133 lines
4.3 KiB
Matlab
133 lines
4.3 KiB
Matlab
%% 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('./src/'); % Path for scripts
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addpath('./mat/'); % Path for data
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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_apa_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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%% Frequency vector for analysis
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freqs = 5*logspace(0, 3, 1000);
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%% Identification of the actuator and sensor "constants"
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% Initialize the APA as a flexible body with unity "constants"
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n_hexapod.actuator = initializeAPA(...
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'type', 'flexible', ...
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'ga', 1, ...
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'gs', 1);
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c_granite = 50; % Rought estimation of the damping added by the air bearing
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% Identify the dynamics
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G_norm = linearize(mdl, io, 0.0, opts);
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G_norm.InputName = {'u'};
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G_norm.OutputName = {'Vs', 'de'};
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% Load Identification Data to estimate the two gains
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load('meas_apa_frf.mat', 'f', 'Ts', 'enc_frf', 'iff_frf', 'apa_nums');
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% Actuator Constant in [N/V]
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ga = -mean(abs(enc_frf(f>10 & f<20)))./dcgain(G_norm('de', 'u'));
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% Sensor Constant in [V/m]
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gs = -mean(abs(iff_frf(f>400 & f<500)))./(ga*abs(squeeze(freqresp(G_norm('Vs', 'u'), 1e3, 'Hz'))));
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%% Idenfify the dynamics of the Simscape model with correct actuator and sensor "constants"
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% Initialize the APA
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n_hexapod.actuator = initializeAPA(...
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'type', 'flexible', ...
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'ga', 23.2, ... % Actuator sensitivity [N/V]
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'gs', -4.9e6); % Sensor sensitivity [V/m]
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% Identify with updated constants
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G_flex = exp(-Ts*s)*linearize(mdl, io, 0.0, opts);
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G_flex.InputName = {'u'};
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G_flex.OutputName = {'Vs', 'de'};
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%% Comparison of the measured FRF and the "Flexible" model of the APA300ML
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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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plot(f, abs(enc_frf(:, 1)), 'color', [0,0,0,0.2], 'DisplayName', 'Identified');
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for i = 1:length(apa_nums)
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plot(f, abs(enc_frf(:, i)), 'color', [0,0,0,0.2], 'HandleVisibility', 'off');
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end
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plot(freqs, abs(squeeze(freqresp(G_flex('de', 'u'), freqs, 'Hz'))), '--', 'color', colors(2,:), 'DisplayName', '"Flexible" 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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legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
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ax2 = nexttile;
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hold on;
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for i = 1:length(apa_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(G_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([ax1,ax2],'x');
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xlim([10, 2e3]);
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%% Comparison of the measured FRF and the "Flexible" model of the APA300ML
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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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plot(f, abs(iff_frf(:, 1)), 'color', [0,0,0,0.2], 'DisplayName', 'Identified');
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for i = 2:length(apa_nums)
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plot(f, abs(iff_frf(:, i)), 'color', [0,0,0,0.2], 'HandleVisibility', 'off');
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end
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plot(freqs, abs(squeeze(freqresp(G_flex('Vs', 'u'), freqs, 'Hz'))), '--', 'color', colors(2,:), 'DisplayName', '"Flexible" 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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legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
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ax2 = nexttile;
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hold on;
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for i = 1:length(apa_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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plot(freqs, 180/pi*angle(squeeze(freqresp(G_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([ax1,ax2],'x');
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xlim([10, 2e3]);
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