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|---|---|---|---|
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1c9d20fbba |
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@@ -1,18 +0,0 @@
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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
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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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|
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@@ -1,79 +0,0 @@
|
||||
%% Clear Workspace and Close figures
|
||||
clear; close all; clc;
|
||||
|
||||
%% Intialize Laplace variable
|
||||
s = zpk('s');
|
||||
|
||||
%% Path for functions, data and scripts
|
||||
addpath('./mat/'); % Path for Data
|
||||
addpath('./src/'); % Path for functions
|
||||
addpath('./subsystems/'); % Path for Subsystems Simulink files
|
||||
|
||||
%% Data directory
|
||||
data_dir = './mat/';
|
||||
|
||||
% Simulink Model name
|
||||
mdl = 'nano_hexapod_model';
|
||||
|
||||
%% Colors for the figures
|
||||
colors = colororder;
|
||||
|
||||
%% Frequency Vector [Hz]
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
%% Estimate the errors associated with approximate forward kinematics using the Jacobian matrix
|
||||
stewart = initializeSimplifiedNanoHexapod('H', 100e-3);
|
||||
|
||||
Xrs = logspace(-6, -1, 10); % Wanted X translation of the mobile platform [m]
|
||||
phis = linspace(-pi, pi, 100); % Tested azimutal angles [rad]
|
||||
thetas = linspace(0, pi, 100); % Tested polar angles [rad]
|
||||
|
||||
% Compute the strut exact length for each X-position
|
||||
Xrs_errors = zeros(1, length(Xrs)); % Maximum distance error [m]
|
||||
Rrs_errors = zeros(1, length(Xrs)); % Maximum angular error [rad]
|
||||
for i = 1:length(Xrs)
|
||||
Xrs_error_min = 0;
|
||||
Rrs_error_min = 0;
|
||||
for theta = thetas
|
||||
for phi = phis
|
||||
ix = [sin(theta)*cos(phi); sin(theta)*sin(phi);cos(theta)]; % Unit vector for the displacement direction
|
||||
[~, L_exact] = inverseKinematics(stewart, 'AP', Xrs(i)*ix); % Compute exact strut length for the wanted position
|
||||
Xrs_approx = inv(stewart.geometry.J)*L_exact; % Approximate the position using the Jacobian
|
||||
Xrs_error = norm(Xrs(i)*ix - Xrs_approx(1:3), 2); % Compute the position estimation error
|
||||
Rrs_error = norm(Xrs_approx(4:6), 2); % Compute the angular estimation error
|
||||
if Xrs_error > Xrs_error_min
|
||||
Xrs_error_min = Xrs_error;
|
||||
end
|
||||
if Rrs_error > Rrs_error_min
|
||||
Rrs_error_min = Rrs_error;
|
||||
end
|
||||
end
|
||||
end
|
||||
Xrs_errors(i) = Xrs_error_min;
|
||||
Rrs_errors(i) = Rrs_error_min;
|
||||
end
|
||||
|
||||
%% Errors associated with the use of the Jacobian matrix to solve the forward kinematic problem
|
||||
figure;
|
||||
yyaxis left
|
||||
hold on;
|
||||
plot(1e6*Xrs, 1e9*Xrs_errors, 'DisplayName', '$\epsilon_D$');
|
||||
plot(1e6*Xrs, 1e6*Xrs, '--', 'DisplayName', '$0.1\%$ error');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
xlim([1, 1e4]); ylim([1, 1e4]);
|
||||
xlabel('Motion Stroke');
|
||||
ylabel('Kinematic Errors');
|
||||
xticks([1, 10, 100, 1000, 10000]);
|
||||
yticks([1, 10, 100, 1000, 10000]);
|
||||
xticklabels({'$1\mu m$', '$10\mu m$', '$100\mu m$', '$1mm$', '$10mm$'});
|
||||
yticklabels({'$1nm$', '$10nm$', '$100nm$', '$1\mu m$', '$10\mu m$'});
|
||||
|
||||
yyaxis right
|
||||
plot(1e6*Xrs, 1e9*Rrs_errors, 'DisplayName', '$\epsilon_R$');
|
||||
set(gca, 'YScale', 'log');
|
||||
ylim([1, 1e4]);
|
||||
yticks([1, 10, 100, 1000, 10000]);
|
||||
yticklabels({'$1$nrad', '$10$nrad', '$100$nrad', '$1\mu$rad', '$10\mu$rad'});
|
||||
@@ -1,224 +0,0 @@
|
||||
%% Clear Workspace and Close figures
|
||||
clear; close all; clc;
|
||||
|
||||
%% Intialize Laplace variable
|
||||
s = zpk('s');
|
||||
|
||||
%% Path for functions, data and scripts
|
||||
addpath('./mat/'); % Path for Data
|
||||
addpath('./src/'); % Path for functions
|
||||
addpath('./subsystems/'); % Path for Subsystems Simulink files
|
||||
|
||||
%% Data directory
|
||||
data_dir = './mat/';
|
||||
|
||||
% Simulink Model name
|
||||
mdl = 'nano_hexapod_model';
|
||||
|
||||
%% Colors for the figures
|
||||
colors = colororder;
|
||||
|
||||
%% Frequency Vector [Hz]
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
%% Plant using Analytical Equations
|
||||
% Stewart platform definition
|
||||
k = 1e6; % Actuator stiffness [N/m]
|
||||
c = 1e1; % Actuator damping [N/(m/s)]
|
||||
|
||||
stewart = initializeSimplifiedNanoHexapod(...
|
||||
'Mpm', 1e-3, ...
|
||||
'actuator_type', '1dof', ...
|
||||
'actuator_k', k, ...
|
||||
'actuator_kp', 0, ...
|
||||
'actuator_c', c ...
|
||||
);
|
||||
|
||||
% Payload: Cylinder
|
||||
h = 300e-3; % Height of the cylinder [m]
|
||||
r = 110e-3; % Radius of the cylinder [m]
|
||||
m = 10; % Mass of the payload [kg]
|
||||
initializeSample('type', 'cylindrical', 'm', m, 'H', h, 'R', r);
|
||||
|
||||
% Mass Matrix
|
||||
M = zeros(6,6);
|
||||
M(1,1) = m;
|
||||
M(2,2) = m;
|
||||
M(3,3) = m;
|
||||
M(4,4) = 1/12*m*(3*r^2 + h^2);
|
||||
M(5,5) = 1/12*m*(3*r^2 + h^2);
|
||||
M(6,6) = 1/2*m*r^2;
|
||||
|
||||
% Stiffness and Damping matrices
|
||||
K = k*eye(6);
|
||||
C = c*eye(6);
|
||||
|
||||
% Compute plant in the frame of the struts
|
||||
G_analytical = inv(ss(inv(stewart.geometry.J')*M*inv(stewart.geometry.J)*s^2 + C*s + K));
|
||||
|
||||
% Compare with Simscape model
|
||||
initializeLoggingConfiguration('log', 'none');
|
||||
initializeController('type', 'open-loop');
|
||||
|
||||
% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Inputs [N]
|
||||
io(io_i) = linio([mdl, '/plant'], 2, 'openoutput', [], 'dL'); io_i = io_i + 1; % Encoders [m]
|
||||
|
||||
G_simscape = linearize(mdl, io);
|
||||
G_simscape.InputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||
G_simscape.OutputName = {'dL1', 'dL2', 'dL3', 'dL4', 'dL5', 'dL6'};
|
||||
|
||||
%% Comparison of the analytical transfer functions and the multi-body model
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
for i = 1:6
|
||||
plot(freqs, abs(squeeze(freqresp(G_simscape(i,1), freqs, 'Hz'))), 'color', [colors(i,:), 0.5], 'linewidth', 2.5, ...
|
||||
'DisplayName', sprintf('$l_%i/f_1$ - Multi-Body', i))
|
||||
end
|
||||
for i = 1:6
|
||||
plot(freqs, abs(squeeze(freqresp(G_analytical(i,1), freqs, 'Hz'))), '--', 'color', [colors(i,:)], ...
|
||||
'DisplayName', sprintf('$l_%i/f_1$ - Analytical', i))
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
ylim([1e-9, 1e-4]);
|
||||
leg = legend('location', 'northwest', 'FontSize', 6, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
for i = 1:6
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_simscape(i,1), freqs, 'Hz'))), 'color', [colors(i,:),0.5], 'linewidth', 2.5);
|
||||
end
|
||||
for i = 1:6
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_analytical(i,1), freqs, 'Hz'))), '--', 'color', colors(i,:));
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([freqs(1), freqs(end)]);
|
||||
|
||||
%% Multi-Body model of the Nano-Hexapod
|
||||
% Initialize 1DoF
|
||||
initializeSimplifiedNanoHexapod('flex_type_F', '2dof', 'flex_type_M', '3dof', 'actuator_type', '1dof');
|
||||
initializeSample('type', 'cylindrical', 'm', 10, 'H', 300e-3);
|
||||
initializeLoggingConfiguration('log', 'none');
|
||||
initializeController('type', 'open-loop');
|
||||
|
||||
% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Inputs [N]
|
||||
io(io_i) = linio([mdl, '/plant'], 2, 'openoutput', [], 'dL'); io_i = io_i + 1; % Encoders [m]
|
||||
io(io_i) = linio([mdl, '/plant'], 2, 'openoutput', [], 'fn'); io_i = io_i + 1; % Force Sensors [N]
|
||||
|
||||
% With no payload
|
||||
G = linearize(mdl, io);
|
||||
G.InputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||
G.OutputName = {'dL1', 'dL2', 'dL3', 'dL4', 'dL5', 'dL6', ...
|
||||
'fn1', 'fn2', 'fn3', 'fn4', 'fn5', 'fn6'};
|
||||
|
||||
%% Multi-Body model of the Nano-Hexapod without parallel stiffness
|
||||
% Initialize 1DoF
|
||||
initializeSimplifiedNanoHexapod('flex_type_F', '2dof', 'flex_type_M', '3dof', 'actuator_type', '1dof', 'actuator_kp', 0);
|
||||
|
||||
% With no payload
|
||||
G_no_kp = linearize(mdl, io);
|
||||
G_no_kp.InputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||
G_no_kp.OutputName = {'dL1', 'dL2', 'dL3', 'dL4', 'dL5', 'dL6', ...
|
||||
'fn1', 'fn2', 'fn3', 'fn4', 'fn5', 'fn6'};
|
||||
|
||||
%% Transfer function from actuator force inputs to displacement of each strut
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
for i = 1:5
|
||||
for j = i+1:6
|
||||
plot(freqs, abs(squeeze(freqresp(G(i,j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(G(1,1), freqs, 'Hz'))), 'color', colors(1,:), ...
|
||||
'DisplayName', '$l_i/f_i$')
|
||||
for i = 2:6
|
||||
plot(freqs, abs(squeeze(freqresp(G(i,i), freqs, 'Hz'))), 'color', colors(1,:), ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(G(1,2), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
|
||||
'DisplayName', '$l_i/f_j$')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
ylim([1e-9, 1e-4]);
|
||||
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
for i = 1:6
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G(i,i), freqs, 'Hz'))), 'color', [colors(1,:),0.5]);
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([freqs(1), freqs(end)]);
|
||||
|
||||
%% Transfer function from actuator force inputs to force sensor in each strut
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
for i = 1:5
|
||||
for j = i+1:6
|
||||
plot(freqs, abs(squeeze(freqresp(G(6+i,j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(G(7,1), freqs, 'Hz'))), 'color', colors(1,:), ...
|
||||
'DisplayName', '$f_{ni}/f_i$')
|
||||
plot(freqs, abs(squeeze(freqresp(G_no_kp(7,1), freqs, 'Hz'))), 'color', colors(2,:), ...
|
||||
'DisplayName', '$f_{ni}/f_i$ (no $k_p$)')
|
||||
for i = 2:6
|
||||
plot(freqs, abs(squeeze(freqresp(G(6+i,i), freqs, 'Hz'))), 'color', colors(1,:), ...
|
||||
'HandleVisibility', 'off');
|
||||
plot(freqs, abs(squeeze(freqresp(G_no_kp(6+i,i), freqs, 'Hz'))), 'color', colors(2,:), ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(G(7,2), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
|
||||
'DisplayName', '$f_{ni}/f_j$')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
|
||||
ylim([1e-4, 1e2]);
|
||||
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
for i = 1:6
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G(6+i,i), freqs, 'Hz'))), 'color', colors(1,:));
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_no_kp(6+i,i), freqs, 'Hz'))), 'color', colors(2,:));
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([freqs(1), freqs(end)]);
|
||||
@@ -1,397 +0,0 @@
|
||||
%% Clear Workspace and Close figures
|
||||
clear; close all; clc;
|
||||
|
||||
%% Intialize Laplace variable
|
||||
s = zpk('s');
|
||||
|
||||
%% Path for functions, data and scripts
|
||||
addpath('./mat/'); % Path for Data
|
||||
addpath('./src/'); % Path for functions
|
||||
addpath('./subsystems/'); % Path for Subsystems Simulink files
|
||||
|
||||
%% Data directory
|
||||
data_dir = './mat/';
|
||||
|
||||
% Simulink Model name
|
||||
mdl = 'nano_hexapod_model';
|
||||
|
||||
%% Colors for the figures
|
||||
colors = colororder;
|
||||
|
||||
%% Frequency Vector [Hz]
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
%% Identify plant from actuator forces to external metrology
|
||||
stewart = initializeSimplifiedNanoHexapod();
|
||||
initializeSample('type', 'cylindrical', 'm', 10, 'H', 300e-3);
|
||||
initializeLoggingConfiguration('log', 'none');
|
||||
initializeController('type', 'open-loop');
|
||||
|
||||
% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Inputs [N]
|
||||
io(io_i) = linio([mdl, '/plant'], 1, 'openoutput'); io_i = io_i + 1; % External Metrology [m, rad]
|
||||
|
||||
% With no payload
|
||||
G = linearize(mdl, io);
|
||||
G.InputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||
G.OutputName = {'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'};
|
||||
|
||||
%% Plant in the Cartesian Frame
|
||||
G_cart = G*inv(stewart.geometry.J');
|
||||
G_cart.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
|
||||
|
||||
%% Plant in the frame of the struts
|
||||
G_struts = stewart.geometry.J*G;
|
||||
G_struts.OutputName = {'D1', 'D2', 'D3', 'D4', 'D5', 'D6'};
|
||||
|
||||
%% Bode plot of the plant projected in the frame of the struts
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
for i = 1:5
|
||||
for j = i+1:6
|
||||
plot(freqs, abs(squeeze(freqresp(G_struts(i,j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(G_struts(1,1), freqs, 'Hz'))), 'color', colors(1,:), ...
|
||||
'DisplayName', '$-\epsilon_{\mathcal{L}i}/f_i$')
|
||||
for i = 2:6
|
||||
plot(freqs, abs(squeeze(freqresp(G_struts(i,i), freqs, 'Hz'))), 'color', colors(1,:), ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(G_struts(1,2), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
|
||||
'DisplayName', '$-\epsilon_{\mathcal{L}i}/f_j$')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
ylim([1e-9, 1e-4]);
|
||||
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
for i = 1:6
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_struts(i,i), freqs, 'Hz'))), 'color', [colors(1,:),0.5]);
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([freqs(1), freqs(end)]);
|
||||
|
||||
%% Bode plot of the plant projected in the Cartesian frame
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
for i = 1:5
|
||||
for j = i+1:6
|
||||
plot(freqs, abs(squeeze(freqresp(G_cart(i,j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(G_cart(1,1), freqs, 'Hz'))), 'color', colors(1,:), ...
|
||||
'DisplayName', '$\epsilon_{D_x}/\mathcal{F}_x$ [m/N]')
|
||||
plot(freqs, abs(squeeze(freqresp(G_cart(2,2), freqs, 'Hz'))), 'color', colors(2,:), ...
|
||||
'DisplayName', '$\epsilon_{D_y}/\mathcal{F}_y$ [m/N]')
|
||||
plot(freqs, abs(squeeze(freqresp(G_cart(3,3), freqs, 'Hz'))), 'color', colors(3,:), ...
|
||||
'DisplayName', '$\epsilon_{D_z}/\mathcal{F}_z$ [m/N]')
|
||||
plot(freqs, abs(squeeze(freqresp(G_cart(4,4), freqs, 'Hz'))), 'color', colors(4,:), ...
|
||||
'DisplayName', '$\epsilon_{R_x}/\mathcal{M}_x$ [rad/Nm]')
|
||||
plot(freqs, abs(squeeze(freqresp(G_cart(5,5), freqs, 'Hz'))), 'color', colors(5,:), ...
|
||||
'DisplayName', '$\epsilon_{R_y}/\mathcal{M}_y$ [rad/Nm]')
|
||||
plot(freqs, abs(squeeze(freqresp(G_cart(6,6), freqs, 'Hz'))), 'color', colors(6,:), ...
|
||||
'DisplayName', '$\epsilon_{R_z}/\mathcal{M}_z$ [rad/Nm]')
|
||||
plot(freqs, abs(squeeze(freqresp(G_cart(1,5), freqs, 'Hz'))), 'color', [0, 0, 0, 0.5], ...
|
||||
'DisplayName', 'Coupling')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude'); set(gca, 'XTickLabel',[]);
|
||||
ylim([1e-9, 4e-3]);
|
||||
leg = legend('location', 'southwest', 'FontSize', 7, 'NumColumns', 3);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
for i = 1:6
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_cart(i,i), freqs, 'Hz'))), 'color', colors(i,:));
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([freqs(1), freqs(end)]);
|
||||
|
||||
%% Identify the IFF Plant
|
||||
stewart = initializeSimplifiedNanoHexapod('actuator_kp', 0); % Ignoring parallel stiffness for now
|
||||
initializeSample('type', 'cylindrical', 'm', 10, 'H', 300e-3);
|
||||
initializeLoggingConfiguration('log', 'none');
|
||||
initializeController('type', 'open-loop');
|
||||
|
||||
% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Inputs [N]
|
||||
io(io_i) = linio([mdl, '/plant'], 2, 'openoutput', [], 'fn'); io_i = io_i + 1; % Force Sensors [N]
|
||||
|
||||
% With no payload
|
||||
G_iff = linearize(mdl, io);
|
||||
G_iff.InputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||
G_iff.OutputName = {'fm1', 'fm2', 'fm3', 'fm4', 'fm5', 'fm6'};
|
||||
|
||||
%% IFF Controller Design
|
||||
Kiff = -500/s * ... % Gain
|
||||
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 plot of the Decentralized IFF Control
|
||||
gains = logspace(-2, 1, 200);
|
||||
|
||||
figure;
|
||||
tiledlayout(1, 1, 'TileSpacing', 'compact', 'Padding', 'None');
|
||||
nexttile();
|
||||
hold on;
|
||||
plot(real(pole(G_iff)), imag(pole(G_iff)), 'x', 'color', colors(1,:), ...
|
||||
'DisplayName', '$g = 0$');
|
||||
plot(real(tzero(G_iff)), imag(tzero(G_iff)), 'o', 'color', colors(1,:), ...
|
||||
'HandleVisibility', 'off');
|
||||
|
||||
for g = gains
|
||||
clpoles = pole(feedback(G_iff, g*Kiff, +1));
|
||||
plot(real(clpoles), imag(clpoles), '.', 'color', colors(1,:), ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
|
||||
% Optimal gain
|
||||
clpoles = pole(feedback(G_iff, Kiff, +1));
|
||||
plot(real(clpoles), imag(clpoles), 'kx', ...
|
||||
'DisplayName', '$g_{opt}$');
|
||||
hold off;
|
||||
axis equal;
|
||||
xlim([-600, 50]); ylim([-50, 600]);
|
||||
xticks([-600:100:0]);
|
||||
yticks([0:100:600]);
|
||||
set(gca, 'XTickLabel',[]); set(gca, 'YTickLabel',[]);
|
||||
xlabel('Real part'); ylabel('Imaginary part');
|
||||
|
||||
%% Loop gain for the Decentralized IFF
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(-G_iff(1,1)*Kiff(1,1), freqs, 'Hz'))));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Loop Gain'); set(gca, 'XTickLabel',[]);
|
||||
ylim([1e-2, 1e2]);
|
||||
% leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
% leg.ItemTokenSize(1) = 15;
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(-G_iff(1,1)*Kiff(1,1), 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([1, 1e3]);
|
||||
|
||||
%% Identify the IFF Plant
|
||||
initializeController('type', 'iff');
|
||||
|
||||
% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/Controller'], 1, 'input'); io_i = io_i + 1; % Actuator Inputs [N]
|
||||
io(io_i) = linio([mdl, '/plant'], 1, 'openoutput'); io_i = io_i + 1; % External Metrology [m,rad]
|
||||
|
||||
% With no payload
|
||||
G_hac = linearize(mdl, io);
|
||||
G_hac.InputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||
G_hac.OutputName = {'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'};
|
||||
|
||||
%% Plant in the frame of the struts
|
||||
G_hac_struts = stewart.geometry.J*G_hac;
|
||||
G_hac_struts.OutputName = {'D1', 'D2', 'D3', 'D4', 'D5', 'D6'};
|
||||
|
||||
%% Bode plot of the plant projected in the frame of the struts
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
for i = 1:5
|
||||
for j = i+1:6
|
||||
plot(freqs, abs(squeeze(freqresp(G_struts(i,j), freqs, 'Hz'))), 'color', [0,0,0,0.1], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(G_struts(1,1), freqs, 'Hz'))), 'color', colors(1,:), ...
|
||||
'DisplayName', '$-\epsilon_{\mathcal{L}i}/f_i$')
|
||||
for i = 2:6
|
||||
plot(freqs, abs(squeeze(freqresp(G_struts(i,i), freqs, 'Hz'))), 'color', colors(1,:), ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(G_struts(1,2), freqs, 'Hz'))), 'color', [0,0,0,0.1], ...
|
||||
'DisplayName', '$-\epsilon_{\mathcal{L}i}/f_j$')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
ylim([1e-9, 1e-4]);
|
||||
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
for i = 1:6
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_struts(i,i), freqs, 'Hz'))), 'color', colors(1,:));
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([freqs(1), freqs(end)]);
|
||||
|
||||
%% Bode plot of the plant projected in the frame of the struts
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
for i = 1:5
|
||||
for j = i+1:6
|
||||
plot(freqs, abs(squeeze(freqresp(G_hac_struts(i,j), freqs, 'Hz'))), 'color', [0,0,0,0.1], ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(G_struts(1,1), freqs, 'Hz'))), 'color', [colors(1,:), 0.2], ...
|
||||
'DisplayName', '$-\epsilon_{\mathcal{L}i}/f_i$')
|
||||
plot(freqs, abs(squeeze(freqresp(G_hac_struts(1,1), freqs, 'Hz'))), 'color', colors(2,:), ...
|
||||
'DisplayName', '$-\epsilon_{\mathcal{L}i}/f_i^\prime$')
|
||||
for i = 2:6
|
||||
plot(freqs, abs(squeeze(freqresp(G_struts(i,i), freqs, 'Hz'))), 'color', [colors(1,:), 0.2], ...
|
||||
'HandleVisibility', 'off');
|
||||
plot(freqs, abs(squeeze(freqresp(G_hac_struts(i,i), freqs, 'Hz'))), 'color', colors(2,:), ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(G_hac_struts(1,2), freqs, 'Hz'))), 'color', [0,0,0,0.1], ...
|
||||
'DisplayName', '$-\epsilon_{\mathcal{L}i}/f_j^\prime$')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
ylim([1e-9, 1e-4]);
|
||||
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
for i = 1:6
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_struts(i,i), freqs, 'Hz'))), 'color', [colors(1,:), 0.2]);
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_hac_struts(i,i), freqs, 'Hz'))), 'color', colors(2,:));
|
||||
end
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([freqs(1), freqs(end)]);
|
||||
|
||||
%% High Authority Controller - Mid Stiffness Nano-Hexapod
|
||||
% Wanted crossover
|
||||
wc = 2*pi*20; % [rad/s]
|
||||
|
||||
% Integrator
|
||||
H_int = wc/s;
|
||||
|
||||
% Lead to increase phase margin
|
||||
a = 2; % Amount of phase lead / width of the phase lead / high frequency gain
|
||||
H_lead = 1/sqrt(a)*(1 + s/(wc/sqrt(a)))/(1 + s/(wc*sqrt(a)));
|
||||
|
||||
% Low Pass filter to increase robustness
|
||||
H_lpf = 1/(1 + s/2/pi/200);
|
||||
|
||||
% Gain to have unitary crossover at 5Hz
|
||||
H_gain = 1./abs(evalfr(G_hac_struts(1, 1), 1j*wc));
|
||||
|
||||
% Decentralized HAC
|
||||
Khac = H_gain * ... % Gain
|
||||
H_int * ... % Integrator
|
||||
H_lpf * ... % Low Pass filter
|
||||
eye(6); % 6x6 Diagonal
|
||||
|
||||
%% Plot of the eigenvalues of L in the complex plane
|
||||
Ldet = zeros(6, length(freqs));
|
||||
Lmimo = squeeze(freqresp(G_hac_struts*Khac, freqs, 'Hz'));
|
||||
for i_f = 2:length(freqs)
|
||||
Ldet(:, i_f) = eig(squeeze(Lmimo(:,:,i_f)));
|
||||
end
|
||||
mod_margin = min(min(abs(Ldet + ones(size(Ldet)))));
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
for i = 1:6
|
||||
plot(real(squeeze(Ldet(i,:))), imag(squeeze(Ldet(i,:))), ...
|
||||
'.', 'color', colors(1, :), ...
|
||||
'HandleVisibility', 'off');
|
||||
plot(real(squeeze(Ldet(i,:))), -imag(squeeze(Ldet(i,:))), ...
|
||||
'.', 'color', colors(1, :), ...
|
||||
'HandleVisibility', 'off');
|
||||
end
|
||||
plot(-1, 0, 'kx', 'HandleVisibility', 'off');
|
||||
patch(-1 + mod_margin*cos([0:0.1:2*pi+0.1]), mod_margin*sin([0:0.1:2*pi+0.1]), colors(5,:), 'linestyle', '--', 'EdgeColor','black', 'FaceAlpha', 0.5, 'HandleVisibility', 'off');
|
||||
text(-1,0.1, 'Robustness', 'FontSize', 8, 'horizontalalignment', 'center')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'lin'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Real Part'); ylabel('Imaginary Part');
|
||||
axis square
|
||||
xlim([-1.8, 0.2]); ylim([-1, 1]);
|
||||
|
||||
%% Loop gain for the Decentralized HAC_IFF
|
||||
i_fb = find(abs(squeeze(freqresp(G_hac_struts(1,1)*Khac(1,1), freqs, 'Hz')))<1, 1);
|
||||
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
patch([freqs(1:i_fb), freqs(i_fb), freqs(1)], [abs(squeeze(freqresp(G_hac_struts(1,1)*Khac(1,1), [freqs(1:i_fb)], 'Hz'))); 1; 1], colors(5,:), 'EdgeColor','none', 'FaceAlpha', 0.5)
|
||||
plot(freqs, abs(squeeze(freqresp(G_hac_struts(1,1)*Khac(1,1), freqs, 'Hz'))));
|
||||
text(1.2,2.5,{'Disturbance', 'rejection'}, 'FontSize', 8)
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Loop Gain'); set(gca, 'XTickLabel',[]);
|
||||
ylim([1e-2, 1e2]);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_hac_struts(1,1)*Khac(1,1), 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([1, 1e3]);
|
||||
@@ -29,16 +29,13 @@ fprintf('ACTUATORS:\n')
|
||||
if stewart.actuators.type == 1
|
||||
fprintf('- The actuators are modelled as 1DoF.\n')
|
||||
fprintf('- The Stiffness and Damping of each actuators is:\n')
|
||||
fprintf('\t k = %.0e [N/m] \t c = %.0e [N/(m/s)]\n', stewart.actuators.k(1), stewart.actuators.c(1))
|
||||
if stewart.actuators.kp > 0
|
||||
fprintf('\t Added parallel stiffness: kp = %.0e [N/m] \t c = %.0e [N/(m/s)]\n', stewart.actuators.kp(1))
|
||||
end
|
||||
fprintf('\t k = %.0e [N/m] \t c = %.0e [N/(m/s)]\n', stewart.actuators.K(1), stewart.actuators.C(1))
|
||||
elseif stewart.actuators.type == 2
|
||||
fprintf('- The actuators are modelled as 2DoF (APA).\n')
|
||||
fprintf('- The vertical stiffness and damping contribution of the piezoelectric stack is:\n')
|
||||
fprintf('\t ka = %.0e [N/m] \t ca = %.0e [N/(m/s)]\n', stewart.actuators.ka(1), stewart.actuators.ca(1))
|
||||
fprintf('\t ka = %.0e [N/m] \t ca = %.0e [N/(m/s)]\n', stewart.actuators.Ka(1), stewart.actuators.Ca(1))
|
||||
fprintf('- Vertical stiffness when the piezoelectric stack is removed is:\n')
|
||||
fprintf('\t kr = %.0e [N/m] \t cr = %.0e [N/(m/s)]\n', stewart.actuators.kr(1), stewart.actuators.cr(1))
|
||||
fprintf('\t kr = %.0e [N/m] \t cr = %.0e [N/(m/s)]\n', stewart.actuators.Kr(1), stewart.actuators.Cr(1))
|
||||
elseif stewart.actuators.type == 3
|
||||
fprintf('- The actuators are modelled with a flexible element (FEM).\n')
|
||||
end
|
||||
|
||||
@@ -19,10 +19,10 @@ function [stewart] = generateGeneralConfiguration(stewart, args)
|
||||
|
||||
arguments
|
||||
stewart
|
||||
args.FH (1,1) double {mustBeNumeric, mustBeNonnegative} = 15e-3
|
||||
args.FH (1,1) double {mustBeNumeric, mustBePositive} = 15e-3
|
||||
args.FR (1,1) double {mustBeNumeric, mustBePositive} = 115e-3;
|
||||
args.FTh (6,1) double {mustBeNumeric} = [-10, 10, 120-10, 120+10, 240-10, 240+10]*(pi/180);
|
||||
args.MH (1,1) double {mustBeNumeric, mustBeNonnegative} = 15e-3
|
||||
args.MH (1,1) double {mustBeNumeric, mustBePositive} = 15e-3
|
||||
args.MR (1,1) double {mustBeNumeric, mustBePositive} = 90e-3;
|
||||
args.MTh (6,1) double {mustBeNumeric} = [-60+10, 60-10, 60+10, 180-10, 180+10, -60-10]*(pi/180);
|
||||
end
|
||||
|
||||
@@ -1,7 +1,7 @@
|
||||
function [] = initializeController(args)
|
||||
|
||||
arguments
|
||||
args.type char {mustBeMember(args.type,{'open-loop', 'iff'})} = 'open-loop'
|
||||
args.type char {mustBeMember(args.type,{'open-loop', 'iff', 'dvf', 'hac-dvf', 'ref-track-L', 'ref-track-iff-L', 'cascade-hac-lac', 'hac-iff', 'stabilizing'})} = 'open-loop'
|
||||
end
|
||||
|
||||
controller = struct();
|
||||
@@ -10,9 +10,30 @@ function [] = initializeController(args)
|
||||
case 'open-loop'
|
||||
controller.type = 1;
|
||||
controller.name = 'Open-Loop';
|
||||
case 'iff'
|
||||
case 'dvf'
|
||||
controller.type = 2;
|
||||
controller.name = 'Decentralized Direct Velocity Feedback';
|
||||
case 'iff'
|
||||
controller.type = 3;
|
||||
controller.name = 'Decentralized Integral Force Feedback';
|
||||
case 'hac-dvf'
|
||||
controller.type = 4;
|
||||
controller.name = 'HAC-DVF';
|
||||
case 'ref-track-L'
|
||||
controller.type = 5;
|
||||
controller.name = 'Reference Tracking in the frame of the legs';
|
||||
case 'ref-track-iff-L'
|
||||
controller.type = 6;
|
||||
controller.name = 'Reference Tracking in the frame of the legs + IFF';
|
||||
case 'cascade-hac-lac'
|
||||
controller.type = 7;
|
||||
controller.name = 'Cascade Control + HAC-LAC';
|
||||
case 'hac-iff'
|
||||
controller.type = 8;
|
||||
controller.name = 'HAC-IFF';
|
||||
case 'stabilizing'
|
||||
controller.type = 9;
|
||||
controller.name = 'Stabilizing Controller';
|
||||
end
|
||||
|
||||
if exist('./mat', 'dir')
|
||||
|
||||
@@ -5,20 +5,18 @@ function [nano_hexapod] = initializeSimplifiedNanoHexapod(args)
|
||||
args.H (1,1) double {mustBeNumeric, mustBePositive} = 95e-3 % Height of the nano-hexapod [m]
|
||||
args.MO_B (1,1) double {mustBeNumeric} = 150e-3 % Height of {B} w.r.t. {M} [m]
|
||||
%% generateGeneralConfiguration
|
||||
args.FH (1,1) double {mustBeNumeric, mustBeNonnegative} = 15e-3 % Height of fixed joints [m]
|
||||
args.FH (1,1) double {mustBeNumeric, mustBePositive} = 20e-3 % Height of fixed joints [m]
|
||||
args.FR (1,1) double {mustBeNumeric, mustBePositive} = 120e-3 % Radius of fixed joints [m]
|
||||
args.FTh (6,1) double {mustBeNumeric} = [220, 320, 340, 80, 100, 200]*(pi/180) % Angles of fixed joints [rad]
|
||||
args.MH (1,1) double {mustBeNumeric, mustBeNonnegative} = 15e-3 % Height of mobile joints [m]
|
||||
args.MH (1,1) double {mustBeNumeric, mustBePositive} = 20e-3 % Height of mobile joints [m]
|
||||
args.MR (1,1) double {mustBeNumeric, mustBePositive} = 110e-3 % Radius of mobile joints [m]
|
||||
args.MTh (6,1) double {mustBeNumeric} = [255, 285, 15, 45, 135, 165]*(pi/180) % Angles of fixed joints [rad]
|
||||
%% Actuators
|
||||
args.actuator_type char {mustBeMember(args.actuator_type,{'1dof', '2dof', 'flexible'})} = '1dof'
|
||||
args.actuator_k (1,1) double {mustBeNumeric, mustBePositive} = 1e6
|
||||
args.actuator_kp (1,1) double {mustBeNumeric, mustBeNonnegative} = 1e4
|
||||
args.actuator_k (1,1) double {mustBeNumeric, mustBePositive} = 380000
|
||||
args.actuator_ke (1,1) double {mustBeNumeric, mustBePositive} = 4952605
|
||||
args.actuator_ka (1,1) double {mustBeNumeric, mustBePositive} = 2476302
|
||||
args.actuator_c (1,1) double {mustBeNumeric, mustBePositive} = 50
|
||||
args.actuator_cp (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.actuator_c (1,1) double {mustBeNumeric, mustBePositive} = 5
|
||||
args.actuator_ce (1,1) double {mustBeNumeric, mustBePositive} = 100
|
||||
args.actuator_ca (1,1) double {mustBeNumeric, mustBePositive} = 50
|
||||
%% initializeCylindricalPlatforms
|
||||
@@ -78,11 +76,9 @@ function [nano_hexapod] = initializeSimplifiedNanoHexapod(args)
|
||||
stewart = initializeStrutDynamics(stewart, ...
|
||||
'type', args.actuator_type, ...
|
||||
'k', args.actuator_k, ...
|
||||
'kp', args.actuator_kp, ...
|
||||
'ke', args.actuator_ke, ...
|
||||
'ka', args.actuator_ka, ...
|
||||
'c', args.actuator_c, ...
|
||||
'cp', args.actuator_cp, ...
|
||||
'ce', args.actuator_ce, ...
|
||||
'ca', args.actuator_ca);
|
||||
|
||||
|
||||
@@ -18,11 +18,9 @@ function [stewart] = initializeStrutDynamics(stewart, args)
|
||||
stewart
|
||||
args.type char {mustBeMember(args.type,{'1dof', '2dof', 'flexible'})} = '1dof'
|
||||
args.k (1,1) double {mustBeNumeric, mustBeNonnegative} = 20e6
|
||||
args.kp (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.ke (1,1) double {mustBeNumeric, mustBeNonnegative} = 5e6
|
||||
args.ka (1,1) double {mustBeNumeric, mustBeNonnegative} = 60e6
|
||||
args.c (1,1) double {mustBeNumeric, mustBeNonnegative} = 2e1
|
||||
args.cp (1,1) double {mustBeNumeric, mustBeNonnegative} = 0
|
||||
args.ce (1,1) double {mustBeNumeric, mustBeNonnegative} = 1e6
|
||||
args.ca (1,1) double {mustBeNumeric, mustBeNonnegative} = 10
|
||||
|
||||
@@ -42,10 +40,6 @@ function [stewart] = initializeStrutDynamics(stewart, args)
|
||||
stewart.actuators.k = args.k;
|
||||
stewart.actuators.c = args.c;
|
||||
|
||||
% Parallel stiffness
|
||||
stewart.actuators.kp = args.kp;
|
||||
stewart.actuators.cp = args.cp;
|
||||
|
||||
stewart.actuators.ka = args.ka;
|
||||
stewart.actuators.ca = args.ca;
|
||||
|
||||
|
||||
@@ -12,8 +12,5 @@
|
||||
\setabbreviationstyle[acronym]{long-short}
|
||||
\setglossarystyle{long-name-desc}
|
||||
|
||||
\usepackage{amssymb}
|
||||
\usepackage{amsmath}
|
||||
|
||||
\makeindex
|
||||
\makeglossaries
|
||||
@@ -10,329 +10,6 @@
|
||||
|
||||
|
||||
|
||||
@article{nazaretski15_pushin_limit,
|
||||
author = {E. Nazaretski and K. Lauer and H. Yan and N. Bouet and J.
|
||||
Zhou and R. Conley and X. Huang and W. Xu and M. Lu and K.
|
||||
Gofron and S. Kalbfleisch and U. Wagner and C. Rau and Y. S.
|
||||
Chu},
|
||||
title = {Pushing the Limits: an Instrument for Hard X-Ray Imaging
|
||||
Below 20 Nm},
|
||||
journal = {Journal of Synchrotron Radiation},
|
||||
volume = 22,
|
||||
number = 2,
|
||||
pages = {336-341},
|
||||
year = 2015,
|
||||
doi = {10.1107/s1600577514025715},
|
||||
url = {https://doi.org/10.1107/s1600577514025715},
|
||||
keywords = {nass},
|
||||
}
|
||||
|
||||
|
||||
|
||||
@inproceedings{geraldes23_sapot_carnaub_sirius_lnls,
|
||||
author = {Renan R. Geraldes and Gabriel B. Z. L. Moreno and Francesco
|
||||
R. Lena and Erik O. Pereira and Matheus H. S. da Silva and
|
||||
Gabriel G. Bas{\'i}lio and Pedro P. R. Proen{\c{c}}a and
|
||||
Rodrigo C. Gomes and Cassiano S. N. C. Bueno and Sergio A. L.
|
||||
Luiz and Artur C. Pinto and Bernd C. Meyer and Douglas Galante
|
||||
and Carlos A. P{\'e}rez and Verônica C. Teixeira and Leonardo
|
||||
M. Kofukuda and Anna P. S. Sotero and Theo A. M. Ruijl and
|
||||
Walter Aarden and Piet Peters and Maryn Wijnhoven and Helio C.
|
||||
N. Tolentino},
|
||||
title = {The high-dynamic cryogenic sample stage for
|
||||
SAPOTI/CARNA{\'U}BA at Sirius/LNLS},
|
||||
booktitle = {PROCEEDINGS OF THE 15TH INTERNATIONAL CONFERENCE ON X-RAY
|
||||
MICROSCOPY - XRM2022},
|
||||
year = 2023,
|
||||
pages = {nil},
|
||||
doi = {10.1063/5.0168438},
|
||||
url = {http://dx.doi.org/10.1063/5.0168438},
|
||||
DATE_ADDED = {Thu May 2 18:09:04 2024},
|
||||
month = {-},
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
@article{villar18_nanop_esrf_id16a_nano_imagin_beaml,
|
||||
author = {F. Villar and L. Andre and R. Baker and S. Bohic and J. C.
|
||||
da Silva and C. Guilloud and O. Hignette and J. Meyer and A.
|
||||
Pacureanu and M. Perez and M. Salome and P. van der Linden and
|
||||
Y. Yang and P. Cloetens},
|
||||
title = {Nanopositioning for the Esrf Id16a Nano-Imaging Beamline},
|
||||
journal = {Synchrotron Radiation News},
|
||||
volume = 31,
|
||||
number = 5,
|
||||
pages = {9-14},
|
||||
year = 2018,
|
||||
doi = {10.1080/08940886.2018.1506234},
|
||||
url = {http://dx.doi.org/10.1080/08940886.2018.1506234},
|
||||
keywords = {esrf},
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
@article{schropp20_ptynam,
|
||||
author = {Andreas Schropp and Ralph D{\"o}hrmann and Stephan Botta
|
||||
and Dennis Br{\"u}ckner and Maik Kahnt and Mikhail
|
||||
Lyubomirskiy and Christina Ossig and Maria Scholz and Martin
|
||||
Seyrich and Michael E. Stuckelberger and Patrik Wiljes and
|
||||
Felix Wittwer and Jan Garrevoet and Gerald Falkenberg and
|
||||
Yakub Fam and Thomas L. Sheppard and Jan-Dierk Grunwaldt and
|
||||
Christian G. Schroer},
|
||||
title = {Ptynami: Ptychographic Nano-Analytical Microscope},
|
||||
journal = {Journal of Applied Crystallography},
|
||||
volume = 53,
|
||||
number = 4,
|
||||
pages = {957-971},
|
||||
year = 2020,
|
||||
doi = {10.1107/s1600576720008420},
|
||||
url = {http://dx.doi.org/10.1107/s1600576720008420},
|
||||
DATE_ADDED = {Thu May 2 16:01:03 2024},
|
||||
}
|
||||
|
||||
|
||||
|
||||
@inproceedings{schroer17_ptynam,
|
||||
author = {Christian G. Schroer and Martin Seyrich and Maik Kahnt and
|
||||
Stephan Botta and Ralph D{\"o}hrmann and Gerald Falkenberg and
|
||||
Jan Garrevoet and Mikhail Lyubomirskiy and Maria Scholz and
|
||||
Andreas Schropp and Felix Wittwer},
|
||||
title = {PtyNAMi: Ptychographic Nano-Analytical Microscope at PETRA
|
||||
III: interferometrically tracking positions for 3D x-ray
|
||||
scanning microscopy using a ball-lens retroreflector},
|
||||
booktitle = {X-Ray Nanoimaging: Instruments and Methods III},
|
||||
year = 2017,
|
||||
doi = {10.1117/12.2273710},
|
||||
url = {https://doi.org/10.1117/12.2273710},
|
||||
keywords = {nass, metrology},
|
||||
month = 9,
|
||||
}
|
||||
|
||||
|
||||
|
||||
@article{holler17_omny_pin_versat_sampl_holder,
|
||||
author = {M. Holler and J. Raabe and R. Wepf and S. H. Shahmoradian
|
||||
and A. Diaz and B. Sarafimov and T. Lachat and H. Walther and
|
||||
M. Vitins},
|
||||
title = {Omny Pin-A Versatile Sample Holder for Tomographic
|
||||
Measurements At Room and Cryogenic Temperatures},
|
||||
journal = {Review of Scientific Instruments},
|
||||
volume = 88,
|
||||
number = 11,
|
||||
pages = 113701,
|
||||
year = 2017,
|
||||
doi = {10.1063/1.4996092},
|
||||
url = {https://doi.org/10.1063/1.4996092},
|
||||
keywords = {nass},
|
||||
}
|
||||
|
||||
|
||||
|
||||
@article{holler18_omny_tomog_nano_cryo_stage,
|
||||
author = {M. Holler and J. Raabe and A. Diaz and M. Guizar-Sicairos
|
||||
and R. Wepf and M. Odstrcil and F. R. Shaik and V. Panneels
|
||||
and A. Menzel and B. Sarafimov and S. Maag and X. Wang and V.
|
||||
Thominet and H. Walther and T. Lachat and M. Vitins and O.
|
||||
Bunk},
|
||||
title = {Omny-A Tomography Nano Cryo Stage},
|
||||
journal = {Review of Scientific Instruments},
|
||||
volume = 89,
|
||||
number = 4,
|
||||
pages = 043706,
|
||||
year = 2018,
|
||||
doi = {10.1063/1.5020247},
|
||||
url = {https://doi.org/10.1063/1.5020247},
|
||||
keywords = {nass},
|
||||
}
|
||||
|
||||
|
||||
|
||||
@article{stankevic17_inter_charac_rotat_stages_x_ray_nanot,
|
||||
author = {Tomas Stankevic and Christer Engblom and Florent Langlois
|
||||
and Filipe Alves and Alain Lestrade and Nicolas Jobert and
|
||||
Gilles Cauchon and Ulrich Vogt and Stefan Kubsky},
|
||||
title = {Interferometric Characterization of Rotation Stages for
|
||||
X-Ray Nanotomography},
|
||||
journal = {Review of Scientific Instruments},
|
||||
volume = 88,
|
||||
number = 5,
|
||||
pages = 053703,
|
||||
year = 2017,
|
||||
doi = {10.1063/1.4983405},
|
||||
url = {https://doi.org/10.1063/1.4983405},
|
||||
keywords = {nass, metrology},
|
||||
}
|
||||
|
||||
|
||||
|
||||
@inproceedings{engblom18_nanop_resul,
|
||||
author = {C. Engblom and others},
|
||||
title = {Nanoprobe Results: Metrology \& Control in Stacked
|
||||
Closed-Loop Systems},
|
||||
booktitle = {Proc. of International Conference on Accelerator and Large
|
||||
Experimental Control Systems (ICALEPCS'17)},
|
||||
year = 2018,
|
||||
doi = {10.18429/JACoW-ICALEPCS2017-WEAPL04},
|
||||
url = {https://doi.org/10.18429/JACoW-ICALEPCS2017-WEAPL04},
|
||||
isbn = {978-3-95450-193-9},
|
||||
month = {Jan.},
|
||||
publisher = {JACoW},
|
||||
keywords = {nass},
|
||||
}
|
||||
|
||||
|
||||
|
||||
@article{nazaretski22_new_kirkp_baez_based_scann,
|
||||
author = {E. Nazaretski and D. S. Coburn and W. Xu and J. Ma and H.
|
||||
Xu and R. Smith and X. Huang and Y. Yang and L. Huang and M.
|
||||
Idir and A. Kiss and Y. S. Chu},
|
||||
title = {A New Kirkpatrick-Baez-Based Scanning Microscope for the
|
||||
Submicron Resolution X-Ray Spectroscopy (SRX) Beamline At
|
||||
Nsls-Ii},
|
||||
journal = {Journal of Synchrotron Radiation},
|
||||
volume = 29,
|
||||
number = 5,
|
||||
pages = {1284-1291},
|
||||
year = 2022,
|
||||
doi = {10.1107/s1600577522007056},
|
||||
url = {http://dx.doi.org/10.1107/s1600577522007056},
|
||||
DATE_ADDED = {Thu May 2 16:33:47 2024},
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
@article{kelly22_delta_robot_long_travel_nano,
|
||||
author = {Jon Kelly and Andrew Male and Nicholas Rubies and David
|
||||
Mahoney and Jessica M. Walker and Miguel A. Gomez-Gonzalez and
|
||||
Guy Wilkin and Julia E. Parker and Paul D. Quinn},
|
||||
title = {The Delta Robot-A Long Travel Nano-Positioning Stage for
|
||||
Scanning X-Ray Microscopy},
|
||||
journal = {Review of Scientific Instruments},
|
||||
volume = 93,
|
||||
number = 4,
|
||||
pages = {nil},
|
||||
year = 2022,
|
||||
doi = {10.1063/5.0084806},
|
||||
url = {http://dx.doi.org/10.1063/5.0084806},
|
||||
DATE_ADDED = {Thu May 2 20:27:54 2024},
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
@inproceedings{dehaeze18_sampl_stabil_for_tomog_exper,
|
||||
author = {Thomas Dehaeze and M. Magnin Mattenet and Christophe
|
||||
Collette},
|
||||
title = {Sample Stabilization For Tomography Experiments In Presence
|
||||
Of Large Plant Uncertainty},
|
||||
booktitle = {MEDSI'18},
|
||||
year = 2018,
|
||||
number = 10,
|
||||
pages = {153--157},
|
||||
doi = {10.18429/JACoW-MEDSI2018-WEOAMA02},
|
||||
url = {https://doi.org/10.18429/JACoW-MEDSI2018-WEOAMA02},
|
||||
address = {Geneva, Switzerland},
|
||||
isbn = {978-3-95450-207-3},
|
||||
keywords = {nass, esrf},
|
||||
language = {english},
|
||||
month = {Dec},
|
||||
publisher = {JACoW Publishing},
|
||||
series = {Mechanical Engineering Design of Synchrotron Radiation
|
||||
Equipment and Instrumentation},
|
||||
venue = {Paris, France},
|
||||
}
|
||||
|
||||
|
||||
|
||||
@inproceedings{dehaeze21_mechat_approac_devel_nano_activ_stabil_system,
|
||||
author = {Dehaeze, T. and Bonnefoy, J. and Collette, C.},
|
||||
title = {Mechatronics Approach for the Development of a
|
||||
Nano-Active-Stabilization-System},
|
||||
booktitle = {MEDSI'20},
|
||||
year = 2021,
|
||||
language = {english},
|
||||
publisher = {JACoW Publishing},
|
||||
series = {Mechanical Engineering Design of Synchrotron Radiation
|
||||
Equipment and Instrumentation},
|
||||
venue = {Chicago, USA},
|
||||
keywords = {nass, esrf},
|
||||
}
|
||||
|
||||
|
||||
|
||||
@article{dong07_desig_precis_compl_paral_posit,
|
||||
author = {W. Dong and L.N. Sun and Z.J. Du},
|
||||
title = {Design of a Precision Compliant Parallel Positioner Driven
|
||||
By Dual Piezoelectric Actuators},
|
||||
journal = {Sensors and Actuators A: Physical},
|
||||
volume = 135,
|
||||
number = 1,
|
||||
pages = {250-256},
|
||||
year = 2007,
|
||||
doi = {10.1016/j.sna.2006.07.011},
|
||||
url = {https://doi.org/10.1016/j.sna.2006.07.011},
|
||||
keywords = {parallel robot, flexure},
|
||||
}
|
||||
|
||||
|
||||
|
||||
@article{shen19_dynam_analy_flexur_nanop_stage,
|
||||
author = {Yiping Shen and Xin Luo and Songlai Wang and Xuejun Li},
|
||||
title = {Dynamic Analysis of a 5‐dof Flexure‐based Nanopositioning
|
||||
Stage},
|
||||
journal = {Mathematical Problems in Engineering},
|
||||
volume = 2019,
|
||||
number = 1,
|
||||
pages = {nil},
|
||||
year = 2019,
|
||||
doi = {10.1155/2019/8501583},
|
||||
url = {http://dx.doi.org/10.1155/2019/8501583},
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
@article{kenton12_desig_contr_three_axis_serial,
|
||||
author = {Brian J. Kenton and Kam K. Leang},
|
||||
title = {Design and Control of a Three-Axis Serial-Kinematic
|
||||
High-Bandwidth Nanopositioner},
|
||||
journal = {IEEE/ASME Transactions on Mechatronics},
|
||||
volume = 17,
|
||||
number = 2,
|
||||
pages = {356-369},
|
||||
year = 2012,
|
||||
doi = {10.1109/tmech.2011.2105499},
|
||||
url = {http://dx.doi.org/10.1109/TMECH.2011.2105499},
|
||||
}
|
||||
|
||||
|
||||
@inproceedings{abu02_stiff_soft_stewar_platf_activ,
|
||||
author = {Abu Hanieh, Ahmed and Horodinca, Mihaita and Preumont,
|
||||
Andre},
|
||||
title = {Stiff and Soft Stewart Platforms for Active Damping and
|
||||
Active Isolation of Vibrations},
|
||||
booktitle = {Actuator 2002, 8th International Conference on New
|
||||
Actuators},
|
||||
year = 2002,
|
||||
keywords = {parallel robot},
|
||||
}
|
||||
|
||||
|
||||
|
||||
@phdthesis{hanieh03_activ_stewar,
|
||||
author = {Hanieh, Ahmed Abu},
|
||||
keywords = {parallel robot},
|
||||
school = {Universit{\'e} Libre de Bruxelles, Brussels, Belgium},
|
||||
title = {Active isolation and damping of vibrations via Stewart
|
||||
platform},
|
||||
year = 2003,
|
||||
}
|
||||
|
||||
|
||||
|
||||
@article{preumont07_six_axis_singl_stage_activ,
|
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author = {A. Preumont and M. Horodinca and I. Romanescu and B. de
|
||||
Marneffe and M. Avraam and A. Deraemaeker and F. Bossens and
|
||||
@@ -351,102 +28,14 @@
|
||||
|
||||
|
||||
|
||||
@article{furutani04_nanom_cuttin_machin_using_stewar,
|
||||
author = {Katsushi Furutani and Michio Suzuki and Ryusei Kudoh},
|
||||
title = {Nanometre-Cutting Machine Using a Stewart-Platform Parallel
|
||||
Mechanism},
|
||||
journal = {Measurement Science and Technology},
|
||||
volume = 15,
|
||||
number = 2,
|
||||
pages = {467-474},
|
||||
year = 2004,
|
||||
doi = {10.1088/0957-0233/15/2/022},
|
||||
url = {https://doi.org/10.1088/0957-0233/15/2/022},
|
||||
keywords = {parallel robot, cubic configuration},
|
||||
}
|
||||
|
||||
|
||||
|
||||
@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},
|
||||
}
|
||||
|
||||
|
||||
|
||||
@article{stewart65_platf_with_six_degrees_freed,
|
||||
author = {Stewart, Doug},
|
||||
title = {A Platform With Six Degrees of Freedom},
|
||||
journal = {Proceedings of the institution of mechanical engineers},
|
||||
volume = 180,
|
||||
number = 1,
|
||||
pages = {371--386},
|
||||
year = 1965,
|
||||
publisher = {Sage Publications Sage UK: London, England},
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
@article{afzali-far16_inert_matrix_hexap_strut_joint_space,
|
||||
author = {Afzali-Far, Behrouz and Per Lidstr{\"o}m},
|
||||
title = {On the Inertia Matrix of Hexapod Struts in the Joint-Space},
|
||||
journal = {To be submitted},
|
||||
year = 2016,
|
||||
keywords = {parallel robot},
|
||||
}
|
||||
|
||||
|
||||
|
||||
@article{chen04_decoup_contr_flexur_joint_hexap,
|
||||
author = {Y. Chen and J.E. McInroy},
|
||||
title = {Decoupled Control of Flexure-Jointed Hexapods Using
|
||||
Estimated Joint-Space Mass-Inertia Matrix},
|
||||
journal = {IEEE Transactions on Control Systems Technology},
|
||||
volume = 12,
|
||||
number = 3,
|
||||
pages = {413-421},
|
||||
year = 2004,
|
||||
doi = {10.1109/tcst.2004.824339},
|
||||
url = {https://doi.org/10.1109/tcst.2004.824339},
|
||||
keywords = {parallel robot},
|
||||
}
|
||||
|
||||
|
||||
|
||||
@article{mcinroy00_desig_contr_flexur_joint_hexap,
|
||||
author = {J.E. McInroy and J.C. Hamann},
|
||||
title = {Design and Control of Flexure Jointed Hexapods},
|
||||
journal = {IEEE Transactions on Robotics and Automation},
|
||||
volume = 16,
|
||||
number = 4,
|
||||
pages = {372-381},
|
||||
year = 2000,
|
||||
doi = {10.1109/70.864229},
|
||||
url = {https://doi.org/10.1109/70.864229},
|
||||
keywords = {parallel robot},
|
||||
}
|
||||
|
||||
|
||||
|
||||
@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},
|
||||
@book{skogestad07_multiv_feedb_contr,
|
||||
author = {Skogestad, Sigurd and Postlethwaite, Ian},
|
||||
title = {Multivariable Feedback Control: Analysis and Design -
|
||||
Second Edition},
|
||||
year = 2007,
|
||||
publisher = {John Wiley},
|
||||
isbn = 978-0470011683,
|
||||
keywords = {favorite},
|
||||
}
|
||||
|
||||
|
||||
@@ -463,15 +52,3 @@
|
||||
year = 2008,
|
||||
}
|
||||
|
||||
|
||||
|
||||
@book{skogestad07_multiv_feedb_contr,
|
||||
author = {Skogestad, Sigurd and Postlethwaite, Ian},
|
||||
title = {Multivariable Feedback Control: Analysis and Design -
|
||||
Second Edition},
|
||||
year = 2007,
|
||||
publisher = {John Wiley},
|
||||
isbn = 978-0470011683,
|
||||
keywords = {favorite},
|
||||
}
|
||||
|
||||