Verification that Matlab scripts are working
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@ -149,9 +149,6 @@ add_mass_cc.de = add_mass_cc.de - mean(add_mass_cc.de(add_mass_cc.t<11));
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apa_k_oc = 9.8 * added_mass / (mean(add_mass_oc.de(add_mass_oc.t > 12 & add_mass_oc.t < 12.5)) - mean(add_mass_oc.de(add_mass_oc.t > 20 & add_mass_oc.t < 20.5)));
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apa_k_sc = 9.8 * added_mass / (mean(add_mass_cc.de(add_mass_cc.t > 12 & add_mass_cc.t < 12.5)) - mean(add_mass_cc.de(add_mass_cc.t > 20 & add_mass_cc.t < 20.5)));
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%% Estimated coupling factor
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sqrt(1 - apa_k_sc/apa_k_oc)
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% Dynamics
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% <<ssec:test_apa_meas_dynamics>>
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@ -493,7 +490,6 @@ opts.cmplx_ss = 0; % Create real state space model with block diagonal A
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opts.spy1 = 0; % No plotting for first stage of vector fitting
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opts.spy2 = 0; % Create magnitude plot for fitting of f(s)
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Niter = 100; % Number of iteration.
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N = 2; % Order of approximation
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poles = [-25 - 1i*60, -25 + 1i*60]; % First get for the pole location
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@ -501,7 +497,7 @@ poles = [-25 - 1i*60, -25 + 1i*60]; % First get for the pole location
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G_dL_id = {zeros(1,length(i_kept))};
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% Identification just between two frequencies
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f_keep = (f>20 & f<200);
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f_keep = (f>5 & f<200);
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for i = 1:length(i_kept)
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%% Estimate resonance frequency and damping
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@ -543,12 +539,11 @@ legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
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%% Root Locus of the APA300ML with Integral Force Feedback
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% Comparison between the computed root locus from the plant model and the root locus estimated from the damped plant pole identification
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figure;
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gains = logspace(-1, 3, 1000);
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figure;
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hold on;
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G_iff_poles = pole(G_iff_model);
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G_iff_poles = pole(pade(G_iff_model));
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i = imag(G_iff_poles) > 100; % Only keep relevant poles
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plot(real(G_iff_poles(i)), imag(G_iff_poles(i)), 'kx', ...
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'DisplayName', '$g = 0$');
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@ -558,7 +553,7 @@ plot(real(G_iff_zeros(i)), imag(G_iff_zeros(i)), 'ko', ...
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'HandleVisibility', 'off');
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for g = gains
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clpoles = pole(feedback(G_iff_model, g*K_iff, 1));
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clpoles = pole(feedback(pade(G_iff_model), g*K_iff, 1));
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i = imag(clpoles) > 100; % Only keep relevant poles
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plot(real(clpoles(i)), imag(clpoles(i)), 'k.', ...
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'HandleVisibility', 'off');
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@ -84,7 +84,7 @@ ga = -abs(enc_frf(i_f,1))./abs(evalfr(G_norm('de', 'u'), 1i*2*pi*fa));
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% Estimation ot the Sensor Gain
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fs = 600; % Frequency where the two FRF should match [Hz]
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[~, i_f] = min(abs(f - fs))
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[~, i_f] = min(abs(f - fs));
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gs = -abs(iff_frf(i_f,1))./abs(evalfr(G_norm('Vs', 'u'), 1i*2*pi*fs))/ga;
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% Obtained Dynamics
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@ -1,566 +0,0 @@
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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('./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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%% 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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% First Identification
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% <<sec:simscape_bench_apa_first_id>>
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% The APA is first initialized with default parameters:
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%% Initialize the structure with default values
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n_hexapod = struct();
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n_hexapod.actuator = initializeAPA(...
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'type', '2dof', ...
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'Ga', 1, ... % Actuator constant [N/V]
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'Gs', 1); % Sensor constant [V/m]
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% The transfer function from excitation voltage $V_a$ (before the amplification of $20$ due to the PD200 amplifier) to:
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% 1. the sensor stack voltage $V_s$
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% 2. the measured displacement by the encoder $d_e$
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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, '/Va'], 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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%% Linearization options
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opts = linearizeOptions;
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opts.SampleTime = 0;
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%% Run the linearization
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Ga = linearize(mdl, io, 0.0, opts);
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Ga.InputName = {'Va'};
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Ga.OutputName = {'Vs', 'de', 'da'};
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% The obtain dynamics are shown in Figure ref:fig:apa_model_bench_bode_vs and ref:fig:apa_model_bench_bode_dl_z.
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% It can be seen that:
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% - the shape of these bode plots are very similar to the one measured in Section ref:sec:dynamical_meas_apa expect from a change in gain and exact location of poles and zeros
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% - there is a sign error for the transfer function from $V_a$ to $V_s$.
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% This will be corrected by taking a negative "sensor gain".
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% - the low frequency zero of the transfer function from $V_a$ to $V_s$ is minimum phase as expected.
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% The measured FRF are showing non-minimum phase zero, but it is most likely due to measurements artifacts.
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%% Bode plot of the transfer function from u to taum
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freqs = logspace(1, 3, 1000);
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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(freqs, abs(squeeze(freqresp(Ga('Vs', 'Va'), freqs, 'Hz'))), 'k-')
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]);
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hold off;
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ax2 = nexttile;
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hold on;
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plot(freqs, 180/pi*angle(squeeze(freqresp(Ga('Vs', 'Va'), freqs, 'Hz'))), 'k-')
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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(-360:45:360);
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ylim([-180, 0])
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linkaxes([ax1,ax2],'x');
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xlim([freqs(1), freqs(end)]);
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% #+name: fig:apa_model_bench_bode_vs
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% #+caption: Bode plot of the transfer function from $V_a$ to $V_s$
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% #+RESULTS:
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% [[file:figs/apa_model_bench_bode_vs.png]]
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%% Bode plot of the transfer function from Va to de and da
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freqs = logspace(1, 3, 1000);
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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(freqs, abs(squeeze(freqresp(Ga('de', 'Va'), freqs, 'Hz'))), 'DisplayName', 'Encoder')
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude $d/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
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hold off;
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legend('location', 'southwest');
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ax2 = nexttile;
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hold on;
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plot(freqs, 180/pi*angle(squeeze(freqresp(Ga('de', 'Va'), freqs, 'Hz'))))
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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(-360:45:360);
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ylim([-180, 0])
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linkaxes([ax1,ax2],'x');
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% Identification Data
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% Let's load the measured FRF from the DAC voltage to the measured encoder and to the sensor stack voltage.
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%% Load Data
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load('meas_apa_frf.mat', 'f', 'Ts', 'enc_frf', 'iff_frf', 'apa_nums');
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% 2DoF APA
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% Let's initialize the APA as a 2DoF model with unity sensor and actuator gains.
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%% Initialize a 2DoF APA with Ga=Gs=1
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n_hexapod.actuator = initializeAPA(...
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'type', '2dof', ...
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'ga', 1, ...
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'gs', 1);
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% Identification without actuator or sensor constants
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% The transfer function from $V_a$ to $V_s$, $d_e$ and $d_a$ is identified.
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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, '/Va'], 1, 'openinput'); io_i = io_i + 1; % Actuator 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; % Attocube
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%% Identification
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Gs = linearize(mdl, io, 0.0, options);
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Gs.InputName = {'Va'};
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Gs.OutputName = {'Vs', 'de', 'da'};
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% Actuator Constant
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% Then, the actuator constant can be computed as shown in Eq. eqref:eq:actuator_constant_formula by dividing the measured DC gain of the transfer function from $V_a$ to $d_e$ by the estimated DC gain of the transfer function from $V_a$ (in truth the actuator force called $F_a$) to $d_e$ using the Simscape model.
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%% Estimated Actuator Constant
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ga = -mean(abs(enc_frf(f>10 & f<20)))./dcgain(Gs('de', 'Va')); % [N/V]
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% Sensor Constant
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% Similarly, the sensor constant can be estimated using Eq. eqref:eq:sensor_constant_formula.
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%% Estimated Sensor Constant
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gs = -mean(abs(iff_frf(f>400 & f<500)))./(ga*abs(squeeze(freqresp(Gs('Vs', 'Va'), 1e3, 'Hz')))); % [V/m]
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% Comparison
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% Let's now initialize the APA with identified sensor and actuator constant:
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%% Set the identified constants
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n_hexapod.actuator = initializeAPA(...
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'type', '2dof', ...
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'ga', ga, ... % Actuator gain [N/V]
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'gs', gs); % Sensor gain [V/m]
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% And identify the dynamics with included constants.
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%% Identify again the dynamics with correct Ga,Gs
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Gs = linearize(mdl, io, 0.0, options);
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Gs = Gs*exp(-Ts*s);
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Gs.InputName = {'Va'};
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Gs.OutputName = {'Vs', 'de', 'da'};
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% The transfer functions from $V_a$ to $d_e$ are compared in Figure ref:fig:apa_act_constant_comp and the one from $V_a$ to $V_s$ are compared in Figure ref:fig:apa_sens_constant_comp.
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%% Bode plot of the transfer function from u to de
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freqs = logspace(1,4,1000);
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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(apa_nums)
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plot(f, abs(enc_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, abs(squeeze(freqresp(Gs('de', 'Va'), freqs, 'Hz'))))
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude $d\mathcal{L}_m/u$ [m/V]'); set(gca, 'XTickLabel',[]);
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hold off;
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ylim([1e-8, 1e-3]);
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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(:,1)), '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('de', 'Va'), freqs, 'Hz'))))
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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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% #+name: fig:apa_act_constant_comp
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% #+caption: Comparison of the experimental data and Simscape model ($V_a$ to $d_e$)
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% #+RESULTS:
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% [[file:figs/apa_act_constant_comp.png]]
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%% Bode plot of the transfer function from Va to Vs (both Simscape and measured FRF)
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freqs = logspace(1,4,1000);
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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(apa_nums)
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plot(f, abs(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, abs(squeeze(freqresp(Gs('Vs', 'Va'), freqs, 'Hz'))))
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude $\tau_m/u$ [V/V]'); set(gca, 'XTickLabel',[]);
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hold off;
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ylim([1e-2, 1e2]);
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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(:,1)), '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('Vs', 'Va'), freqs, 'Hz'))))
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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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% #+name: fig:apa_sens_constant_comp
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% #+caption: Comparison of the experimental data and Simscape model ($V_a$ to $V_s$)
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% #+RESULTS:
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% [[file:figs/apa_sens_constant_comp.png]]
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%% Compare the FRF and identified dynamics from Va to Vs and da
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colors = colororder;
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figure;
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tiledlayout(3, 2, '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], ...
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'DisplayName', 'FRF');
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for i = 2:length(apa_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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set(gca,'ColorOrderIndex',1);
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plot(freqs, abs(squeeze(freqresp(Gs('da', 'Va'), freqs, 'Hz'))), '--', ...
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'DisplayName', '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 $d_a/V_a$ [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', 'southwest');
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ax1b = 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(apa_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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set(gca,'ColorOrderIndex',1);
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plot(freqs, abs(squeeze(freqresp(Gs('Vs', 'Va'), freqs, 'Hz'))), '--', ...
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'DisplayName', '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 $V_s/V_a$ [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');
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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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set(gca,'ColorOrderIndex',1);
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gs('da', 'Va'), freqs, 'Hz'))), '--')
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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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ax2b = 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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set(gca,'ColorOrderIndex',1);
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gs('Vs', 'Va'), freqs, 'Hz'))), '--')
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hold off;
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||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:90:360); ylim([-180, 180]);
|
||||
|
||||
linkaxes([ax1,ax2,ax1b,ax2b],'x');
|
||||
xlim([10, 2e3]);
|
||||
|
||||
% Flexible APA
|
||||
% The Simscape APA model is initialized as a flexible one with unity "constants".
|
||||
|
||||
%% Initialize the APA as a flexible body
|
||||
n_hexapod.actuator = initializeAPA(...
|
||||
'type', 'flexible', ...
|
||||
'ga', 1, ...
|
||||
'gs', 1);
|
||||
|
||||
% Identification without actuator or sensor constants
|
||||
% The dynamics from $V_a$ to $V_s$, $d_e$ and $d_a$ is identified.
|
||||
|
||||
%% Identify the dynamics
|
||||
Gs = linearize(mdl, io, 0.0, options);
|
||||
Gs.InputName = {'Va'};
|
||||
Gs.OutputName = {'Vs', 'de', 'da'};
|
||||
|
||||
% Actuator Constant
|
||||
% Then, the actuator constant can be computed as shown in Eq. eqref:eq:actuator_constant_formula:
|
||||
|
||||
%% Actuator Constant
|
||||
ga = -mean(abs(enc_frf(f>10 & f<20)))./dcgain(Gs('de', 'Va')); % [N/V]
|
||||
|
||||
% Sensor Constant
|
||||
|
||||
%% Sensor Constant
|
||||
gs = -mean(abs(iff_frf(f>400 & f<500)))./(ga*abs(squeeze(freqresp(Gs('Vs', 'Va'), 1e3, 'Hz')))); % [V/m]
|
||||
|
||||
% Comparison
|
||||
% Let's now initialize the flexible APA with identified sensor and actuator constant:
|
||||
|
||||
%% Set the identified constants
|
||||
n_hexapod.actuator = initializeAPA(...
|
||||
'type', 'flexible', ...
|
||||
'ga', ga, ... % Actuator gain [N/V]
|
||||
'gs', gs); % Sensor gain [V/m]
|
||||
|
||||
|
||||
|
||||
% And identify the dynamics with included constants.
|
||||
|
||||
%% Identify with updated constants
|
||||
Gs = linearize(mdl, io, 0.0, options);
|
||||
Gs = Gs*exp(-Ts*s);
|
||||
Gs.InputName = {'Va'};
|
||||
Gs.OutputName = {'Vs', 'de', 'da'};
|
||||
|
||||
|
||||
|
||||
% The obtained dynamics is compared with the measured one in Figures ref:fig:apa_act_constant_comp_flex and ref:fig:apa_sens_constant_comp_flex.
|
||||
|
||||
|
||||
%% Bode plot of the transfer function from V_a to d_e (both Simscape and measured FRF)
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
for i = 1:length(apa_nums)
|
||||
plot(f, abs(enc_frf(:, i)), 'color', [0,0,0,0.2]);
|
||||
end
|
||||
set(gca,'ColorOrderIndex',1);
|
||||
plot(freqs, abs(squeeze(freqresp(Gs('de', 'Va'), freqs, 'Hz'))))
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $d\mathcal{L}_m/u$ [m/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
ylim([1e-9, 1e-3]);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
for i = 1:length(apa_nums)
|
||||
plot(f, 180/pi*angle(enc_frf(:,1)), 'color', [0,0,0,0.2]);
|
||||
end
|
||||
set(gca,'ColorOrderIndex',1);
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gs('de', 'Va'), freqs, 'Hz'))))
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:90:360); ylim([-180, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([10, 2e3]);
|
||||
|
||||
|
||||
|
||||
% #+name: fig:apa_act_constant_comp_flex
|
||||
% #+caption: Comparison of the experimental data and Simscape model ($u$ to $d\mathcal{L}_m$)
|
||||
% #+RESULTS:
|
||||
% [[file:figs/apa_act_constant_comp_flex.png]]
|
||||
|
||||
|
||||
%% Bode plot of the transfer function from Va to Vs (both Simscape and measured FRF)
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
for i = 1:length(apa_nums)
|
||||
plot(f, abs(iff_frf(:, i)), 'color', [0,0,0,0.2]);
|
||||
end
|
||||
set(gca,'ColorOrderIndex',1);
|
||||
plot(freqs, abs(squeeze(freqresp(Gs('Vs', 'Va'), freqs, 'Hz'))))
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $\tau_m/u$ [V/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
ylim([1e-2, 1e2]);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
for i = 1:length(apa_nums)
|
||||
plot(f, 180/pi*angle(iff_frf(:,1)), 'color', [0,0,0,0.2]);
|
||||
end
|
||||
set(gca,'ColorOrderIndex',1);
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gs('Vs', 'Va'), freqs, 'Hz'))))
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:90:360); ylim([-180, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([10, 2e3]);
|
||||
|
||||
% Optimize 2-DoF model to fit the experimental Data
|
||||
% <<sec:simscape_bench_apa_tune_2dof_model>>
|
||||
% The parameters of the 2DoF model presented in Section ref:sec:apa_2dof_model are now optimize such that the model best matches the measured FRF.
|
||||
|
||||
% After optimization, the following parameters are used:
|
||||
|
||||
%% Optimized parameters
|
||||
n_hexapod.actuator = initializeAPA('type', '2dof', ...
|
||||
'Ga', -32.2, ...
|
||||
'Gs', 0.088, ...
|
||||
'k', ones(6,1)*0.38e6, ...
|
||||
'ke', ones(6,1)*1.75e6, ...
|
||||
'ka', ones(6,1)*3e7, ...
|
||||
'c', ones(6,1)*1.3e2, ...
|
||||
'ce', ones(6,1)*1e1, ...
|
||||
'ca', ones(6,1)*1e1 ...
|
||||
);
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/Va'], 1, 'openinput'); io_i = io_i + 1; % Actuator Voltage
|
||||
io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; % Sensor Voltage
|
||||
io(io_i) = linio([mdl, '/de'], 1, 'openoutput'); io_i = io_i + 1; % Encoder
|
||||
|
||||
%% Identification with optimized parameters
|
||||
Gs = exp(-s*Ts)*linearize(mdl, io, 0.0, options);
|
||||
Gs.InputName = {'Va'};
|
||||
Gs.OutputName = {'Vs', 'de'};
|
||||
|
||||
|
||||
|
||||
% The dynamics is identified using the Simscape model and compared with the measured FRF in Figure ref:fig:comp_apa_plant_after_opt.
|
||||
|
||||
%% Comparison of the experimental data and Simscape Model
|
||||
freqs = 5*logspace(0, 3, 1000);
|
||||
figure;
|
||||
tiledlayout(3, 2, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
for i = 1:length(apa_nums)
|
||||
plot(f, abs(enc_frf(:, i)), 'color', [0,0,0,0.2]);
|
||||
end
|
||||
set(gca,'ColorOrderIndex',1);
|
||||
plot(freqs, abs(squeeze(freqresp(Gs('de', 'Va'), freqs, 'Hz'))))
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $d_e/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
ylim([1e-8, 1e-3]);
|
||||
|
||||
ax1b = nexttile([2,1]);
|
||||
hold on;
|
||||
for i = 1:length(apa_nums)
|
||||
plot(f, abs(iff_frf(:, i)), 'color', [0,0,0,0.2]);
|
||||
end
|
||||
set(gca,'ColorOrderIndex',1);
|
||||
plot(freqs, abs(squeeze(freqresp(Gs('Vs', 'Va'), freqs, 'Hz'))))
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
ylim([1e-2, 1e2]);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
for i = 1:length(apa_nums)
|
||||
plot(f, 180/pi*angle(enc_frf(:, i)), 'color', [0,0,0,0.2]);
|
||||
end
|
||||
set(gca,'ColorOrderIndex',1);
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gs('de', 'Va'), freqs, 'Hz'))))
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:90:360); ylim([-180, 180]);
|
||||
|
||||
ax2b = nexttile;
|
||||
hold on;
|
||||
for i = 1:length(apa_nums)
|
||||
plot(f, 180/pi*angle(iff_frf(:, i)), 'color', [0,0,0,0.2]);
|
||||
end
|
||||
set(gca,'ColorOrderIndex',1);
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gs('Vs', 'Va'), freqs, 'Hz'))))
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:90:360); ylim([-180, 180]);
|
||||
|
||||
linkaxes([ax1,ax2,ax1b,ax2b],'x');
|
||||
xlim([10, 2e3]);
|
||||
@ -116,6 +116,7 @@ ka = cE*A/L; % Stiffness of the two stacks [N/m]
|
||||
ga = d33*n*ka; % Actuator Constant [N/V]
|
||||
|
||||
% Comparison of the obtained dynamics
|
||||
% <<ssec:test_apa_flexible_comp_frf>>
|
||||
|
||||
% The obtained dynamics using the /super element/ with the tuned "sensor gain" and "actuator gain" are compared with the experimentally identified frequency response functions in Figure ref:fig:test_apa_super_element_comp_frf.
|
||||
|
||||
|
||||
@ -699,9 +699,6 @@ add_mass_cc.de = add_mass_cc.de - mean(add_mass_cc.de(add_mass_cc.t<11));
|
||||
%% Estimation of the stiffness in Open Circuit and Closed-Circuit
|
||||
apa_k_oc = 9.8 * added_mass / (mean(add_mass_oc.de(add_mass_oc.t > 12 & add_mass_oc.t < 12.5)) - mean(add_mass_oc.de(add_mass_oc.t > 20 & add_mass_oc.t < 20.5)));
|
||||
apa_k_sc = 9.8 * added_mass / (mean(add_mass_cc.de(add_mass_cc.t > 12 & add_mass_cc.t < 12.5)) - mean(add_mass_cc.de(add_mass_cc.t > 20 & add_mass_cc.t < 20.5)));
|
||||
|
||||
%% Estimated coupling factor
|
||||
sqrt(1 - apa_k_sc/apa_k_oc)
|
||||
#+end_src
|
||||
|
||||
** Dynamics
|
||||
@ -1051,7 +1048,7 @@ Noverlap = floor(Nfft/2);
|
||||
[~, f] = tfestimate(data.data(1).id_plant(1:end), data.data(1).dL(1:end), win, Noverlap, Nfft, 1/Ts);
|
||||
|
||||
%% Gains used for analysis are between 1 and 50
|
||||
i_kept = [5:10]
|
||||
i_kept = [5:10];
|
||||
|
||||
%% Identify the damped plant from u' to de for different IFF gains
|
||||
G_dL_frf = {zeros(1,length(i_kept))};
|
||||
@ -1080,7 +1077,6 @@ opts.cmplx_ss = 0; % Create real state space model with block diagonal A
|
||||
opts.spy1 = 0; % No plotting for first stage of vector fitting
|
||||
opts.spy2 = 0; % Create magnitude plot for fitting of f(s)
|
||||
|
||||
|
||||
Niter = 100; % Number of iteration.
|
||||
N = 2; % Order of approximation
|
||||
poles = [-25 - 1i*60, -25 + 1i*60]; % First get for the pole location
|
||||
@ -1088,7 +1084,7 @@ poles = [-25 - 1i*60, -25 + 1i*60]; % First get for the pole location
|
||||
G_dL_id = {zeros(1,length(i_kept))};
|
||||
|
||||
% Identification just between two frequencies
|
||||
f_keep = (f>20 & f<200);
|
||||
f_keep = (f>5 & f<200);
|
||||
|
||||
for i = 1:length(i_kept)
|
||||
%% Estimate resonance frequency and damping
|
||||
@ -1135,12 +1131,11 @@ The two obtained root loci are compared in Figure ref:fig:test_apa_iff_root_locu
|
||||
#+begin_src matlab :exports none :results none
|
||||
%% Root Locus of the APA300ML with Integral Force Feedback
|
||||
% Comparison between the computed root locus from the plant model and the root locus estimated from the damped plant pole identification
|
||||
figure;
|
||||
gains = logspace(-1, 3, 1000);
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
G_iff_poles = pole(G_iff_model);
|
||||
G_iff_poles = pole(pade(G_iff_model));
|
||||
i = imag(G_iff_poles) > 100; % Only keep relevant poles
|
||||
plot(real(G_iff_poles(i)), imag(G_iff_poles(i)), 'kx', ...
|
||||
'DisplayName', '$g = 0$');
|
||||
@ -1150,7 +1145,7 @@ plot(real(G_iff_zeros(i)), imag(G_iff_zeros(i)), 'ko', ...
|
||||
'HandleVisibility', 'off');
|
||||
|
||||
for g = gains
|
||||
clpoles = pole(feedback(G_iff_model, g*K_iff, 1));
|
||||
clpoles = pole(feedback(pade(G_iff_model), g*K_iff, 1));
|
||||
i = imag(clpoles) > 100; % Only keep relevant poles
|
||||
plot(real(clpoles(i)), imag(clpoles(i)), 'k.', ...
|
||||
'HandleVisibility', 'off');
|
||||
@ -1318,7 +1313,7 @@ ga = -abs(enc_frf(i_f,1))./abs(evalfr(G_norm('de', 'u'), 1i*2*pi*fa));
|
||||
|
||||
% Estimation ot the Sensor Gain
|
||||
fs = 600; % Frequency where the two FRF should match [Hz]
|
||||
[~, i_f] = min(abs(f - fs))
|
||||
[~, i_f] = min(abs(f - fs));
|
||||
gs = -abs(iff_frf(i_f,1))./abs(evalfr(G_norm('Vs', 'u'), 1i*2*pi*fs))/ga;
|
||||
#+end_src
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user