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683
C5-test-bench-id31/test_id31_2_open_loop_plant.m
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683
C5-test-bench-id31/test_id31_2_open_loop_plant.m
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%% test_id31_2_open_loop_plant.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 STEPS
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addpath('./subsystems/'); % Path for Subsystems Simulink files
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%% Data directory
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data_dir = './mat/';
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% Simulink Model name
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mdl = 'nass_model_id31';
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%% Colors for the figures
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colors = colororder;
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%% Frequency Vector
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freqs = logspace(log10(1), log10(2e3), 1000);
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%% Sampling Time
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Ts = 1e-4;
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%% Specifications for Experiments
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specs_dz_peak = 50; % [nm]
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specs_dy_peak = 100; % [nm]
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specs_ry_peak = 0.85; % [urad]
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specs_dz_rms = 15; % [nm RMS]
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specs_dy_rms = 30; % [nm RMS]
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specs_ry_rms = 0.25; % [urad RMS]
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%% Identify the plant dynamics using the Simscape model
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% Initialize each Simscape model elements
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initializeGround();
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initializeGranite();
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initializeTy();
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initializeRy();
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initializeRz();
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initializeMicroHexapod();
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initializeNanoHexapod('flex_bot_type', '2dof', ...
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'flex_top_type', '3dof', ...
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'motion_sensor_type', 'plates', ...
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'actuator_type', '2dof');
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initializeSample('type', '0');
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initializeSimscapeConfiguration('gravity', false);
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initializeDisturbances('enable', false);
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initializeLoggingConfiguration('log', 'none');
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initializeController('type', 'open-loop');
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initializeReferences();
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% Input/Output definition
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clear io; io_i = 1;
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io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Inputs [V]
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io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Vs'); io_i = io_i + 1; % Force Sensors voltages [V]
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io(io_i) = linio([mdl, '/Tracking Error'], 1, 'openoutput', [], 'EdL'); io_i = io_i + 1; % Position Errors [m]
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% With no payload
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Gm = exp(-1e-4*s)*linearize(mdl, io);
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Gm.InputName = {'u1', 'u2', 'u3', 'u4', 'u5', 'u6'};
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Gm.OutputName = {'Vs1', 'Vs2', 'Vs3', 'Vs4', 'Vs5', 'Vs6', ...
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'eL1', 'eL2', 'eL3', 'eL4', 'eL5', 'eL6'};
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%% Identify the plant from experimental data
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% Load identification data
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data = load('2023-08-08_16-17_ol_plant_m0_Wz0.mat');
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% Frequency analysis parameters
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Ts = 1e-4; % Sampling Time [s]
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Nfft = floor(2.0/Ts);
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win = hanning(Nfft);
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Noverlap = floor(Nfft/2);
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[~, f] = tfestimate(data.uL1.id_plant, data.uL1.e_L1, win, Noverlap, Nfft, 1/Ts);
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G_iff = zeros(length(f), 6, 6); % Force sensor outputs
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G_int = zeros(length(f), 6, 6); % Estimated strut errors
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for i_strut = 1:6
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Vs = [data.(sprintf("uL%i", i_strut)).Vs1 ; data.(sprintf("uL%i", i_strut)).Vs2 ; data.(sprintf("uL%i", i_strut)).Vs3 ; data.(sprintf("uL%i", i_strut)).Vs4 ; data.(sprintf("uL%i", i_strut)).Vs5 ; data.(sprintf("uL%i", i_strut)).Vs6]';
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eL = [data.(sprintf("uL%i", i_strut)).e_L1 ; data.(sprintf("uL%i", i_strut)).e_L2 ; data.(sprintf("uL%i", i_strut)).e_L3 ; data.(sprintf("uL%i", i_strut)).e_L4 ; data.(sprintf("uL%i", i_strut)).e_L5 ; data.(sprintf("uL%i", i_strut)).e_L6]';
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dL = [data.(sprintf("uL%i", i_strut)).dL1 ; data.(sprintf("uL%i", i_strut)).dL2 ; data.(sprintf("uL%i", i_strut)).dL3 ; data.(sprintf("uL%i", i_strut)).dL4 ; data.(sprintf("uL%i", i_strut)).dL5 ; data.(sprintf("uL%i", i_strut)).dL6]';
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G_iff(:,:,i_strut) = tfestimate(data.(sprintf("uL%i", i_strut)).id_plant, Vs, win, Noverlap, Nfft, 1/Ts);
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G_int(:,:,i_strut) = tfestimate(data.(sprintf("uL%i", i_strut)).id_plant, eL, win, Noverlap, Nfft, 1/Ts);
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end
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%% Obtained transfer function from generated voltages to measured voltages on the piezoelectric force sensor
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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 = 1:5
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for j = i+1:6
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plot(f, abs(G_int(:, i, j)), 'color', [colors(1,:), 0.2], ...
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'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(Gm(sprintf('eL%i', i), sprintf('u%i', j)), freqs, 'Hz'))), 'color', [colors(2,:), 0.2], ...
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'HandleVisibility', 'off');
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end
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end
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plot(f, abs(G_int(:, 1, 1)), 'color', [colors(1,:)], ...
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'DisplayName', '$-\epsilon\mathcal{L}_i/u_i$ meas');
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plot(freqs, abs(squeeze(freqresp(Gm(sprintf('eL%i', 1), sprintf('u%i', 1)), freqs, 'Hz'))), 'color', [colors(2,:)], ...
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'DisplayName', '$-\epsilon\mathcal{L}_i/u_i$ model');
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for i = 2:6
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plot(f, abs(G_int(:,i, i)), 'color', [colors(1,:)], ...
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'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(Gm(sprintf('eL%i', i), sprintf('u%i', i)), freqs, 'Hz'))), 'color', [colors(2,:)], ...
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'HandleVisibility', 'off');
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end
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plot(f, abs(G_int(:, 1, 2)), 'color', [colors(1,:), 0.2], ...
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'DisplayName', '$-\epsilon\mathcal{L}_i/u_j$ meas');
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plot(freqs, abs(squeeze(freqresp(Gm(sprintf('eL%i', 1), sprintf('u%i', 2)), freqs, 'Hz'))), 'color', [colors(2,:), 0.2], ...
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'DisplayName', '$-\epsilon\mathcal{L}_i/u_j$ 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 [m/V]'); set(gca, 'XTickLabel',[]);
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ylim([2e-9, 2e-4]);
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leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);
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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 = 1:6
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plot(f, 180/pi*angle(G_int(:,i, i)), 'color', [colors(1,:)]);
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end
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for i = 1:6
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(sprintf('eL%i', i), sprintf('u%i', i)), freqs, 'Hz'))), 'color', [colors(2,:)]);
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end
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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);
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ylim([-90, 180])
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linkaxes([ax1,ax2],'x');
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xlim([1, 1e3]);
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%% Comparison between the measured dynamics and the model dynamics - Force Sensors
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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 = 1:5
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for j = i+1:6
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plot(f, abs(G_iff(:, i, j)), 'color', [colors(1,:), 0.2], ...
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'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(Gm(sprintf('Vs%i', i), sprintf('u%i', j)), freqs, 'Hz'))), 'color', [colors(2,:), 0.2], ...
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'HandleVisibility', 'off');
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end
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end
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plot(f, abs(G_iff(:,1, 1)), 'color', [colors(1,:)], ...
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'DisplayName', '$V_{s,i}/u_i$ meas');
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plot(freqs, abs(squeeze(freqresp(Gm(sprintf('Vs%i', 1), sprintf('u%i', 1)), freqs, 'Hz'))), 'color', [colors(2,:)], ...
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'DisplayName', '$V_{s,i}/u_i$ model');
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for i = 2:6
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plot(f, abs(G_iff(:,i, i)), 'color', [colors(1,:)], ...
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'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(Gm(sprintf('Vs%i', i), sprintf('u%i', i)), freqs, 'Hz'))), 'color', [colors(2,:)], ...
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'HandleVisibility', 'off');
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end
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plot(f, abs(G_iff(:, 1, 2)), 'color', [colors(1,:), 0.2], ...
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'DisplayName', '$V_{s,i}/u_j$ meas');
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plot(freqs, abs(squeeze(freqresp(Gm(sprintf('Vs%i', 1), sprintf('u%i', 2)), freqs, 'Hz'))), 'color', [colors(2,:), 0.2], ...
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'DisplayName', '$V_{s,i}/u_j$ 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/V]'); set(gca, 'XTickLabel',[]);
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ylim([5e-5, 4e1]);
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leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);
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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 = 1:6
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plot(f, 180/pi*angle(G_iff(:,i, i)), 'color', [colors(1,:)]);
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end
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for i = 1:6
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(sprintf('Vs%i', i), sprintf('u%i', i)), freqs, 'Hz'))), 'color', [colors(2,:)]);
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end
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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);
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ylim([-90, 180])
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linkaxes([ax1,ax2],'x');
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xlim([1, 1e3]);
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%% Load Data
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data_1_dx = h5scan(data_dir, 'align_int_enc_Rz', 'tx_first_scan', 2);
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data_1_dy = h5scan(data_dir, 'align_int_enc_Rz', 'tx_first_scan', 3);
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data_2_dx = h5scan(data_dir, 'align_int_enc_Rz', 'verif-after-correct-offset', 1);
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data_2_dy = h5scan(data_dir, 'align_int_enc_Rz', 'verif-after-correct-offset', 2);
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% Estimation of Rz misalignment
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p1 = polyfit(data_1_dx.Dx_int_filtered, data_1_dx.Dy_int_filtered, 1);
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p2 = polyfit(data_1_dy.Dx_int_filtered, data_1_dy.Dy_int_filtered, 1);
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Rz_error = (atan(p1(1)) + atan(p2(1))-pi/2)/2; % ~3 degrees
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%% Estimation of the Rz misalignment
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figure;
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hold on;
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plot(1e6*data_1_dx.Dx_int_filtered, 1e6*data_1_dx.Dy_int_filtered, 'color', colors(2,:), 'DisplayName', 'Measurement')
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plot(1e6*data_1_dy.Dx_int_filtered, 1e6*data_1_dy.Dy_int_filtered, 'color', colors(2,:), 'HandleVisibility', 'off')
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plot( 1e6*[-10:10]*cos(Rz_error), 1e6*[-10:10]*sin(Rz_error), 'k--', 'DisplayName', sprintf('$\\epsilon_{R_z} = %.1f$ deg', Rz_error*180/pi))
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plot(-1e6*[-10:10]*sin(Rz_error), 1e6*[-10:10]*cos(Rz_error), 'k--', 'HandleVisibility', 'off')
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hold off;
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xlabel('Interf $D_x$ [$\mu$m]');
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ylabel('Interf $D_y$ [$\mu$m]');
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axis equal
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xlim([-10, 10]); ylim([-10, 10]);
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xticks([-10:5:10]); yticks([-10:5:10]);
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leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
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leg.ItemTokenSize(1) = 15;
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% Estimation of Rz misalignment after correcting the Rz angle
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p1 = polyfit(data_2_dx.Dx_int_filtered, data_2_dx.Dy_int_filtered, 1);
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p2 = polyfit(data_2_dy.Dx_int_filtered, data_2_dy.Dy_int_filtered, 1);
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Rz_error = (atan(p1(1)) + atan(p2(1))-pi/2)/2; % ~0.2 degrees
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%% Estimation of the Rz misalignment after correcting the Rz offset
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figure;
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hold on;
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plot(1e6*data_2_dx.Dx_int_filtered, 1e6*data_2_dx.Dy_int_filtered, 'color', colors(5,:), 'DisplayName', 'Measurement')
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plot(1e6*data_2_dy.Dx_int_filtered, 1e6*data_2_dy.Dy_int_filtered, 'color', colors(5,:), 'HandleVisibility', 'off')
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plot( 1e6*[-10:10]*cos(Rz_error), 1e6*[-10:10]*sin(Rz_error), 'k--', 'DisplayName', sprintf('$\\epsilon_{R_z} = %.1f$ deg', Rz_error*180/pi))
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plot(-1e6*[-10:10]*sin(Rz_error), 1e6*[-10:10]*cos(Rz_error), 'k--', 'HandleVisibility', 'off')
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hold off;
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xlabel('Interf $D_x$ [$\mu$m]');
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ylabel('Interf $D_y$ [$\mu$m]');
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axis equal
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xlim([-10, 10]); ylim([-10, 10]);
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xticks([-10:5:10]); yticks([-10:5:10]);
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leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
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leg.ItemTokenSize(1) = 15;
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%% Identification of the plant after Rz alignment
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data_align = load('2023-08-17_17-37_ol_plant_m0_Wz0_new_Rz_align.mat');
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G_int_align = zeros(length(f), 6, 6);
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for i_strut = 1:6
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eL = [data_align.(sprintf("uL%i", i_strut)).e_L1 ; data_align.(sprintf("uL%i", i_strut)).e_L2 ; data_align.(sprintf("uL%i", i_strut)).e_L3 ; data_align.(sprintf("uL%i", i_strut)).e_L4 ; data_align.(sprintf("uL%i", i_strut)).e_L5 ; data_align.(sprintf("uL%i", i_strut)).e_L6]';
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G_int_align(:,:,i_strut) = tfestimate(data_align.(sprintf("uL%i", i_strut)).id_plant, eL, win, Noverlap, Nfft, 1/Ts);
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end
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%% Obtained transfer function from generated voltages to measured voltages on the piezoelectric force sensor
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figure;
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tiledlayout(1, 1, 'TileSpacing', 'compact', 'Padding', 'None');
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nexttile();
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hold on;
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for i = 1:5
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for j = i+1:6
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plot(f, abs(G_int_align(:, i, j)), 'color', [colors(1,:), 0.2], ...
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'HandleVisibility', 'off');
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plot(freqs, abs(squeeze(freqresp(Gm(sprintf('eL%i', i), sprintf('u%i', j)), freqs, 'Hz'))), 'color', [colors(2,:), 0.2], ...
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'HandleVisibility', 'off');
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||||
end
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||||
end
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plot(f, abs(G_int_align(:, 1, 1)), 'color', [colors(1,:)], ...
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||||
'DisplayName', '$\epsilon\mathcal{L}_i/u_i$ meas');
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||||
plot(freqs, abs(squeeze(freqresp(Gm(sprintf('eL%i', 1), sprintf('u%i', 1)), freqs, 'Hz'))), 'color', [colors(2,:)], ...
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||||
'DisplayName', '$\epsilon\mathcal{L}_i/u_i$ model');
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||||
for i = 2:6
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plot(f, abs(G_int_align(:,i, i)), 'color', [colors(1,:)], ...
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||||
'HandleVisibility', 'off');
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||||
plot(freqs, abs(squeeze(freqresp(Gm(sprintf('eL%i', i), sprintf('u%i', i)), freqs, 'Hz'))), 'color', [colors(2,:)], ...
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'HandleVisibility', 'off');
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||||
end
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||||
plot(f, abs(G_int_align(:, 1, 2)), 'color', [colors(1,:), 0.2], ...
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'DisplayName', '$\epsilon\mathcal{L}_i/u_j$ meas');
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||||
plot(freqs, abs(squeeze(freqresp(Gm(sprintf('eL%i', 1), sprintf('u%i', 2)), freqs, 'Hz'))), 'color', [colors(2,:), 0.2], ...
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'DisplayName', '$\epsilon\mathcal{L}_i/u_j$ model');
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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/V]');
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||||
xlim([1, 1e3]); ylim([2e-9, 2e-4]);
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||||
leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);
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||||
leg.ItemTokenSize(1) = 15;
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||||
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||||
%% Identify the model dynamics for all payload conditions
|
||||
% Initialize each Simscape model elements
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||||
initializeGround();
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||||
initializeGranite();
|
||||
initializeTy();
|
||||
initializeRy();
|
||||
initializeRz();
|
||||
initializeMicroHexapod();
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||||
initializeNanoHexapod('flex_bot_type', '2dof', ...
|
||||
'flex_top_type', '3dof', ...
|
||||
'motion_sensor_type', 'plates', ...
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||||
'actuator_type', '2dof');
|
||||
initializeSample('type', '0');
|
||||
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||||
initializeSimscapeConfiguration('gravity', false);
|
||||
initializeDisturbances('enable', false);
|
||||
initializeLoggingConfiguration('log', 'none');
|
||||
initializeController('type', 'open-loop');
|
||||
initializeReferences();
|
||||
|
||||
% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Inputs
|
||||
io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Vs'); io_i = io_i + 1; % Force Sensors
|
||||
io(io_i) = linio([mdl, '/Tracking Error'], 1, 'openoutput', [], 'EdL'); io_i = io_i + 1; % Position Errors
|
||||
|
||||
initializeSample('type', '0');
|
||||
Gm_m0_Wz0 = linearize(mdl, io);
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||||
Gm_m0_Wz0.InputName = {'u1', 'u2', 'u3', 'u4', 'u5', 'u6'};
|
||||
Gm_m0_Wz0.OutputName = {'Vs1', 'Vs2', 'Vs3', 'Vs4', 'Vs5', 'Vs6', ...
|
||||
'eL1', 'eL2', 'eL3', 'eL4', 'eL5', 'eL6'};
|
||||
|
||||
initializeSample('type', '1');
|
||||
Gm_m1_Wz0 = linearize(mdl, io);
|
||||
Gm_m1_Wz0.InputName = {'u1', 'u2', 'u3', 'u4', 'u5', 'u6'};
|
||||
Gm_m1_Wz0.OutputName = {'Vs1', 'Vs2', 'Vs3', 'Vs4', 'Vs5', 'Vs6', ...
|
||||
'eL1', 'eL2', 'eL3', 'eL4', 'eL5', 'eL6'};
|
||||
|
||||
initializeSample('type', '2');
|
||||
Gm_m2_Wz0 = linearize(mdl, io);
|
||||
Gm_m2_Wz0.InputName = {'u1', 'u2', 'u3', 'u4', 'u5', 'u6'};
|
||||
Gm_m2_Wz0.OutputName = {'Vs1', 'Vs2', 'Vs3', 'Vs4', 'Vs5', 'Vs6', ...
|
||||
'eL1', 'eL2', 'eL3', 'eL4', 'eL5', 'eL6'};
|
||||
|
||||
initializeSample('type', '3');
|
||||
Gm_m3_Wz0 = linearize(mdl, io);
|
||||
Gm_m3_Wz0.InputName = {'u1', 'u2', 'u3', 'u4', 'u5', 'u6'};
|
||||
Gm_m3_Wz0.OutputName = {'Vs1', 'Vs2', 'Vs3', 'Vs4', 'Vs5', 'Vs6', ...
|
||||
'eL1', 'eL2', 'eL3', 'eL4', 'eL5', 'eL6'};
|
||||
|
||||
%% Identify the plant from experimental data - All payloads
|
||||
|
||||
% Load identification data
|
||||
data_m0_Wz0 = load('2023-08-08_16-17_ol_plant_m0_Wz0.mat');
|
||||
data_m1_Wz0 = load('2023-08-08_18-57_ol_plant_m1_Wz0.mat');
|
||||
data_m2_Wz0 = load('2023-08-08_17-12_ol_plant_m2_Wz0.mat');
|
||||
data_m3_Wz0 = load('2023-08-08_18-20_ol_plant_m3_Wz0.mat');
|
||||
|
||||
% Sampling Time [s]
|
||||
Ts = 1e-4;
|
||||
|
||||
% Hannning Windows
|
||||
Nfft = floor(2.0/Ts);
|
||||
win = hanning(Nfft);
|
||||
Noverlap = floor(Nfft/2);
|
||||
|
||||
% And we get the frequency vector
|
||||
[~, f] = tfestimate(data_m0_Wz0.uL1.id_plant, data_m0_Wz0.uL1.e_L1, win, Noverlap, Nfft, 1/Ts);
|
||||
|
||||
% No payload
|
||||
G_iff_m0_Wz0 = zeros(length(f), 6, 6);
|
||||
for i_strut = 1:6
|
||||
eL = [data_m0_Wz0.(sprintf("uL%i", i_strut)).Vs1 ; data_m0_Wz0.(sprintf("uL%i", i_strut)).Vs2 ; data_m0_Wz0.(sprintf("uL%i", i_strut)).Vs3 ; data_m0_Wz0.(sprintf("uL%i", i_strut)).Vs4 ; data_m0_Wz0.(sprintf("uL%i", i_strut)).Vs5 ; data_m0_Wz0.(sprintf("uL%i", i_strut)).Vs6]';
|
||||
|
||||
G_iff_m0_Wz0(:,:,i_strut) = tfestimate(data_m0_Wz0.(sprintf("uL%i", i_strut)).id_plant, eL, win, Noverlap, Nfft, 1/Ts);
|
||||
end
|
||||
|
||||
G_int_m0_Wz0 = zeros(length(f), 6, 6);
|
||||
for i_strut = 1:6
|
||||
eL = [data_m0_Wz0.(sprintf("uL%i", i_strut)).e_L1 ; data_m0_Wz0.(sprintf("uL%i", i_strut)).e_L2 ; data_m0_Wz0.(sprintf("uL%i", i_strut)).e_L3 ; data_m0_Wz0.(sprintf("uL%i", i_strut)).e_L4 ; data_m0_Wz0.(sprintf("uL%i", i_strut)).e_L5 ; data_m0_Wz0.(sprintf("uL%i", i_strut)).e_L6]';
|
||||
|
||||
G_int_m0_Wz0(:,:,i_strut) = tfestimate(data_m0_Wz0.(sprintf("uL%i", i_strut)).id_plant, eL, win, Noverlap, Nfft, 1/Ts);
|
||||
end
|
||||
|
||||
% 1 "payload layer"
|
||||
G_iff_m1_Wz0 = zeros(length(f), 6, 6);
|
||||
for i_strut = 1:6
|
||||
eL = [data_m1_Wz0.(sprintf("uL%i", i_strut)).Vs1 ; data_m1_Wz0.(sprintf("uL%i", i_strut)).Vs2 ; data_m1_Wz0.(sprintf("uL%i", i_strut)).Vs3 ; data_m1_Wz0.(sprintf("uL%i", i_strut)).Vs4 ; data_m1_Wz0.(sprintf("uL%i", i_strut)).Vs5 ; data_m1_Wz0.(sprintf("uL%i", i_strut)).Vs6]';
|
||||
|
||||
G_iff_m1_Wz0(:,:,i_strut) = tfestimate(data_m1_Wz0.(sprintf("uL%i", i_strut)).id_plant, eL, win, Noverlap, Nfft, 1/Ts);
|
||||
end
|
||||
|
||||
G_int_m1_Wz0 = zeros(length(f), 6, 6);
|
||||
for i_strut = 1:6
|
||||
eL = [data_m1_Wz0.(sprintf("uL%i", i_strut)).e_L1 ; data_m1_Wz0.(sprintf("uL%i", i_strut)).e_L2 ; data_m1_Wz0.(sprintf("uL%i", i_strut)).e_L3 ; data_m1_Wz0.(sprintf("uL%i", i_strut)).e_L4 ; data_m1_Wz0.(sprintf("uL%i", i_strut)).e_L5 ; data_m1_Wz0.(sprintf("uL%i", i_strut)).e_L6]';
|
||||
|
||||
G_int_m1_Wz0(:,:,i_strut) = tfestimate(data_m1_Wz0.(sprintf("uL%i", i_strut)).id_plant, eL, win, Noverlap, Nfft, 1/Ts);
|
||||
end
|
||||
|
||||
% 2 "payload layers"
|
||||
G_iff_m2_Wz0 = zeros(length(f), 6, 6);
|
||||
for i_strut = 1:6
|
||||
eL = [data_m2_Wz0.(sprintf("uL%i", i_strut)).Vs1 ; data_m2_Wz0.(sprintf("uL%i", i_strut)).Vs2 ; data_m2_Wz0.(sprintf("uL%i", i_strut)).Vs3 ; data_m2_Wz0.(sprintf("uL%i", i_strut)).Vs4 ; data_m2_Wz0.(sprintf("uL%i", i_strut)).Vs5 ; data_m2_Wz0.(sprintf("uL%i", i_strut)).Vs6]';
|
||||
|
||||
G_iff_m2_Wz0(:,:,i_strut) = tfestimate(data_m2_Wz0.(sprintf("uL%i", i_strut)).id_plant, eL, win, Noverlap, Nfft, 1/Ts);
|
||||
end
|
||||
|
||||
G_int_m2_Wz0 = zeros(length(f), 6, 6);
|
||||
for i_strut = 1:6
|
||||
eL = [data_m2_Wz0.(sprintf("uL%i", i_strut)).e_L1 ; data_m2_Wz0.(sprintf("uL%i", i_strut)).e_L2 ; data_m2_Wz0.(sprintf("uL%i", i_strut)).e_L3 ; data_m2_Wz0.(sprintf("uL%i", i_strut)).e_L4 ; data_m2_Wz0.(sprintf("uL%i", i_strut)).e_L5 ; data_m2_Wz0.(sprintf("uL%i", i_strut)).e_L6]';
|
||||
|
||||
G_int_m2_Wz0(:,:,i_strut) = tfestimate(data_m2_Wz0.(sprintf("uL%i", i_strut)).id_plant, eL, win, Noverlap, Nfft, 1/Ts);
|
||||
end
|
||||
|
||||
% 3 "payload layers"
|
||||
G_iff_m3_Wz0 = zeros(length(f), 6, 6);
|
||||
for i_strut = 1:6
|
||||
eL = [data_m3_Wz0.(sprintf("uL%i", i_strut)).Vs1 ; data_m3_Wz0.(sprintf("uL%i", i_strut)).Vs2 ; data_m3_Wz0.(sprintf("uL%i", i_strut)).Vs3 ; data_m3_Wz0.(sprintf("uL%i", i_strut)).Vs4 ; data_m3_Wz0.(sprintf("uL%i", i_strut)).Vs5 ; data_m3_Wz0.(sprintf("uL%i", i_strut)).Vs6]';
|
||||
|
||||
G_iff_m3_Wz0(:,:,i_strut) = tfestimate(data_m3_Wz0.(sprintf("uL%i", i_strut)).id_plant, eL, win, Noverlap, Nfft, 1/Ts);
|
||||
end
|
||||
|
||||
G_int_m3_Wz0 = zeros(length(f), 6, 6);
|
||||
for i_strut = 1:6
|
||||
eL = [data_m3_Wz0.(sprintf("uL%i", i_strut)).e_L1 ; data_m3_Wz0.(sprintf("uL%i", i_strut)).e_L2 ; data_m3_Wz0.(sprintf("uL%i", i_strut)).e_L3 ; data_m3_Wz0.(sprintf("uL%i", i_strut)).e_L4 ; data_m3_Wz0.(sprintf("uL%i", i_strut)).e_L5 ; data_m3_Wz0.(sprintf("uL%i", i_strut)).e_L6]';
|
||||
|
||||
G_int_m3_Wz0(:,:,i_strut) = tfestimate(data_m3_Wz0.(sprintf("uL%i", i_strut)).id_plant, eL, win, Noverlap, Nfft, 1/Ts);
|
||||
end
|
||||
|
||||
%% Obtained transfer function from generated voltages to measured voltages on the piezoelectric force sensor
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(f, abs(G_int_m0_Wz0(:, 1, 1)), 'color', [colors(1,:), 0.5], ...
|
||||
'DisplayName', 'Meas (0kg)');
|
||||
for i = 2:6
|
||||
plot(f, abs(G_int_m0_Wz0(:,i, i)), 'color', [colors(1,:), 0.5], ...
|
||||
'HandleVisibility', 'off')
|
||||
end
|
||||
plot(f, abs(G_int_m1_Wz0(:, 1, 1)), 'color', [colors(2,:), 0.5], ...
|
||||
'DisplayName', 'Meas (13kg)');
|
||||
for i = 2:6
|
||||
plot(f, abs(G_int_m1_Wz0(:,i, i)), 'color', [colors(2,:), 0.5], ...
|
||||
'HandleVisibility', 'off')
|
||||
end
|
||||
plot(f, abs(G_int_m2_Wz0(:, 1, 1)), 'color', [colors(3,:), 0.5], ...
|
||||
'DisplayName', 'Meas (26kg)');
|
||||
for i = 2:6
|
||||
plot(f, abs(G_int_m2_Wz0(:,i, i)), 'color', [colors(3,:), 0.5], ...
|
||||
'HandleVisibility', 'off')
|
||||
end
|
||||
plot(f, abs(G_int_m3_Wz0(:, 1, 1)), 'color', [colors(4,:), 0.5], ...
|
||||
'DisplayName', 'Meas (39kg)');
|
||||
for i = 2:6
|
||||
plot(f, abs(G_int_m3_Wz0(:,i, i)), 'color', [colors(4,:), 0.5], ...
|
||||
'HandleVisibility', 'off')
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(Gm_m0_Wz0('eL1', 'u1'), freqs, 'Hz'))), '--', 'color', colors(1,:), ...
|
||||
'DisplayName', 'Model (0kg)');
|
||||
plot(freqs, abs(squeeze(freqresp(Gm_m1_Wz0('eL1', 'u1'), freqs, 'Hz'))), '--', 'color', colors(2,:), ...
|
||||
'DisplayName', 'Model (13kg)');
|
||||
plot(freqs, abs(squeeze(freqresp(Gm_m2_Wz0('eL1', 'u1'), freqs, 'Hz'))), '--', 'color', colors(3,:), ...
|
||||
'DisplayName', 'Model (26kg)');
|
||||
plot(freqs, abs(squeeze(freqresp(Gm_m3_Wz0('eL1', 'u1'), freqs, 'Hz'))), '--', 'color', colors(4,:), ...
|
||||
'DisplayName', 'Model (39kg)');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/V]'); set(gca, 'XTickLabel',[]);
|
||||
ylim([1e-8, 5e-4]);
|
||||
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 2);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
for i =1:6
|
||||
plot(f, 180/pi*angle(G_int_m0_Wz0(:,i, i)), 'color', [colors(1,:), 0.5]);
|
||||
end
|
||||
for i =1:6
|
||||
plot(f, 180/pi*angle(G_int_m1_Wz0(:,i, i)), 'color', [colors(2,:), 0.5]);
|
||||
end
|
||||
for i =1:6
|
||||
plot(f, 180/pi*angle(G_int_m2_Wz0(:,i, i)), 'color', [colors(3,:), 0.5]);
|
||||
end
|
||||
for i =1:6
|
||||
plot(f, 180/pi*angle(G_int_m3_Wz0(:,i, i)), 'color', [colors(4,:), 0.5]);
|
||||
end
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_m0_Wz0('eL1', 'u1'), freqs, 'Hz'))), '--', 'color', colors(1,:))
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_m1_Wz0('eL1', 'u1'), freqs, 'Hz'))), '--', 'color', colors(2,:))
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_m2_Wz0('eL1', 'u1'), freqs, 'Hz'))), '--', 'color', colors(3,:))
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_m3_Wz0('eL1', 'u1'), freqs, 'Hz'))), '--', 'color', colors(4,:))
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:90:360);
|
||||
ylim([-90, 180])
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([10, 5e2]);
|
||||
xticks([10, 20, 50, 100, 200, 500])
|
||||
|
||||
%% Obtained transfer function from generated voltages to measured voltages on the piezoelectric force sensor
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(f, abs(G_iff_m0_Wz0(:, 1, 1)), 'color', [colors(1,:), 0.5], ...
|
||||
'DisplayName', 'Meas (0kg)');
|
||||
for i = 2:6
|
||||
plot(f, abs(G_iff_m0_Wz0(:,i, i)), 'color', [colors(1,:), 0.5], ...
|
||||
'HandleVisibility', 'off')
|
||||
end
|
||||
plot(f, abs(G_iff_m1_Wz0(:, 1, 1)), 'color', [colors(2,:), 0.5], ...
|
||||
'DisplayName', 'Meas (13kg)');
|
||||
for i = 2:6
|
||||
plot(f, abs(G_iff_m1_Wz0(:,i, i)), 'color', [colors(2,:), 0.5], ...
|
||||
'HandleVisibility', 'off')
|
||||
end
|
||||
plot(f, abs(G_iff_m2_Wz0(:, 1, 1)), 'color', [colors(3,:), 0.5], ...
|
||||
'DisplayName', 'Meas (26kg)');
|
||||
for i = 2:6
|
||||
plot(f, abs(G_iff_m2_Wz0(:,i, i)), 'color', [colors(3,:), 0.5], ...
|
||||
'HandleVisibility', 'off')
|
||||
end
|
||||
plot(f, abs(G_iff_m3_Wz0(:, 1, 1)), 'color', [colors(4,:), 0.5], ...
|
||||
'DisplayName', 'Meas (39kg)');
|
||||
for i = 2:6
|
||||
plot(f, abs(G_iff_m3_Wz0(:,i, i)), 'color', [colors(4,:), 0.5], ...
|
||||
'HandleVisibility', 'off')
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(Gm_m0_Wz0('Vs1', 'u1'), freqs, 'Hz'))), '--', 'color', colors(1,:), ...
|
||||
'DisplayName', 'Model (0kg)');
|
||||
plot(freqs, abs(squeeze(freqresp(Gm_m1_Wz0('Vs1', 'u1'), freqs, 'Hz'))), '--', 'color', colors(2,:), ...
|
||||
'DisplayName', 'Model (13kg)');
|
||||
plot(freqs, abs(squeeze(freqresp(Gm_m2_Wz0('Vs1', 'u1'), freqs, 'Hz'))), '--', 'color', colors(3,:), ...
|
||||
'DisplayName', 'Model (26kg)');
|
||||
plot(freqs, abs(squeeze(freqresp(Gm_m3_Wz0('Vs1', 'u1'), freqs, 'Hz'))), '--', 'color', colors(4,:), ...
|
||||
'DisplayName', 'Model (39kg)');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [V/V]'); set(gca, 'XTickLabel',[]);
|
||||
ylim([1e-2, 4e1]);
|
||||
leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
for i =1:6
|
||||
plot(f, 180/pi*angle(G_iff_m0_Wz0(:,i, i)), 'color', [colors(1,:), 0.5]);
|
||||
end
|
||||
for i =1:6
|
||||
plot(f, 180/pi*angle(G_iff_m1_Wz0(:,i, i)), 'color', [colors(2,:), 0.5]);
|
||||
end
|
||||
for i =1:6
|
||||
plot(f, 180/pi*angle(G_iff_m2_Wz0(:,i, i)), 'color', [colors(3,:), 0.5]);
|
||||
end
|
||||
for i =1:6
|
||||
plot(f, 180/pi*angle(G_iff_m3_Wz0(:,i, i)), 'color', [colors(4,:), 0.5]);
|
||||
end
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_m0_Wz0('Vs1', 'u1'), freqs, 'Hz'))), '--', 'color', colors(1,:))
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_m1_Wz0('Vs1', 'u1'), freqs, 'Hz'))), '--', 'color', colors(2,:))
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_m2_Wz0('Vs1', 'u1'), freqs, 'Hz'))), '--', 'color', colors(3,:))
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_m3_Wz0('Vs1', 'u1'), freqs, 'Hz'))), '--', 'color', colors(4,:))
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:90:360);
|
||||
ylim([-90, 180])
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([10, 5e2]);
|
||||
xticks([10, 20, 50, 100, 200, 500])
|
||||
|
||||
%% Identify the model dynamics with Spindle rotation
|
||||
initializeSample('type', '0');
|
||||
initializeReferences(...
|
||||
'Rz_type', 'rotating', ...
|
||||
'Rz_period', 360/36); % 36 deg/s, 6rpm
|
||||
Gm_m0_Wz36 = linearize(mdl, io, 0.1);
|
||||
Gm_m0_Wz36.InputName = {'u1', 'u2', 'u3', 'u4', 'u5', 'u6'};
|
||||
Gm_m0_Wz36.OutputName = {'Vs1', 'Vs2', 'Vs3', 'Vs4', 'Vs5', 'Vs6', ...
|
||||
'eL1', 'eL2', 'eL3', 'eL4', 'eL5', 'eL6'};
|
||||
|
||||
initializeReferences(...
|
||||
'Rz_type', 'rotating', ...
|
||||
'Rz_period', 360/180); % 180 deg/s, 30rpm
|
||||
Gm_m0_Wz180 = linearize(mdl, io, 0.1);
|
||||
Gm_m0_Wz180.InputName = {'u1', 'u2', 'u3', 'u4', 'u5', 'u6'};
|
||||
Gm_m0_Wz180.OutputName = {'Vs1', 'Vs2', 'Vs3', 'Vs4', 'Vs5', 'Vs6', ...
|
||||
'eL1', 'eL2', 'eL3', 'eL4', 'eL5', 'eL6'};
|
||||
|
||||
%% Identify the plant from experimental data - Effect of rotation
|
||||
|
||||
% Load identification data
|
||||
data_m0_Wz36 = load('2023-08-08_16-28_ol_plant_m0_Wz36.mat');
|
||||
data_m0_Wz180 = load('2023-08-08_16-45_ol_plant_m0_Wz180.mat');
|
||||
|
||||
% Spindle Rotation at 36 deg/s
|
||||
G_iff_m0_Wz36 = zeros(length(f), 6, 6);
|
||||
for i_strut = 1:6
|
||||
eL = [data_m0_Wz36.(sprintf("uL%i", i_strut)).Vs1 ; data_m0_Wz36.(sprintf("uL%i", i_strut)).Vs2 ; data_m0_Wz36.(sprintf("uL%i", i_strut)).Vs3 ; data_m0_Wz36.(sprintf("uL%i", i_strut)).Vs4 ; data_m0_Wz36.(sprintf("uL%i", i_strut)).Vs5 ; data_m0_Wz36.(sprintf("uL%i", i_strut)).Vs6]';
|
||||
|
||||
G_iff_m0_Wz36(:,:,i_strut) = tfestimate(data_m0_Wz36.(sprintf("uL%i", i_strut)).id_plant, eL, win, Noverlap, Nfft, 1/Ts);
|
||||
end
|
||||
|
||||
G_int_m0_Wz36 = zeros(length(f), 6, 6);
|
||||
for i_strut = 1:6
|
||||
eL = [data_m0_Wz36.(sprintf("uL%i", i_strut)).e_L1 ; data_m0_Wz36.(sprintf("uL%i", i_strut)).e_L2 ; data_m0_Wz36.(sprintf("uL%i", i_strut)).e_L3 ; data_m0_Wz36.(sprintf("uL%i", i_strut)).e_L4 ; data_m0_Wz36.(sprintf("uL%i", i_strut)).e_L5 ; data_m0_Wz36.(sprintf("uL%i", i_strut)).e_L6]';
|
||||
|
||||
G_int_m0_Wz36(:,:,i_strut) = tfestimate(data_m0_Wz36.(sprintf("uL%i", i_strut)).id_plant, eL, win, Noverlap, Nfft, 1/Ts);
|
||||
end
|
||||
|
||||
% Spindle Rotation at 180 deg/s
|
||||
G_iff_m0_Wz180 = zeros(length(f), 6, 6);
|
||||
for i_strut = 1:6
|
||||
eL = [data_m0_Wz180.(sprintf("uL%i", i_strut)).Vs1 ; data_m0_Wz180.(sprintf("uL%i", i_strut)).Vs2 ; data_m0_Wz180.(sprintf("uL%i", i_strut)).Vs3 ; data_m0_Wz180.(sprintf("uL%i", i_strut)).Vs4 ; data_m0_Wz180.(sprintf("uL%i", i_strut)).Vs5 ; data_m0_Wz180.(sprintf("uL%i", i_strut)).Vs6]';
|
||||
|
||||
G_iff_m0_Wz180(:,:,i_strut) = tfestimate(data_m0_Wz180.(sprintf("uL%i", i_strut)).id_plant, eL, win, Noverlap, Nfft, 1/Ts);
|
||||
end
|
||||
|
||||
G_int_m0_Wz180 = zeros(length(f), 6, 6);
|
||||
for i_strut = 1:6
|
||||
eL = [data_m0_Wz180.(sprintf("uL%i", i_strut)).e_L1 ; data_m0_Wz180.(sprintf("uL%i", i_strut)).e_L2 ; data_m0_Wz180.(sprintf("uL%i", i_strut)).e_L3 ; data_m0_Wz180.(sprintf("uL%i", i_strut)).e_L4 ; data_m0_Wz180.(sprintf("uL%i", i_strut)).e_L5 ; data_m0_Wz180.(sprintf("uL%i", i_strut)).e_L6]';
|
||||
|
||||
G_int_m0_Wz180(:,:,i_strut) = tfestimate(data_m0_Wz180.(sprintf("uL%i", i_strut)).id_plant, eL, win, Noverlap, Nfft, 1/Ts);
|
||||
end
|
||||
|
||||
% The identified dynamics are then saved for further use.
|
||||
save('./mat/test_id31_simscape_open_loop_plants.mat', 'Gm_m0_Wz0', 'Gm_m0_Wz36', 'Gm_m0_Wz180', 'Gm_m1_Wz0', 'Gm_m2_Wz0', 'Gm_m3_Wz0');
|
||||
save('./mat/test_id31_identified_open_loop_plants.mat', 'G_int_m0_Wz0', 'G_int_m0_Wz36', 'G_int_m0_Wz180', 'G_int_m1_Wz0', 'G_int_m2_Wz0', 'G_int_m3_Wz0', ...
|
||||
'G_iff_m0_Wz0', 'G_iff_m0_Wz36', 'G_iff_m0_Wz180', 'G_iff_m1_Wz0', 'G_iff_m2_Wz0', 'G_iff_m3_Wz0', 'f');
|
||||
|
||||
figure;
|
||||
tiledlayout(1, 1, 'TileSpacing', 'compact', 'Padding', 'None');
|
||||
|
||||
nexttile();
|
||||
hold on;
|
||||
plot(f, abs(G_int_m0_Wz0(:, 1, 1)), 'color', [colors(1,:), 0.5], ...
|
||||
'DisplayName', '$\Omega_z = 0$');
|
||||
plot(f, abs(G_int_m0_Wz36(:, 1, 1)), 'color', [colors(2,:), 0.5], ...
|
||||
'DisplayName', '$\Omega_z = 36$ deg/s');
|
||||
plot(f, abs(G_int_m0_Wz180(:, 1, 1)), 'color', [colors(3,:), 0.5], ...
|
||||
'DisplayName', '$\Omega_z = 180$ deg/s');
|
||||
for i = 2:6
|
||||
plot(f, abs(G_int_m0_Wz0(:,i, i)), 'color', [colors(1,:), 0.5], ...
|
||||
'HandleVisibility', 'off')
|
||||
plot(f, abs(G_int_m0_Wz36(:,i, i)), 'color', [colors(2,:), 0.5], ...
|
||||
'HandleVisibility', 'off')
|
||||
plot(f, abs(G_int_m0_Wz180(:,i, i)), 'color', [colors(3,:), 0.5], ...
|
||||
'HandleVisibility', 'off')
|
||||
end
|
||||
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;
|
||||
xlim([10, 1e3]); ylim([1e-8, 2e-4])
|
||||
|
||||
figure;
|
||||
tiledlayout(1, 1, 'TileSpacing', 'compact', 'Padding', 'None');
|
||||
|
||||
nexttile();
|
||||
hold on;
|
||||
plot(f, abs(G_int_m0_Wz0(:, 1, 2)), 'color', [colors(1,:), 0.5], ...
|
||||
'DisplayName', '$\Omega_z = 0$');
|
||||
plot(f, abs(G_int_m0_Wz36(:, 1, 2)), 'color', [colors(2,:), 0.5], ...
|
||||
'DisplayName', '$\Omega_z = 36$ deg/s');
|
||||
plot(f, abs(G_int_m0_Wz180(:, 1, 2)), 'color', [colors(3,:), 0.5], ...
|
||||
'DisplayName', '$\Omega_z = 180$ deg/s');
|
||||
for i = 1:5
|
||||
for j = i+1:6
|
||||
plot(f, abs(G_int_m0_Wz0(:, i, j)), 'color', [colors(1,:), 0.5], ...
|
||||
'HandleVisibility', 'off');
|
||||
plot(f, abs(G_int_m0_Wz36(:, i, j)), 'color', [colors(2,:), 0.5], ...
|
||||
'HandleVisibility', 'off');
|
||||
plot(f, abs(G_int_m0_Wz180(:, i, j)), 'color', [colors(3,:), 0.5], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude [m/V]');
|
||||
leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
xlim([10, 1e3]); ylim([1e-8, 2e-4])
|
||||
Reference in New Issue
Block a user