gs_xy_align{2}('de', 'u'), freqs, 'Hz'))), ...
|
||||
'DisplayName', 'Tuned $d_x$, $d_y$');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
|
||||
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
title('Strut 2');
|
||||
xticks([1e1, 1e2, 1e3]);
|
||||
|
||||
ax3 = nexttile();
|
||||
hold on;
|
||||
plot(f, abs(enc_frf(:, 3)), 'DisplayName', 'Measuremnet');
|
||||
plot(freqs, abs(squeeze(freqresp(Gs_y_align{3}('de', 'u'), freqs, 'Hz'))), ...
|
||||
'DisplayName', '$d_y$ from meas');
|
||||
plot(freqs, abs(squeeze(freqresp(Gs_xy_align{3}('de', 'u'), freqs, 'Hz'))), ...
|
||||
'DisplayName', 'Tuned $d_x$, $d_y$');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); set(gca, 'YTickLabel',[]);
|
||||
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
title('Strut 3');
|
||||
xticks([1e1, 1e2, 1e3]);
|
||||
|
||||
linkaxes([ax1,ax2,ax3],'xy');
|
||||
xlim([10, 2e3]); ylim([1e-8, 1e-3]);
|
||||
|
||||
%% Measurement of the y misalignment between the APA and the flexible joints after strut better alignment
|
||||
|
||||
% Numbers of the measured legs
|
||||
strut_align_nums = [1 2 3 4 5 6];
|
||||
|
||||
% Measured height differences in [mm]
|
||||
% R ("red" side), B ("black" side)
|
||||
% R Top B Top R Bot B Bot
|
||||
strut_align = [[-0.54, -0.50, -0.50, -0.52] % strut 1
|
||||
[-0.44, -0.55, -0.49, -0.49] % strut 2
|
||||
[-0.48, -0.50, -0.50, -0.46] % strut 3
|
||||
[-0.45, -0.51, -0.51, -0.45] % strut 4
|
||||
[-0.50, -0.50, -0.50, -0.50] % strut 5
|
||||
[-0.50, -0.49, -0.43, -0.54]]; % strut 6
|
||||
|
||||
% Verification that the thickness difference between the APA shell and the flexible joints is 1mm
|
||||
thichness_diff_top = strut_align(:,1) + strut_align(:,2); % [mm]
|
||||
thichness_diff_bot = strut_align(:,1) + strut_align(:,2); % [mm]
|
||||
|
||||
% Estimation of the dy misalignment
|
||||
dy_bot = (strut_align(:,1) - strut_align(:,2))/2; % [mm]
|
||||
dy_top = (strut_align(:,3) - strut_align(:,4))/2; % [mm]
|
||||
|
||||
%% New dynamical identified with re-aligned struts
|
||||
% Load the identification data
|
||||
leg_noise = {};
|
||||
for i = 1:length(strut_align_nums)
|
||||
leg_noise(i) = {load(sprintf('frf_struts_align_%i_noise.mat', strut_align_nums(i)), 'u', 'Vs', 'de')};
|
||||
end
|
||||
|
||||
% Parameters for Frequency Analysis
|
||||
Ts = 1e-4; % Sampling Time [s]
|
||||
Nfft = floor(1/Ts); % Number of points for the FFT computation
|
||||
win = hanning(Nfft); % Hanning window
|
||||
Noverlap = floor(Nfft/2); % Overlap between frequency analysis
|
||||
|
||||
% Only used to have the frequency vector "f"
|
||||
[~, f] = tfestimate(leg_noise{1}.u, leg_noise{1}.de, win, Noverlap, Nfft, 1/Ts);
|
||||
|
||||
% Transfer function from u to de (encoder)
|
||||
enc_frf_aligned = zeros(length(f), length(strut_align_nums));
|
||||
|
||||
for i = 1:length(strut_align_nums)
|
||||
enc_frf_aligned(:, i) = tfestimate(leg_noise{i}.u, leg_noise{i}.de, win, Noverlap, Nfft, 1/Ts);
|
||||
end
|
||||
|
||||
%% Bode plot of the FRF from u to de
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, abs(enc_frf(:, 1)), 'color', [colors(1,:), 0.5], ...
|
||||
'DisplayName', 'Initial alignment');
|
||||
for i = 1:length(strut_nums)
|
||||
plot(f, abs(enc_frf(:, i)), 'color', [colors(1,:), 0.5], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
plot(f, abs(enc_frf_aligned(:, 1)), 'color', [colors(2,:), 0.5], ...
|
||||
'DisplayName', 'With positioning pin');
|
||||
for i = 1:length(strut_align_nums)
|
||||
plot(f, abs(enc_frf_aligned(:, i)), 'color', [colors(2,:), 0.5], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude $d_e/u$ [m/V]');
|
||||
legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
xlim([10, 2e3]);
|
||||
ylim([1e-8, 1e-3]);
|
||||
Reference in New Issue
Block a user