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figs/detail_fem_apa95ml_compliance.pdf
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figs/detail_fem_apa95ml_compliance.pdf
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figs/detail_fem_open_loop_identification.pdf
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figs/detail_fem_open_loop_identification.svg
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figs/detail_fem_open_loop_identification.svg
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figs/inkscape/convert_svg.sh
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figs/inkscape/convert_svg.sh
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#!/bin/bash
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# Directory containing SVG files
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INPUT_DIR="."
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# Loop through all SVG files in the directory
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for svg_file in "$INPUT_DIR"/*.svg; do
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# Check if there are SVG files in the directory
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if [ -f "$svg_file" ]; then
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# Output PDF file name
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pdf_file="../${svg_file%.svg}.pdf"
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||||
png_file="../${svg_file%.svg}"
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||||
# Convert SVG to PDF using Inkscape
|
||||
inkscape "$svg_file" --export-filename="$pdf_file" && \
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pdftocairo -png -singlefile -cropbox "$pdf_file" "$png_file"
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fi
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done
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figs/inkscape/detail_fem_apa95ml_mesh.svg
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figs/inkscape/detail_fem_apa95ml_mesh.svg
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@@ -23,13 +23,13 @@
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inkscape:pagecheckerboard="0"
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inkscape:deskcolor="#d1d1d1"
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inkscape:document-units="mm"
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inkscape:zoom="3.0060173"
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inkscape:cx="-10.977981"
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inkscape:cy="86.659515"
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inkscape:zoom="6.0120346"
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inkscape:cx="13.971975"
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inkscape:cy="76.596366"
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inkscape:window-width="2534"
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inkscape:window-height="1367"
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inkscape:window-height="1387"
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inkscape:window-x="11"
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inkscape:window-y="60"
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inkscape:window-y="38"
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inkscape:window-maximized="1"
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inkscape:current-layer="layer1" /><defs
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id="defs1" /><g
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@@ -59,5 +59,5 @@
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sodipodi:nodetypes="sccsccs" /><path
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id="path1-6"
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style="font-variation-settings:normal;opacity:1;vector-effect:none;fill:#ccebff;fill-opacity:1;stroke:#000000;stroke-width:0.264583;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;-inkscape-stroke:none;stop-color:#000000;stop-opacity:1"
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sodipodi:nodetypes="ccscc" /></g></svg>
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sodipodi:nodetypes="cscscscc" /></g></svg>
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1820
matlab/STEPS/APA95ML.STEP
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matlab/STEPS/APA95ML.STEP
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307
matlab/detail_fem_1_flexible_body.m
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307
matlab/detail_fem_1_flexible_body.m
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|
||||
%% Clear Workspace and Close figures
|
||||
clear; close all; clc;
|
||||
|
||||
%% Intialize Laplace variable
|
||||
s = zpk('s');
|
||||
|
||||
%% Path for functions, data and scripts
|
||||
addpath('./src/'); % Path for scripts
|
||||
addpath('./mat/'); % Path for data
|
||||
addpath('./STEPS/'); % Path for Simscape Model
|
||||
addpath('./subsystems/'); % Path for Subsystems Simulink files
|
||||
|
||||
%% Linearization options
|
||||
opts = linearizeOptions;
|
||||
opts.SampleTime = 0;
|
||||
|
||||
%% Open Simscape Model
|
||||
mdl = 'detail_fem_super_element'; % Name of the Simulink File
|
||||
open(mdl); % Open Simscape Model
|
||||
|
||||
%% Colors for the figures
|
||||
colors = colororder;
|
||||
freqs = logspace(1,3,500); % Frequency vector [Hz]
|
||||
|
||||
%% Estimate "Sensor Constant" - (THP5H)
|
||||
d33 = 680e-12; % Strain constant [m/V]
|
||||
n = 160; % Number of layers per stack
|
||||
eT = 4500*8.854e-12; % Permittivity under constant stress [F/m]
|
||||
sD = 21e-12; % Compliance under constant electric displacement [m2/N]
|
||||
|
||||
gs = d33/(eT*sD*n); % Sensor Constant [V/m]
|
||||
|
||||
%% Estimate "Actuator Constant" - (THP5H)
|
||||
d33 = 680e-12; % Strain constant [m/V]
|
||||
n = 320; % Number of layers
|
||||
|
||||
cE = 1/sD; % Youngs modulus [N/m^2]
|
||||
A = (10e-3)^2; % Area of the stacks [m^2]
|
||||
L = 40e-3; % Length of the two stacks [m]
|
||||
ka = cE*A/L; % Stiffness of the two stacks [N/m]
|
||||
|
||||
ga = d33*n*ka; % Actuator Constant [N/V]
|
||||
|
||||
%% Load reduced order model
|
||||
K = readmatrix('APA95ML_K.CSV'); % order: 48
|
||||
M = readmatrix('APA95ML_M.CSV');
|
||||
[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('APA95ML_out_nodes_3D.txt');
|
||||
|
||||
%% Stiffness estimation
|
||||
m = 0.0001; % block-free condition, no payload
|
||||
k_support = 1e9;
|
||||
c_support = 1e3;
|
||||
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/Fd'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/y'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
|
||||
G = linearize(mdl, io);
|
||||
|
||||
% The inverse of the DC gain of the transfer function
|
||||
% from vertical force to vertical displacement is the axial stiffness of the APA
|
||||
k_est = 1/dcgain(G); % [N/m]
|
||||
|
||||
%% Estimated compliance of the APA95ML
|
||||
freqs = logspace(2, log10(5000), 1000);
|
||||
|
||||
% Get first resonance indice
|
||||
i_max = find(abs(squeeze(freqresp(G, freqs(2:end), 'Hz'))) - abs(squeeze(freqresp(G, freqs(1:end-1), 'Hz'))) < 0, 1);
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G, freqs, 'Hz'))), 'DisplayName', 'Compliance');
|
||||
plot([freqs(1), freqs(end)], [1/k_est, 1/k_est], 'k--', 'DisplayName', sprintf('$1/k$ ($k = %.0f N/\\mu m$)', 1e-6*k_est))
|
||||
xline(freqs(i_max), '--', 'linewidth', 1, 'color', [0,0,0], 'DisplayName', sprintf('$f_0 = %.0f$ Hz', freqs(i_max)))
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
|
||||
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
xlim([100, 5000]);
|
||||
|
||||
%% Estimation of the amplification factor and Stroke
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/Fa'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/y'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/d'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
|
||||
G = linearize(mdl, io);
|
||||
|
||||
% Estimated amplification factor
|
||||
ampl_factor = abs(dcgain(G(1,1))./dcgain(G(2,1)));
|
||||
|
||||
% Estimated stroke
|
||||
apa_stroke = ampl_factor * 3 * 20e-6; % [m]
|
||||
|
||||
%% Experimental plant identification
|
||||
% with PD200 amplifier (gain of 20) - 2 stacks as an actuator, 1 as a sensor
|
||||
load('apa95ml_5kg_2a_1s.mat')
|
||||
|
||||
Va = 20*u; % Voltage amplifier gain: 20
|
||||
|
||||
% Spectral Analysis parameters
|
||||
Ts = t(end)/(length(t)-1);
|
||||
Nfft = floor(1/Ts);
|
||||
win = hanning(Nfft);
|
||||
Noverlap = floor(Nfft/2);
|
||||
|
||||
% Identification of the transfer function from Va to di
|
||||
[G_y, f] = tfestimate(detrend(Va, 0), detrend(y, 0), win, Noverlap, Nfft, 1/Ts);
|
||||
[G_Vs, ~] = tfestimate(detrend(Va, 0), detrend(v, 0), win, Noverlap, Nfft, 1/Ts);
|
||||
|
||||
%% Plant Identification from Multi-Body model
|
||||
% Load Reduced Order Matrices
|
||||
K = readmatrix('APA95ML_K.CSV'); % order: 48
|
||||
M = readmatrix('APA95ML_M.CSV');
|
||||
[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('APA95ML_out_nodes_3D.txt');
|
||||
|
||||
m = 5.5; % Mass of the suspended granite [kg]
|
||||
k_support = 4e7;
|
||||
c_support = 3e2;
|
||||
|
||||
% Compute transfer functions
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/Va'], 1, 'openinput'); io_i = io_i + 1; % Voltage accros piezo stacks [V]
|
||||
io(io_i) = linio([mdl, '/y'], 1, 'openoutput'); io_i = io_i + 1; % Vertical Displacement [m]
|
||||
io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; % Sensor stack voltage [V]
|
||||
|
||||
Gm = linearize(mdl, io);
|
||||
Gm.InputName = {'Va'};
|
||||
Gm.OutputName = {'y', 'Vs'};
|
||||
|
||||
%% Comparison of the identified transfer function from Va to di to the multi-body model
|
||||
freqs = logspace(1, 3, 500);
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(f, abs(G_y), '-', 'color', [colors(2,:), 0.5], 'linewidth', 2.5, 'DisplayName', 'Measured FRF');
|
||||
plot(freqs, abs(squeeze(freqresp(Gm('y', 'Va'), freqs, 'Hz'))), '--', 'color', colors(2,:), 'DisplayName', 'Model')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $y/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
ylim([1e-8, 1e-5]);
|
||||
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(f, 180/pi*angle(G_y), '-', 'color' , [colors(2,:), 0.5], 'linewidth', 2.5);
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm('y', 'Va'), freqs, 'Hz'))), '--', 'color', colors(2,:))
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:45:360);
|
||||
ylim([-45, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([10, 1e3]);
|
||||
|
||||
%% Comparison of the identified transfer function from Va to Vs to the multi-body model
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(f, abs(G_Vs), '-', 'color', [colors(1,:), 0.5], 'linewidth', 2.5, 'DisplayName', 'Measured FRF');
|
||||
plot(freqs, abs(squeeze(freqresp(Gm('Vs', 'Va'), freqs, 'Hz'))), '--', 'color', colors(1,:), 'DisplayName', 'Model')
|
||||
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-3, 1e1]);
|
||||
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(f, 180/pi*angle(G_Vs), '-', 'color', [colors(1,:), 0.5], 'linewidth', 2.5);
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm('Vs', 'Va'), freqs, 'Hz'))), '--', 'color', colors(1,:))
|
||||
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, 1e3]);
|
||||
|
||||
%% Integral Force Feedback Controller
|
||||
K_iff = (1/(s + 2*2*pi))*(s/(s + 0.5*2*pi));
|
||||
K_iff.inputname = {'Vs'};
|
||||
K_iff.outputname = {'u_iff'};
|
||||
|
||||
% New damped plant input
|
||||
S1 = sumblk("u = u_iff + u_damp");
|
||||
|
||||
% Voltage amplifier with gain of 20
|
||||
voltage_amplifier = tf(20);
|
||||
voltage_amplifier.inputname = {'u'};
|
||||
voltage_amplifier.outputname = {'Va'};
|
||||
|
||||
%% Load experimental data with IFF implemented with different gains
|
||||
load('apa95ml_iff_test.mat', 'results');
|
||||
|
||||
% Tested gains
|
||||
g_iff = [0, 10, 50, 100, 500, 1000];
|
||||
|
||||
% Spectral Analysis parameters
|
||||
Ts = t(end)/(length(t)-1);
|
||||
Nfft = floor(1/Ts);
|
||||
win = hanning(Nfft);
|
||||
Noverlap = floor(Nfft/2);
|
||||
|
||||
%% Computed the identified FRF of the damped plants
|
||||
tf_iff = {zeros(1, length(g_iff))};
|
||||
for i=1:length(g_iff)
|
||||
[tf_est, f] = tfestimate(results{i}.u, results{i}.y, win, Noverlap, Nfft, 1/Ts);
|
||||
tf_iff(i) = {tf_est};
|
||||
end
|
||||
|
||||
%% Estimate the damped plants from the multi-body model
|
||||
Gm_iff = {zeros(1, length(g_iff))};
|
||||
|
||||
for i=1:length(g_iff)
|
||||
K_iff_g = -K_iff*g_iff(i); K_iff_g.inputname = {'Vs'}; K_iff_g.outputname = {'u_iff'};
|
||||
Gm_iff(i) = {connect(Gm, K_iff_g, S1, voltage_amplifier, {'u_damp'}, {'y'})};
|
||||
end
|
||||
|
||||
%% Identify second order plants from the experimental data
|
||||
% This is mandatory to estimate the experimental "poles"
|
||||
% an place them in the root-locus plot
|
||||
G_id = {zeros(1,length(results))};
|
||||
|
||||
f_start = 70; % [Hz]
|
||||
f_end = 500; % [Hz]
|
||||
|
||||
for i = 1:length(results)
|
||||
tf_id = tf_iff{i}(sum(f<f_start):length(f)-sum(f>f_end));
|
||||
f_id = f(sum(f<f_start):length(f)-sum(f>f_end));
|
||||
|
||||
gfr = idfrd(tf_id, 2*pi*f_id, Ts);
|
||||
G_id(i) = {procest(gfr,'P2UDZ')};
|
||||
end
|
||||
|
||||
%% Comparison of the Root-Locus computed from the multi-body model and the identified closed-loop poles
|
||||
gains = logspace(0, 5, 1000);
|
||||
figure;
|
||||
hold on;
|
||||
plot(real( pole(Gm('Vs', 'Va'))), imag( pole(Gm('Vs', 'Va'))), 'kx', 'HandleVisibility', 'off');
|
||||
plot(real(tzero(Gm('Vs', 'Va'))), imag(tzero(Gm('Vs', 'Va'))), 'ko', 'HandleVisibility', 'off');
|
||||
for i = 1:length(gains)
|
||||
cl_poles = pole(feedback(Gm('Vs', 'Va'), gains(i)*K_iff));
|
||||
plot(real(cl_poles(imag(cl_poles)>100)), imag(cl_poles(imag(cl_poles)>100)), 'k.', 'HandleVisibility', 'off');
|
||||
end
|
||||
for i = 1:length(g_iff)
|
||||
cl_poles = pole(Gm_iff{i});
|
||||
plot(real(cl_poles(imag(cl_poles)>100)), imag(cl_poles(imag(cl_poles)>100)), '.', 'MarkerSize', 20, 'color', colors(i,:), 'HandleVisibility', 'off');
|
||||
plot(real(pole(G_id{i})), imag(pole(G_id{i})), 'x', 'color', colors(i,:), 'DisplayName', sprintf('g = %0.f', g_iff(i)), 'DisplayName', sprintf('$g = %.0f$', g_iff(i)));
|
||||
end
|
||||
xlabel('Real Part');
|
||||
ylabel('Imaginary Part');
|
||||
axis equal;
|
||||
ylim([-100, 2100]);
|
||||
xlim([-2100,100]);
|
||||
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
|
||||
%% Experimental damped plant for several IFF gains and estimated damped plants from the model
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2, 1]);
|
||||
hold on;
|
||||
plot(f, abs(tf_iff{1}), '-', 'DisplayName', '$g = 0$', 'color', [0,0,0, 0.5], 'linewidth', 2.5)
|
||||
plot(f, abs(squeeze(freqresp(Gm_iff{1}, f, 'Hz'))), 'k--', 'HandleVisibility', 'off')
|
||||
for i = 2:length(results)
|
||||
plot(f, abs(tf_iff{i}), '-', 'DisplayName', sprintf('g = %0.f', g_iff(i)), 'color', [colors(i-1,:), 0.5], 'linewidth', 2.5)
|
||||
end
|
||||
for i = 2:length(results)
|
||||
plot(f, abs(squeeze(freqresp(Gm_iff{i}, f, 'Hz'))), '--', 'color', colors(i-1,:), 'HandleVisibility', 'off')
|
||||
end
|
||||
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||
ylabel('Amplitude $y/V_a$ [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
ylim([1e-6, 2e-4]);
|
||||
leg = legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(f, 180/pi*angle(tf_iff{1}./squeeze(freqresp(exp(-s*2e-4), f, 'Hz'))), '-', 'color', [0,0,0, 0.5], 'linewidth', 2.5)
|
||||
plot(f, 180/pi*angle(squeeze(freqresp(Gm_iff{1}, f, 'Hz'))), 'k--')
|
||||
for i = 2:length(results)
|
||||
plot(f, 180/pi*angle(tf_iff{i}./squeeze(freqresp(exp(-s*2e-4), f, 'Hz'))), '-', 'color', [colors(i-1,:), 0.5], 'linewidth', 2.5)
|
||||
plot(f, 180/pi*angle(squeeze(freqresp(Gm_iff{i}, f, 'Hz'))), '--', 'color', colors(i-1,:))
|
||||
end
|
||||
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
hold off;
|
||||
yticks(-360:45:360);
|
||||
ylim([-10, 190]);
|
||||
|
||||
linkaxes([ax1,ax2], 'x');
|
||||
xlim([150, 500]);
|
||||
318
matlab/detail_fem_2_actuators.m
Normal file
318
matlab/detail_fem_2_actuators.m
Normal file
@@ -0,0 +1,318 @@
|
||||
%% Clear Workspace and Close figures
|
||||
clear; close all; clc;
|
||||
|
||||
%% Intialize Laplace variable
|
||||
s = zpk('s');
|
||||
|
||||
%% Path for functions, data and scripts
|
||||
addpath('./src/'); % Path for scripts
|
||||
addpath('./mat/'); % Path for data
|
||||
addpath('./STEPS/'); % Path for Simscape Model
|
||||
addpath('./subsystems/'); % Path for Subsystems Simulink files
|
||||
|
||||
%% Linearization options
|
||||
opts = linearizeOptions;
|
||||
opts.SampleTime = 0;
|
||||
|
||||
%% Open Simscape Model
|
||||
mdl = 'detail_fem_APA300ML'; % Name of the Simulink File
|
||||
open(mdl); % Open Simscape Model
|
||||
|
||||
% Piezoelectric parameters
|
||||
ga = -25.9; % [N/V]
|
||||
gs = -5.08e6; % [V/m]
|
||||
|
||||
%% Colors for the figures
|
||||
colors = colororder;
|
||||
freqs = logspace(1,3,500); % Frequency vector [Hz]
|
||||
|
||||
%% Identify dynamics with "Reduced Order Flexible Body"
|
||||
K = readmatrix('APA300ML_mat_K.CSV');
|
||||
M = readmatrix('APA300ML_mat_M.CSV');
|
||||
[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('APA300ML_out_nodes_3D.txt');
|
||||
|
||||
m = 5; % [kg]
|
||||
ga = 25.9; % [N/V]
|
||||
gs = 5.08e6; % [V/m]
|
||||
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/Va'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/Fd'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/z'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
|
||||
G_fem = linearize(mdl, io);
|
||||
G_fem_z = G_fem('z','Va');
|
||||
G_fem_Vs = G_fem('Vs', 'Va');
|
||||
G_fem_comp = G_fem('z', 'Fd');
|
||||
|
||||
%% Determine c1 and k1 from the zero
|
||||
G_zeros = zero(minreal(G_fem_Vs));
|
||||
G_zeros = G_zeros(imag(G_zeros)>0);
|
||||
[~, i_sort] = sort(imag(G_zeros));
|
||||
G_zeros = G_zeros(i_sort);
|
||||
G_zero = G_zeros(1);
|
||||
|
||||
% Solving 2nd order equations
|
||||
c1 = -2*m*real(G_zero);
|
||||
k1 = m*(imag(G_zero)^2 + real(G_zero)^2);
|
||||
|
||||
%% Determine ka, ke, ca, ce from the first pole
|
||||
G_poles = pole(minreal(G_fem_z));
|
||||
G_poles = G_poles(imag(G_poles)>0);
|
||||
[~, i_sort] = sort(imag(G_poles));
|
||||
G_poles = G_poles(i_sort);
|
||||
G_pole = G_poles(1);
|
||||
|
||||
% Solving 2nd order equations
|
||||
ce = 3*(-2*m*real(G_pole(1)) - c1);
|
||||
ca = 1/2*ce;
|
||||
|
||||
ke = 3*(m*(imag(G_pole)^2 + real(G_pole)^2) - k1);
|
||||
ka = 1/2*ke;
|
||||
|
||||
%% Matching sensor/actuator constants
|
||||
% ga = dcgain(G_fem_z) / (1/(ka + k1*ke/(k1 + ke)));
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '_2dof', '/Fa'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '_2dof', '/z'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
ga = dcgain(G_fem_z)/dcgain(linearize([mdl, '_2dof'], io));
|
||||
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '_2dof', '/Va'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '_2dof', '/dL'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
gs = dcgain(G_fem_Vs)/dcgain(linearize([mdl, '_2dof'], io));
|
||||
|
||||
%% Identify dynamics with tuned 2DoF model
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '_2dof', '/Va'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '_2dof', '/Fd'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '_2dof', '/z'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '_2dof', '/Vs'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
|
||||
G_2dof = linearize([mdl, '_2dof'], io);
|
||||
G_2dof_z = G_2dof('z','Va');
|
||||
G_2dof_Vs = G_2dof('Vs', 'Va');
|
||||
G_2dof_comp = G_2dof('z', 'Fd');
|
||||
|
||||
%% Comparison of the transfer functions from Va to vertical motion - FEM vs 2DoF
|
||||
freqs = logspace(1, 3, 500);
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_fem_z, freqs, 'Hz'))), '-', 'color', [colors(2,:), 0.5], 'linewidth', 2.5, 'DisplayName', 'FEM')
|
||||
plot(freqs, abs(squeeze(freqresp(G_2dof_z, freqs, 'Hz'))), '--', 'color', colors(2,:), 'DisplayName', '2DoF Model')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $y/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
ylim([1e-8, 2e-4]);
|
||||
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_fem_z, freqs, 'Hz')))), '-', 'color', [colors(2,:), 0.5], 'linewidth', 2.5);
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_2dof_z, freqs, 'Hz')))), '--', 'color', colors(2,:))
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:45:360); ylim([-20, 200]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([10, 1e3]);
|
||||
|
||||
%% Comparison of the transfer functions from Va to Vs - FEM vs 2DoF
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G_fem_Vs, freqs, 'Hz'))), '-', 'color', [colors(1,:), 0.5], 'linewidth', 2.5, 'DisplayName', 'FEM');
|
||||
plot(freqs, abs(squeeze(freqresp(G_2dof_Vs, freqs, 'Hz'))), '--', 'color', colors(1,:), 'DisplayName', '2DoF Model')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
ylim([6e-4, 3e1]);
|
||||
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_fem_Vs, freqs, 'Hz')))), '-', 'color', [colors(1,:), 0.5], 'linewidth', 2.5);
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_2dof_Vs, freqs, 'Hz')))), '--', 'color', colors(1,:))
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:45:360); ylim([-20, 200]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([10, 1e3]);
|
||||
|
||||
%% Effect of electrical boundaries on the
|
||||
oc = load('detail_fem_apa95ml_open_circuit.mat', 't', 'encoder', 'u');
|
||||
sc = load('detail_fem_apa95ml_short_circuit.mat', 't', 'encoder', 'u');
|
||||
|
||||
% Spectral Analysis parameters
|
||||
Ts = sc.t(end)/(length(sc.t)-1);
|
||||
Nfft = floor(2/Ts);
|
||||
win = hanning(Nfft);
|
||||
Noverlap = floor(Nfft/2);
|
||||
|
||||
% Identification of the transfer function from Va to di
|
||||
[G_oc, f] = tfestimate(detrend(oc.u, 0), detrend(oc.encoder, 0), win, Noverlap, Nfft, 1/Ts);
|
||||
[G_sc, f] = tfestimate(detrend(sc.u, 0), detrend(sc.encoder, 0), win, Noverlap, Nfft, 1/Ts);
|
||||
|
||||
% Find resonance frequencies
|
||||
[~, i_oc] = max(abs(G_oc(f<300)));
|
||||
[~, i_sc] = max(abs(G_sc(f<300)));
|
||||
|
||||
%% Effect of the electrical bondaries of the force sensor stack on the APA95ML resonance frequency
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(f, abs(G_oc), '-', 'DisplayName', sprintf('Open-Circuit - $f_0 = %.1f Hz$', f(i_oc)))
|
||||
plot(f, abs(G_sc), '-', 'DisplayName', sprintf('Short-Circuit - $f_0 = %.1f Hz$', f(i_sc)))
|
||||
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
ylim([1e-6, 1e-4]);
|
||||
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(f, 180/pi*angle(G_oc), '-')
|
||||
plot(f, 180/pi*angle(G_sc), '-')
|
||||
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
|
||||
ylabel('Phase'); xlabel('Frequency [Hz]');
|
||||
hold off;
|
||||
yticks(-360:45:360);
|
||||
ylim([-20, 200]);
|
||||
axis padded 'auto x'
|
||||
|
||||
linkaxes([ax1,ax2], 'x');
|
||||
xlim([100, 300]);
|
||||
|
||||
%% Compare Dynamics between "Reduced Order" flexible joints and "2-dof and 3-dof" joints
|
||||
% Let's initialize all the stages with default parameters.
|
||||
initializeGround('type', 'rigid');
|
||||
initializeGranite('type', 'rigid');
|
||||
initializeTy('type', 'rigid');
|
||||
initializeRy('type', 'rigid');
|
||||
initializeRz('type', 'rigid');
|
||||
initializeMicroHexapod('type', 'rigid');
|
||||
initializeSample('m', 50);
|
||||
|
||||
initializeSimscapeConfiguration();
|
||||
initializeDisturbances('enable', false);
|
||||
initializeLoggingConfiguration('log', 'none');
|
||||
initializeController('type', 'open-loop');
|
||||
initializeReferences();
|
||||
|
||||
mdl = 'detail_fem_nass';
|
||||
|
||||
% 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, '/Tracking Error'], 1, 'openoutput', [], 'EdL'); io_i = io_i + 1; % Errors in the frame of the struts
|
||||
io(io_i) = linio([mdl, '/NASS'], 3, 'openoutput', [], 'fn'); io_i = io_i + 1; % Force Sensors
|
||||
|
||||
% Flexible actuators
|
||||
initializeSimplifiedNanoHexapod('actuator_type', 'flexible', ...
|
||||
'flex_type_F', '2dof', ...
|
||||
'flex_type_M', '3dof');
|
||||
|
||||
G_flex = linearize(mdl, io);
|
||||
G_flex.InputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||
G_flex.OutputName = {'l1', 'l2', 'l3', 'l4', 'l5', 'l6', 'fm1', 'fm2', 'fm3', 'fm4', 'fm5', 'fm6'};
|
||||
|
||||
% Actuators modeled as 2DoF system
|
||||
initializeSimplifiedNanoHexapod('actuator_type', 'apa300ml', ...
|
||||
'flex_type_F', '2dof', ...
|
||||
'flex_type_M', '3dof');
|
||||
|
||||
G_ideal = linearize(mdl, io);
|
||||
G_ideal.InputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||
G_ideal.OutputName = {'l1', 'l2', 'l3', 'l4', 'l5', 'l6', 'fm1', 'fm2', 'fm3', 'fm4', 'fm5', 'fm6'};
|
||||
|
||||
%% Comparison of the dynamics for actuators modeled using "reduced order flexible body" and using 2DoF system - HAC plant
|
||||
freqs = logspace(1, 4, 1000);
|
||||
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
for j = 1:5
|
||||
for k = j+1:6
|
||||
plot(freqs, abs(squeeze(freqresp(G_flex("l"+k,"f"+j), freqs, 'Hz'))), 'color', [colors(1,:), 0.1], ...
|
||||
'HandleVisibility', 'off');
|
||||
plot(freqs, abs(squeeze(freqresp(G_ideal("l"+k,"f"+j), freqs, 'Hz'))), 'color', [colors(2,:), 0.1], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(G_flex("l1","f1"), freqs, 'Hz'))), 'color', colors(1,:), 'DisplayName', 'FEM');
|
||||
plot(freqs, abs(squeeze(freqresp(G_ideal("l1","f1"), freqs, 'Hz'))), 'color', colors(2,:), 'DisplayName', '2-DoF');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
leg = legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
ylim([1e-10, 1e-4]);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_flex("l1","f1"), freqs, 'Hz'))));
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_ideal("l1","f1"), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-20, 200]);
|
||||
yticks([-360:45:360]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
|
||||
%% Comparison of the dynamics for actuators modeled using "reduced order flexible body" and using 2DoF system - IFF plant
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
for j = 1:5
|
||||
for k = j+1:6
|
||||
plot(freqs, abs(squeeze(freqresp(G_flex("fm"+k,"f"+j), freqs, 'Hz'))), 'color', [colors(1,:), 0.1], ...
|
||||
'HandleVisibility', 'off');
|
||||
plot(freqs, abs(squeeze(freqresp(G_ideal("fm"+k,"f"+j), freqs, 'Hz'))), 'color', [colors(2,:), 0.1], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(G_flex("fm1","f1"), freqs, 'Hz'))), 'color', colors(1,:), 'DisplayName', 'FEM');
|
||||
plot(freqs, abs(squeeze(freqresp(G_ideal("fm1","f1"), freqs, 'Hz'))), 'color', colors(2,:), 'DisplayName', '2-DoF');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
|
||||
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
ylim([1e-5, 1e1]);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_flex("fm1","f1"), freqs, 'Hz'))));
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_ideal("fm1","f1"), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-20, 200]);
|
||||
yticks([-360:45:360]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
623
matlab/detail_fem_3_flexible_joints.m
Normal file
623
matlab/detail_fem_3_flexible_joints.m
Normal file
@@ -0,0 +1,623 @@
|
||||
%% Clear Workspace and Close figures
|
||||
clear; close all; clc;
|
||||
|
||||
%% Intialize Laplace variable
|
||||
s = zpk('s');
|
||||
|
||||
%% Path for functions, data and scripts
|
||||
addpath('./src/'); % Path for scripts
|
||||
addpath('./mat/'); % Path for data
|
||||
addpath('./STEPS/'); % Path for Simscape Model
|
||||
addpath('./subsystems/'); % Path for Subsystems Simulink files
|
||||
|
||||
%% Linearization options
|
||||
opts = linearizeOptions;
|
||||
opts.SampleTime = 0;
|
||||
|
||||
%% Open Simscape Model
|
||||
mdl = 'detail_fem_nass'; % Name of the Simulink File
|
||||
open(mdl); % Open Simscape Model
|
||||
|
||||
%% Colors for the figures
|
||||
colors = colororder;
|
||||
freqs = logspace(1,3,500); % Frequency vector [Hz]
|
||||
|
||||
%% Identify the dynamics for several considered bending stiffnesses
|
||||
% Let's initialize all the stages with default parameters.
|
||||
initializeGround('type', 'rigid');
|
||||
initializeGranite('type', 'rigid');
|
||||
initializeTy('type', 'rigid');
|
||||
initializeRy('type', 'rigid');
|
||||
initializeRz('type', 'rigid');
|
||||
initializeMicroHexapod('type', 'rigid');
|
||||
initializeSample('m', 50);
|
||||
|
||||
initializeSimscapeConfiguration();
|
||||
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, '/Tracking Error'], 1, 'openoutput', [], 'EdL'); io_i = io_i + 1; % Errors in the frame of the struts
|
||||
io(io_i) = linio([mdl, '/NASS'], 3, 'openoutput', [], 'fn'); io_i = io_i + 1; % Force Sensors
|
||||
|
||||
% Effect of bending stiffness
|
||||
Kf = [0, 50, 100, 500]; % [Nm/rad]
|
||||
G_Kf = {zeros(length(Kf), 1)};
|
||||
|
||||
for i = 1:length(Kf)
|
||||
% Limited joint axial compliance
|
||||
initializeSimplifiedNanoHexapod('actuator_type', '1dof', ...
|
||||
'flex_type_F', '2dof', ...
|
||||
'flex_type_M', '3dof', ...
|
||||
'actuator_k', 1e6, ...
|
||||
'actuator_c', 1e1, ...
|
||||
'actuator_kp', 0, ...
|
||||
'actuator_cp', 0, ...
|
||||
'Fsm', 56e-3, ... % APA300ML weight 112g
|
||||
'Msm', 56e-3, ...
|
||||
'Kf_F', Kf(i), ...
|
||||
'Kf_M', Kf(i));
|
||||
|
||||
G_Kf(i) = {linearize(mdl, io)};
|
||||
G_Kf{i}.InputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||
G_Kf{i}.OutputName = {'l1', 'l2', 'l3', 'l4', 'l5', 'l6', 'fm1', 'fm2', 'fm3', 'fm4', 'fm5', 'fm6'};
|
||||
end
|
||||
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
%% Effect of the flexible joint bending stiffness on the HAC-plant
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
for i = 1:length(Kf)
|
||||
for j = 1:5
|
||||
for k = j+1:6
|
||||
plot(freqs, abs(squeeze(freqresp(G_Kf{i}("l"+k,"f"+j), freqs, 'Hz'))), 'color', [colors(i,:), 0.1], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(G_Kf{i}("l1","f1"), freqs, 'Hz'))), 'color', colors(i,:), 'DisplayName', sprintf('$k_f = %.0f $ [Nm/rad]', Kf(i)));
|
||||
for j = 2:6
|
||||
plot(freqs, abs(squeeze(freqresp(G_Kf{i}("l"+j,"f"+j), freqs, 'Hz'))), 'color', colors(i,:), 'HandleVisibility', 'off');
|
||||
end
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
ylim([1e-10, 1e-4]);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
for i = 1:length(Kf)
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_Kf{i}(1, 1), freqs, 'Hz')))));
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-200, 20]);
|
||||
yticks([-360:45:360]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
|
||||
%% Effect of the flexible joint bending stiffness on the IFF plant
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
for i = 1:length(Kf)
|
||||
for j = 1:5
|
||||
for k = j+1:6
|
||||
plot(freqs, abs(squeeze(freqresp(G_Kf{i}("fm"+k,"f"+j), freqs, 'Hz'))), 'color', [colors(i,:), 0.1], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(G_Kf{i}("fm1","f1"), freqs, 'Hz'))), 'color', colors(i,:), 'DisplayName', sprintf('$k_f = %.0f $ [Nm/rad]', Kf(i)));
|
||||
for j = 2:6
|
||||
plot(freqs, abs(squeeze(freqresp(G_Kf{i}("fm"+j,"f"+j), freqs, 'Hz'))), 'color', colors(i,:), 'HandleVisibility', 'off');
|
||||
end
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
|
||||
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
ylim([1e-4, 1e2]);
|
||||
|
||||
ax2 = nexttile();
|
||||
hold on;
|
||||
for i = 1:length(Kf)
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_Kf{i}("fm1", "f1"), freqs, 'Hz')))));
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-20, 200]);
|
||||
yticks([-360:45:360]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
|
||||
%% Decentalized IFF
|
||||
Kiff = -200 * ... % Gain
|
||||
1/s * ... % LPF: provides integral action
|
||||
eye(6); % Diagonal 6x6 controller (i.e. decentralized)
|
||||
|
||||
Kiff.InputName = {'fm1', 'fm2', 'fm3', 'fm4', 'fm5', 'fm6'};
|
||||
Kiff.OutputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||
|
||||
%% Root Locus for decentralized IFF - 1dof actuator - Effect of joint bending stiffness
|
||||
gains = logspace(-1, 2, 400);
|
||||
|
||||
figure;
|
||||
tiledlayout(1, 1, 'TileSpacing', 'compact', 'Padding', 'None');
|
||||
nexttile();
|
||||
hold on;
|
||||
|
||||
for i = 1:length(Kf)
|
||||
plot(real(pole(G_Kf{i}({"fm1", "fm2", "fm3", "fm4", "fm5", "fm6"}, {"f1", "f2", "f3", "f4", "f5", "f6"}))), imag(pole(G_Kf{i}({"fm1", "fm2", "fm3", "fm4", "fm5", "fm6"}, {"f1", "f2", "f3", "f4", "f5", "f6"}))), 'x', 'color', colors(i,:), ...
|
||||
'DisplayName', sprintf('$k_f = %.0f$ Nm/rad', Kf(i)));
|
||||
plot(real(tzero(G_Kf{i}({"fm1", "fm2", "fm3", "fm4", "fm5", "fm6"}, {"f1", "f2", "f3", "f4", "f5", "f6"}))), imag(tzero(G_Kf{i}({"fm1", "fm2", "fm3", "fm4", "fm5", "fm6"}, {"f1", "f2", "f3", "f4", "f5", "f6"}))), 'o', 'color', colors(i,:), ...
|
||||
'HandleVisibility', 'off');
|
||||
|
||||
for g = gains
|
||||
clpoles = pole(feedback(G_Kf{i}({"fm1", "fm2", "fm3", "fm4", "fm5", "fm6"}, {"f1", "f2", "f3", "f4", "f5", "f6"}), g*Kiff, +1));
|
||||
plot(real(clpoles), imag(clpoles), '.', 'color', colors(i,:), ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
xline(0, 'HandleVisibility', 'off'); yline(0, 'HandleVisibility', 'off');
|
||||
hold off;
|
||||
axis equal;
|
||||
xlim(1.1*[-900, 100]); ylim(1.1*[-100, 900]);
|
||||
xticks(1.1*[-900:100:0]);
|
||||
yticks(1.1*[0:100:900]);
|
||||
set(gca, 'XTickLabel',[]); set(gca, 'YTickLabel',[]);
|
||||
xlabel('Real part'); ylabel('Imaginary part');
|
||||
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
|
||||
%% Identify the dynamics for several considered bending stiffnesses - APA300ML
|
||||
G_Kf_apa300ml = {zeros(length(Kf), 1)};
|
||||
|
||||
for i = 1:length(Kf)
|
||||
% Limited joint axial compliance
|
||||
initializeSimplifiedNanoHexapod('actuator_type', 'apa300ml', ...
|
||||
'flex_type_F', '2dof', ...
|
||||
'flex_type_M', '3dof', ...
|
||||
'Fsm', 56e-3, ... % APA300ML weight 112g
|
||||
'Msm', 56e-3, ...
|
||||
'Kf_F', Kf(i), ...
|
||||
'Kf_M', Kf(i));
|
||||
|
||||
G_Kf_apa300ml(i) = {linearize(mdl, io)};
|
||||
G_Kf_apa300ml{i}.InputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||
G_Kf_apa300ml{i}.OutputName = {'l1', 'l2', 'l3', 'l4', 'l5', 'l6', 'fm1', 'fm2', 'fm3', 'fm4', 'fm5', 'fm6'};
|
||||
end
|
||||
|
||||
Kiff = -1000 * ... % Gain
|
||||
1/(s) * ... % LPF: provides integral action
|
||||
eye(6); % Diagonal 6x6 controller (i.e. decentralized)
|
||||
|
||||
Kiff.InputName = {'fm1', 'fm2', 'fm3', 'fm4', 'fm5', 'fm6'};
|
||||
Kiff.OutputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||
|
||||
%% Root Locus for decentralized IFF - APA300ML actuator - Effect of joint bending stiffness
|
||||
gains = logspace(-1, 2, 300);
|
||||
|
||||
figure;
|
||||
tiledlayout(1, 1, 'TileSpacing', 'compact', 'Padding', 'None');
|
||||
nexttile();
|
||||
hold on;
|
||||
|
||||
for i = 1:length(Kf)
|
||||
plot(real(pole(G_Kf_apa300ml{i}({"fm1", "fm2", "fm3", "fm4", "fm5", "fm6"}, {"f1", "f2", "f3", "f4", "f5", "f6"}))), imag(pole(G_Kf_apa300ml{i}({"fm1", "fm2", "fm3", "fm4", "fm5", "fm6"}, {"f1", "f2", "f3", "f4", "f5", "f6"}))), 'x', 'color', colors(i,:), ...
|
||||
'DisplayName', sprintf('$k_f = %.0f$ [Nm/rad]', Kf(i)));
|
||||
plot(real(tzero(G_Kf_apa300ml{i}({"fm1", "fm2", "fm3", "fm4", "fm5", "fm6"}, {"f1", "f2", "f3", "f4", "f5", "f6"}))), imag(tzero(G_Kf_apa300ml{i}({"fm1", "fm2", "fm3", "fm4", "fm5", "fm6"}, {"f1", "f2", "f3", "f4", "f5", "f6"}))), 'o', 'color', colors(i,:), ...
|
||||
'HandleVisibility', 'off');
|
||||
|
||||
for g = gains
|
||||
clpoles = pole(feedback(G_Kf_apa300ml{i}({"fm1", "fm2", "fm3", "fm4", "fm5", "fm6"}, {"f1", "f2", "f3", "f4", "f5", "f6"}), g*Kiff, +1));
|
||||
plot(real(clpoles), imag(clpoles), '.', 'color', colors(i,:), ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
xline(0, 'HandleVisibility', 'off'); yline(0, 'HandleVisibility', 'off');
|
||||
hold off;
|
||||
axis equal;
|
||||
xlim(1.4*[-900, 100]); ylim(1.4*[-100, 900]);
|
||||
xticks(1.4*[-900:100:0]);
|
||||
yticks(1.4*[0:100:900]);
|
||||
set(gca, 'XTickLabel',[]); set(gca, 'YTickLabel',[]);
|
||||
xlabel('Real part'); ylabel('Imaginary part');
|
||||
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
|
||||
%% Identify the dynamics for several considered axial stiffnesses
|
||||
% Let's initialize all the stages with default parameters.
|
||||
initializeGround('type', 'rigid');
|
||||
initializeGranite('type', 'rigid');
|
||||
initializeTy('type', 'rigid');
|
||||
initializeRy('type', 'rigid');
|
||||
initializeRz('type', 'rigid');
|
||||
initializeMicroHexapod('type', 'rigid');
|
||||
initializeSample('m', 50);
|
||||
|
||||
initializeSimscapeConfiguration();
|
||||
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, '/Tracking Error'], 1, 'openoutput', [], 'EdL'); io_i = io_i + 1; % Errors in the frame of the struts
|
||||
io(io_i) = linio([mdl, '/NASS'], 3, 'openoutput', [], 'fn'); io_i = io_i + 1; % Force Sensors
|
||||
|
||||
% Effect of bending stiffness
|
||||
Ka = 1e6*[1000, 100, 10, 1]; % [Nm/rad]
|
||||
G_Ka = {zeros(length(Ka), 1)};
|
||||
|
||||
for i = 1:length(Ka)
|
||||
% Limited joint axial compliance
|
||||
initializeSimplifiedNanoHexapod('actuator_type', '1dof', ...
|
||||
'flex_type_F', '2dof_axial', ...
|
||||
'flex_type_M', '4dof', ...
|
||||
'actuator_k', 1e6, ...
|
||||
'actuator_c', 1e1, ...
|
||||
'actuator_kp', 0, ...
|
||||
'actuator_cp', 0, ...
|
||||
'Fsm', 56e-3, ... % APA300ML weight 112g
|
||||
'Msm', 56e-3, ...
|
||||
'Ca_F', 1, ...
|
||||
'Ca_M', 1, ...
|
||||
'Ka_F', Ka(i), ...
|
||||
'Ka_M', Ka(i));
|
||||
|
||||
G_Ka(i) = {linearize(mdl, io)};
|
||||
G_Ka{i}.InputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||
G_Ka{i}.OutputName = {'l1', 'l2', 'l3', 'l4', 'l5', 'l6', 'fm1', 'fm2', 'fm3', 'fm4', 'fm5', 'fm6'};
|
||||
end
|
||||
|
||||
freqs = logspace(1, 4, 1000);
|
||||
|
||||
%% Effect of the flexible joint axial stiffness on the HAC-plant
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
for i = 1:length(Ka)
|
||||
for j = 1:5
|
||||
for k = j+1:6
|
||||
plot(freqs, abs(squeeze(freqresp(G_Ka{i}("l"+k,"f"+j), freqs, 'Hz'))), 'color', [colors(i,:), 0.1], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
end
|
||||
end
|
||||
for i = 1:length(Ka)
|
||||
plot(freqs, abs(squeeze(freqresp(G_Ka{i}("l1","f1"), freqs, 'Hz'))), 'color', colors(i,:), 'DisplayName', sprintf('$k_a = %.0f$ [N/$\\mu$m]', 1e-6*Ka(i)));
|
||||
% for j = 2:6
|
||||
% plot(freqs, abs(squeeze(freqresp(G_Ka{i}("l"+j,"f"+j), freqs, 'Hz'))), 'color', colors(i,:), 'HandleVisibility', 'off');
|
||||
% end
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
ylim([1e-10, 1e-4]);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
for i = 1:length(Ka)
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_Ka{i}(1, 1), freqs, 'Hz')))));
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-200, 20]);
|
||||
yticks([-360:45:360]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
|
||||
%% Effect of the flexible joint axial stiffness on the IFF plant
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
for i = 1:length(Ka)
|
||||
for j = 1:5
|
||||
for k = j+1:6
|
||||
plot(freqs, abs(squeeze(freqresp(G_Ka{i}("fm"+k,"f"+j), freqs, 'Hz'))), 'color', [colors(i,:), 0.1], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
end
|
||||
end
|
||||
for i = 1:length(Ka)
|
||||
plot(freqs, abs(squeeze(freqresp(G_Ka{i}("fm1","f1"), freqs, 'Hz'))), 'color', colors(i,:), 'DisplayName', sprintf('$k_a = %.0f$ [N/$\\mu$m]', 1e-6*Ka(i)));
|
||||
% for j = 2:6
|
||||
% plot(freqs, abs(squeeze(freqresp(G_Ka{i}("fm"+j,"f"+j), freqs, 'Hz'))), 'color', colors(i,:), 'HandleVisibility', 'off');
|
||||
% end
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
|
||||
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
ylim([1e-4, 1e2]);
|
||||
|
||||
ax2 = nexttile();
|
||||
hold on;
|
||||
for i = 1:length(Ka)
|
||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G_Ka{i}("fm1", "f1"), freqs, 'Hz')))));
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-20, 200]);
|
||||
yticks([-360:45:360]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
|
||||
%% Decentalized IFF
|
||||
Kiff = -200 * ... % Gain
|
||||
1/s * ... % LPF: provides integral action
|
||||
eye(6); % Diagonal 6x6 controller (i.e. decentralized)
|
||||
|
||||
Kiff.InputName = {'fm1', 'fm2', 'fm3', 'fm4', 'fm5', 'fm6'};
|
||||
Kiff.OutputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||
|
||||
%% Root Locus for decentralized IFF - 1dof actuator - Effect of joint bending stiffness
|
||||
gains = logspace(-1, 2, 400);
|
||||
|
||||
figure;
|
||||
tiledlayout(1, 1, 'TileSpacing', 'compact', 'Padding', 'None');
|
||||
nexttile();
|
||||
hold on;
|
||||
|
||||
for i = 1:length(Ka)
|
||||
plot(real(pole(G_Ka{i}({"fm1", "fm2", "fm3", "fm4", "fm5", "fm6"}, {"f1", "f2", "f3", "f4", "f5", "f6"}))), imag(pole(G_Ka{i}({"fm1", "fm2", "fm3", "fm4", "fm5", "fm6"}, {"f1", "f2", "f3", "f4", "f5", "f6"}))), 'x', 'color', colors(i,:), ...
|
||||
'DisplayName', sprintf('$k_a = %.0f$ N/$\\mu$m', 1e-6*Ka(i)));
|
||||
plot(real(tzero(G_Ka{i}({"fm1", "fm2", "fm3", "fm4", "fm5", "fm6"}, {"f1", "f2", "f3", "f4", "f5", "f6"}))), imag(tzero(G_Ka{i}({"fm1", "fm2", "fm3", "fm4", "fm5", "fm6"}, {"f1", "f2", "f3", "f4", "f5", "f6"}))), 'o', 'color', colors(i,:), ...
|
||||
'HandleVisibility', 'off');
|
||||
|
||||
for g = gains
|
||||
clpoles = pole(feedback(G_Ka{i}({"fm1", "fm2", "fm3", "fm4", "fm5", "fm6"}, {"f1", "f2", "f3", "f4", "f5", "f6"}), g*Kiff, +1));
|
||||
plot(real(clpoles), imag(clpoles), '.', 'color', colors(i,:), ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
xline(0, 'HandleVisibility', 'off'); yline(0, 'HandleVisibility', 'off');
|
||||
hold off;
|
||||
axis equal;
|
||||
xlim(1.1*[-900, 100]); ylim(1.1*[-100, 900]);
|
||||
xticks(1.1*[-900:100:0]);
|
||||
yticks(1.1*[0:100:900]);
|
||||
set(gca, 'XTickLabel',[]); set(gca, 'YTickLabel',[]);
|
||||
xlabel('Real part'); ylabel('Imaginary part');
|
||||
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
|
||||
%% Compute the damped plants
|
||||
Kiff = -500 * ... % Gain
|
||||
1/(s + 2*pi*0.1) * ... % LPF: provides integral action
|
||||
eye(6); % Diagonal 6x6 controller (i.e. decentralized)
|
||||
|
||||
Kiff.InputName = {'fm1', 'fm2', 'fm3', 'fm4', 'fm5', 'fm6'};
|
||||
Kiff.OutputName = {'u1iff', 'u2iff', 'u3iff', 'u4iff', 'u5iff', 'u6iff'};
|
||||
|
||||
% New damped plant input
|
||||
S1 = sumblk("f1 = u1iff + u1");
|
||||
S2 = sumblk("f2 = u2iff + u2");
|
||||
S3 = sumblk("f3 = u3iff + u3");
|
||||
S4 = sumblk("f4 = u4iff + u4");
|
||||
S5 = sumblk("f5 = u5iff + u5");
|
||||
S6 = sumblk("f6 = u6iff + u6");
|
||||
|
||||
G_Ka_iff = {zeros(1,length(Ka))};
|
||||
for i=1:length(Ka)
|
||||
G_Ka_iff(i) = {connect(G_Ka{i}, Kiff, S1, S2, S3, S4, S5, S6, {'u1', 'u2', 'u3', 'u4', 'u5', 'u6'}, {'l1', 'l2', 'l3', 'l4', 'l5', 'l6'})};
|
||||
end
|
||||
|
||||
%% Interaction Analysis - RGA Number
|
||||
rga = zeros(length(Ka), length(freqs));
|
||||
for i = 1:length(Ka)
|
||||
for j = 1:length(freqs)
|
||||
rga(i,j) = sum(sum(abs(inv(evalfr(G_Ka_iff{i}({"l1", "l2", "l3", "l4", "l5", "l6"}, {"u1", "u2", "u3", "u4", "u5", "u6"}), 1j*2*pi*freqs(j)).').*evalfr(G_Ka_iff{i}({"l1", "l2", "l3", "l4", "l5", "l6"}, {"u1", "u2", "u3", "u4", "u5", "u6"}), 1j*2*pi*freqs(j)) - eye(6))));
|
||||
end
|
||||
end
|
||||
|
||||
%% RGA number for the damped plants - Effect of the flexible joint axial stiffness
|
||||
figure;
|
||||
hold on;
|
||||
for i = 1:length(Ka)
|
||||
plot(freqs, rga(i,:), 'DisplayName', sprintf('$k_a = %.0f$ N/$\\mu$m', 1e-6*Ka(i)))
|
||||
end
|
||||
hold off;
|
||||
xlabel('Frequency [Hz]'); ylabel('RGA number');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylim([0, 10]); xlim([10, 5e3]);
|
||||
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
|
||||
%% Extract stiffness of the joint from the reduced order model
|
||||
% We first extract the stiffness and mass matrices.
|
||||
K = readmatrix('flex025_mat_K.CSV');
|
||||
M = readmatrix('flex025_mat_M.CSV');
|
||||
% Then, we extract the coordinates of the interface nodes.
|
||||
[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('flex025_out_nodes_3D.txt');
|
||||
|
||||
m = 1;
|
||||
|
||||
%% Name of the Simulink File
|
||||
mdl = 'detail_fem_joint';
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/T'], 1, 'openinput'); io_i = io_i + 1; % Forces and Torques
|
||||
io(io_i) = linio([mdl, '/D'], 1, 'openoutput'); io_i = io_i + 1; % Translations and Rotations
|
||||
|
||||
G = linearize(mdl, io);
|
||||
|
||||
% Stiffness extracted from the Simscape model
|
||||
k_a = 1/dcgain(G(3,3)); % Axial stiffness [N/m]
|
||||
k_f = 1/dcgain(G(4,4)); % Bending stiffness [N/m]
|
||||
k_t = 1/dcgain(G(6,6)); % Torsion stiffness [N/m]
|
||||
|
||||
|
||||
% Stiffness extracted from the Stiffness matrix
|
||||
k_s = K(1,1); % shear [N/m]
|
||||
% k_s = K(2,2); % shear [N/m]
|
||||
k_a = K(3,3); % axial [N/m]
|
||||
k_f = K(4,4); % bending [Nm/rad]
|
||||
% k_f = K(5,5); % bending [Nm/rad]
|
||||
k_t = K(6,6); % torsion [Nm/rad]
|
||||
|
||||
%% Compare Dynamics between "Reduced Order" flexible joints and "2-dof and 3-dof" joints
|
||||
% Let's initialize all the stages with default parameters.
|
||||
initializeGround('type', 'rigid');
|
||||
initializeGranite('type', 'rigid');
|
||||
initializeTy('type', 'rigid');
|
||||
initializeRy('type', 'rigid');
|
||||
initializeRz('type', 'rigid');
|
||||
initializeMicroHexapod('type', 'rigid');
|
||||
initializeSample('m', 50);
|
||||
|
||||
initializeSimscapeConfiguration();
|
||||
initializeDisturbances('enable', false);
|
||||
initializeLoggingConfiguration('log', 'none');
|
||||
initializeController('type', 'open-loop');
|
||||
initializeReferences();
|
||||
|
||||
mdl = 'detail_fem_nass';
|
||||
|
||||
% 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, '/Tracking Error'], 1, 'openoutput', [], 'EdL'); io_i = io_i + 1; % Errors in the frame of the struts
|
||||
io(io_i) = linio([mdl, '/NASS'], 3, 'openoutput', [], 'fn'); io_i = io_i + 1; % Force Sensors
|
||||
|
||||
% Fully flexible joints
|
||||
initializeSimplifiedNanoHexapod('actuator_type', 'apa300ml', ...
|
||||
'flex_type_F', 'flexible', ...
|
||||
'flex_type_M', 'flexible', ...
|
||||
'Fsm', 56e-3, ... % APA300ML weight 112g
|
||||
'Msm', 56e-3);
|
||||
|
||||
G_flex = linearize(mdl, io);
|
||||
G_flex.InputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||
G_flex.OutputName = {'l1', 'l2', 'l3', 'l4', 'l5', 'l6', 'fm1', 'fm2', 'fm3', 'fm4', 'fm5', 'fm6'};
|
||||
|
||||
% Flexible joints modelled by 2DoF and 3DoF joints
|
||||
initializeSimplifiedNanoHexapod('actuator_type', 'apa300ml', ...
|
||||
'flex_type_F', '2dof_axial', ...
|
||||
'flex_type_M', '4dof', ...
|
||||
'Kf_F', k_f, ...
|
||||
'Kt_F', k_t, ...
|
||||
'Ka_F', k_a, ...
|
||||
'Kf_M', k_f, ...
|
||||
'Kt_M', k_t, ...
|
||||
'Ka_M', k_a, ...
|
||||
'Cf_F', 1e-2, ...
|
||||
'Ct_F', 1e-2, ...
|
||||
'Ca_F', 1e-2, ...
|
||||
'Cf_M', 1e-2, ...
|
||||
'Ct_M', 1e-2, ...
|
||||
'Ca_M', 1e-2, ...
|
||||
'Fsm', 56e-3, ... % APA300ML weight 112g
|
||||
'Msm', 56e-3);
|
||||
|
||||
G_ideal = linearize(mdl, io);
|
||||
G_ideal.InputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||
G_ideal.OutputName = {'l1', 'l2', 'l3', 'l4', 'l5', 'l6', 'fm1', 'fm2', 'fm3', 'fm4', 'fm5', 'fm6'};
|
||||
|
||||
%% Comparison of the dynamics with joints modelled with FEM and modelled with "ideal joints" - HAC plant
|
||||
freqs = logspace(1, 4, 1000);
|
||||
|
||||
%% Effect of the flexible joint axial stiffness on the HAC-plant
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
for j = 1:5
|
||||
for k = j+1:6
|
||||
plot(freqs, abs(squeeze(freqresp(G_flex("l"+k,"f"+j), freqs, 'Hz'))), 'color', [colors(1,:), 0.1], ...
|
||||
'HandleVisibility', 'off');
|
||||
plot(freqs, abs(squeeze(freqresp(G_ideal("l"+k,"f"+j), freqs, 'Hz'))), 'color', [colors(2,:), 0.1], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(G_flex("l1","f1"), freqs, 'Hz'))), 'color', colors(1,:), 'DisplayName', 'Reduced Order Flexible Joints');
|
||||
plot(freqs, abs(squeeze(freqresp(G_ideal("l1","f1"), freqs, 'Hz'))), 'color', colors(2,:), 'DisplayName', 'Bot: $k_f$, $k_a$, Top: $k_f$, $k_t$, $k_a$');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
ylim([1e-10, 1e-4]);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_flex("l1","f1"), freqs, 'Hz'))));
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_ideal("l1","f1"), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-20, 200]);
|
||||
yticks([-360:45:360]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
%% Effect of the flexible joint axial stiffness on the HAC-plant
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
for j = 1:5
|
||||
for k = j+1:6
|
||||
plot(freqs, abs(squeeze(freqresp(G_flex("fm"+k,"f"+j), freqs, 'Hz'))), 'color', [colors(1,:), 0.1], ...
|
||||
'HandleVisibility', 'off');
|
||||
plot(freqs, abs(squeeze(freqresp(G_ideal("fm"+k,"f"+j), freqs, 'Hz'))), 'color', [colors(2,:), 0.1], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(G_flex("fm1","f1"), freqs, 'Hz'))), 'color', colors(1,:), 'DisplayName', 'Reduced Order Flexible Joints');
|
||||
plot(freqs, abs(squeeze(freqresp(G_ideal("fm1","f1"), freqs, 'Hz'))), 'color', colors(2,:), 'DisplayName', 'Bot: $k_f$, $k_a$, Top: $k_f$, $k_t$, $k_a$');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
|
||||
leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
ylim([1e-5, 1e1]);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_flex("fm1","f1"), freqs, 'Hz'))));
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_ideal("fm1","f1"), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-20, 200]);
|
||||
yticks([-360:45:360]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
Binary file not shown.
Binary file not shown.
BIN
matlab/mat/detail_fem_apa95ml_open_circuit.mat
Normal file
BIN
matlab/mat/detail_fem_apa95ml_open_circuit.mat
Normal file
Binary file not shown.
BIN
matlab/mat/detail_fem_apa95ml_short_circuit.mat
Normal file
BIN
matlab/mat/detail_fem_apa95ml_short_circuit.mat
Normal file
Binary file not shown.
Binary file not shown.
Binary file not shown.
Binary file not shown.
91
matlab/src/extractNodes.m
Normal file
91
matlab/src/extractNodes.m
Normal file
@@ -0,0 +1,91 @@
|
||||
function [int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes(filename)
|
||||
% extractNodes -
|
||||
%
|
||||
% Syntax: [n_xyz, nodes] = extractNodes(filename)
|
||||
%
|
||||
% Inputs:
|
||||
% - filename - relative or absolute path of the file that contains the Matrix
|
||||
%
|
||||
% Outputs:
|
||||
% - n_xyz -
|
||||
% - nodes - table containing the node numbers and corresponding dof of the interfaced DoFs
|
||||
|
||||
arguments
|
||||
filename
|
||||
end
|
||||
|
||||
fid = fopen(filename,'rt');
|
||||
|
||||
if fid == -1
|
||||
error('Error opening the file');
|
||||
end
|
||||
|
||||
n_xyz = []; % Contains nodes coordinates
|
||||
n_i = []; % Contains nodes indices
|
||||
|
||||
n_num = []; % Contains node numbers
|
||||
n_dof = {}; % Contains node directions
|
||||
|
||||
while 1
|
||||
% Read a line
|
||||
nextline = fgetl(fid);
|
||||
|
||||
% End of the file
|
||||
if ~isstr(nextline), break, end
|
||||
|
||||
% Line just before the list of nodes coordinates
|
||||
if contains(nextline, 'NODE') && ...
|
||||
contains(nextline, 'X') && ...
|
||||
contains(nextline, 'Y') && ...
|
||||
contains(nextline, 'Z')
|
||||
|
||||
while 1
|
||||
nextline = fgetl(fid);
|
||||
|
||||
if nextline < 0, break, end
|
||||
|
||||
c = sscanf(nextline, ' %f');
|
||||
|
||||
if isempty(c), break, end
|
||||
|
||||
n_xyz = [n_xyz; c(2:4)'];
|
||||
n_i = [n_i; c(1)];
|
||||
end
|
||||
end
|
||||
|
||||
if nextline < 0, break, end
|
||||
|
||||
% Line just before the list of node DOF
|
||||
if contains(nextline, 'NODE') && ...
|
||||
contains(nextline, 'LABEL')
|
||||
|
||||
while 1
|
||||
nextline = fgetl(fid);
|
||||
|
||||
if nextline < 0, break, end
|
||||
|
||||
c = sscanf(nextline, ' %d %s');
|
||||
|
||||
if isempty(c), break, end
|
||||
|
||||
n_num = [n_num; c(1)];
|
||||
|
||||
n_dof{length(n_dof)+1} = char(c(2:end)');
|
||||
end
|
||||
|
||||
nodes = table(n_num, string(n_dof'), 'VariableNames', {'node_i', 'node_dof'});
|
||||
end
|
||||
|
||||
if nextline < 0, break, end
|
||||
end
|
||||
|
||||
fclose(fid);
|
||||
|
||||
int_i = unique(nodes.('node_i')); % indices of interface nodes
|
||||
|
||||
% Extract XYZ coordinates of only the interface nodes
|
||||
if length(n_xyz) > 0 && length(n_i) > 0
|
||||
int_xyz = n_xyz(logical(sum(n_i.*ones(1, length(int_i)) == int_i', 2)), :);
|
||||
else
|
||||
int_xyz = n_xyz;
|
||||
end
|
||||
166
nass-fem.bib
166
nass-fem.bib
@@ -1,15 +1,15 @@
|
||||
@article{souleille18_concep_activ_mount_space_applic,
|
||||
author = {Souleille, Adrien and Lampert, Thibault and Lafarga, V and
|
||||
Hellegouarch, Sylvain and Rondineau, Alan and Rodrigues,
|
||||
Gon{\c{c}}alo and Collette, Christophe},
|
||||
title = {A Concept of Active Mount for Space Applications},
|
||||
journal = {CEAS Space Journal},
|
||||
volume = 10,
|
||||
number = 2,
|
||||
pages = {157--165},
|
||||
year = 2018,
|
||||
publisher = {Springer},
|
||||
keywords = {parallel robot, iff},
|
||||
@article{mcinroy02_model_desig_flexur_joint_stewar,
|
||||
author = {J.E. McInroy},
|
||||
title = {Modeling and Design of Flexure Jointed Stewart Platforms
|
||||
for Control Purposes},
|
||||
journal = {IEEE/ASME Transactions on Mechatronics},
|
||||
volume = 7,
|
||||
number = 1,
|
||||
pages = {95-99},
|
||||
year = 2002,
|
||||
doi = {10.1109/3516.990892},
|
||||
url = {https://doi.org/10.1109/3516.990892},
|
||||
keywords = {parallel robot, flexure},
|
||||
}
|
||||
|
||||
|
||||
@@ -33,6 +33,15 @@
|
||||
|
||||
|
||||
|
||||
@book{hatch00_vibrat_matlab_ansys,
|
||||
author = {Hatch, Michael R},
|
||||
title = {Vibration simulation using MATLAB and ANSYS},
|
||||
year = 2000,
|
||||
publisher = {CRC Press},
|
||||
}
|
||||
|
||||
|
||||
|
||||
@phdthesis{rankers98_machin,
|
||||
author = {Rankers, Adrian Mathias},
|
||||
keywords = {favorite},
|
||||
@@ -44,15 +53,21 @@
|
||||
|
||||
|
||||
|
||||
@book{hatch00_vibrat_matlab_ansys,
|
||||
author = {Hatch, Michael R},
|
||||
title = {Vibration simulation using MATLAB and ANSYS},
|
||||
year = 2000,
|
||||
publisher = {CRC Press},
|
||||
@article{craig68_coupl_subst_dynam_analy,
|
||||
author = {ROY R. CRAIG and MERVYN C. C. BAMPTON},
|
||||
title = {Coupling of Substructures for Dynamic Analyses.},
|
||||
journal = {AIAA Journal},
|
||||
volume = 6,
|
||||
number = 7,
|
||||
pages = {1313-1319},
|
||||
year = 1968,
|
||||
doi = {10.2514/3.4741},
|
||||
url = {http://dx.doi.org/10.2514/3.4741},
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
@article{claeyssen07_amplif_piezoel_actuat,
|
||||
author = {Frank Claeyssen and R. Le Letty and F. Barillot and O.
|
||||
Sosnicki},
|
||||
@@ -96,6 +111,53 @@
|
||||
|
||||
|
||||
|
||||
@book{pintelon12_system_ident,
|
||||
author = {Rik Pintelon and Johan Schoukens},
|
||||
title = {System Identification : a Frequency Domain Approach},
|
||||
year = 2012,
|
||||
publisher = {Wiley IEEE Press},
|
||||
url = {https://doi.org/10.1002/9781118287422},
|
||||
address = {Hoboken, N.J. Piscataway, NJ},
|
||||
doi = {10.1002/9781118287422},
|
||||
isbn = 9780470640371,
|
||||
}
|
||||
|
||||
|
||||
|
||||
@article{souleille18_concep_activ_mount_space_applic,
|
||||
author = {Souleille, Adrien and Lampert, Thibault and Lafarga, V and
|
||||
Hellegouarch, Sylvain and Rondineau, Alan and Rodrigues,
|
||||
Gon{\c{c}}alo and Collette, Christophe},
|
||||
title = {A Concept of Active Mount for Space Applications},
|
||||
journal = {CEAS Space Journal},
|
||||
volume = 10,
|
||||
number = 2,
|
||||
pages = {157--165},
|
||||
year = 2018,
|
||||
publisher = {Springer},
|
||||
keywords = {parallel robot, iff},
|
||||
}
|
||||
|
||||
|
||||
|
||||
@article{verma20_dynam_stabil_thin_apert_light,
|
||||
author = {Mohit Verma and Adrien Pece and Sylvain Hellegouarch and
|
||||
Jennifer Watchi and Gilles Durand and Simon Chesn{\'e} and
|
||||
Christophe Collette},
|
||||
title = {Dynamic Stabilization of Thin Aperture Light Collector
|
||||
Space Telescope Using Active Rods},
|
||||
journal = {Journal of Astronomical Telescopes, Instruments, and
|
||||
Systems},
|
||||
volume = 6,
|
||||
number = 01,
|
||||
pages = 1,
|
||||
year = 2020,
|
||||
doi = {10.1117/1.jatis.6.1.014002},
|
||||
url = {http://dx.doi.org/10.1117/1.JATIS.6.1.014002},
|
||||
DATE_ADDED = {Thu Apr 3 21:25:20 2025},
|
||||
}
|
||||
|
||||
|
||||
@phdthesis{hanieh03_activ_stewar,
|
||||
author = {Hanieh, Ahmed Abu},
|
||||
keywords = {parallel robot},
|
||||
@@ -107,37 +169,13 @@
|
||||
|
||||
|
||||
|
||||
@article{mcinroy02_model_desig_flexur_joint_stewar,
|
||||
author = {J.E. McInroy},
|
||||
title = {Modeling and Design of Flexure Jointed Stewart Platforms
|
||||
for Control Purposes},
|
||||
journal = {IEEE/ASME Transactions on Mechatronics},
|
||||
volume = 7,
|
||||
number = 1,
|
||||
pages = {95-99},
|
||||
year = 2002,
|
||||
doi = {10.1109/3516.990892},
|
||||
url = {https://doi.org/10.1109/3516.990892},
|
||||
keywords = {parallel robot, flexure},
|
||||
}
|
||||
|
||||
|
||||
|
||||
@article{yang19_dynam_model_decoup_contr_flexib,
|
||||
author = {Yang, XiaoLong and Wu, HongTao and Chen, Bai and Kang,
|
||||
ShengZheng and Cheng, ShiLi},
|
||||
title = {Dynamic Modeling and Decoupled Control of a Flexible
|
||||
Stewart Platform for Vibration Isolation},
|
||||
journal = {Journal of Sound and Vibration},
|
||||
volume = 439,
|
||||
pages = {398-412},
|
||||
year = 2019,
|
||||
doi = {10.1016/j.jsv.2018.10.007},
|
||||
url = {https://doi.org/10.1016/j.jsv.2018.10.007},
|
||||
issn = {0022-460X},
|
||||
keywords = {parallel robot, flexure, decoupled control},
|
||||
month = {Jan},
|
||||
publisher = {Elsevier BV},
|
||||
@book{schmidt20_desig_high_perfor_mechat_third_revis_edition,
|
||||
author = {Schmidt, R Munnig and Schitter, Georg and Rankers, Adrian},
|
||||
title = {The Design of High Performance Mechatronics - Third Revised
|
||||
Edition},
|
||||
year = 2020,
|
||||
publisher = {Ios Press},
|
||||
keywords = {favorite},
|
||||
}
|
||||
|
||||
|
||||
@@ -160,6 +198,25 @@
|
||||
|
||||
|
||||
|
||||
@article{yang19_dynam_model_decoup_contr_flexib,
|
||||
author = {Yang, XiaoLong and Wu, HongTao and Chen, Bai and Kang,
|
||||
ShengZheng and Cheng, ShiLi},
|
||||
title = {Dynamic Modeling and Decoupled Control of a Flexible
|
||||
Stewart Platform for Vibration Isolation},
|
||||
journal = {Journal of Sound and Vibration},
|
||||
volume = 439,
|
||||
pages = {398-412},
|
||||
year = 2019,
|
||||
doi = {10.1016/j.jsv.2018.10.007},
|
||||
url = {https://doi.org/10.1016/j.jsv.2018.10.007},
|
||||
issn = {0022-460X},
|
||||
keywords = {parallel robot, flexure, decoupled control},
|
||||
month = 1,
|
||||
publisher = {Elsevier BV},
|
||||
}
|
||||
|
||||
|
||||
|
||||
@article{du14_piezo_actuat_high_precis_flexib,
|
||||
author = {Zhijiang Du and Ruochong Shi and Wei Dong},
|
||||
title = {A Piezo-Actuated High-Precision Flexible Parallel Pointing
|
||||
@@ -174,3 +231,16 @@
|
||||
keywords = {parallel robot},
|
||||
}
|
||||
|
||||
|
||||
|
||||
@book{preumont18_vibrat_contr_activ_struc_fourt_edition,
|
||||
author = {Andre Preumont},
|
||||
title = {Vibration Control of Active Structures - Fourth Edition},
|
||||
year = 2018,
|
||||
publisher = {Springer International Publishing},
|
||||
url = {https://doi.org/10.1007/978-3-319-72296-2},
|
||||
doi = {10.1007/978-3-319-72296-2},
|
||||
keywords = {favorite, parallel robot},
|
||||
series = {Solid Mechanics and Its Applications},
|
||||
}
|
||||
|
||||
|
||||
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