302 lines
10 KiB
Mathematica
302 lines
10 KiB
Mathematica
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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simulinkproject('../');
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% Coupling between the actuators and sensors - Cubic Architecture
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% Let's generate a Cubic architecture where the cube's center and the frames $\{A\}$ and $\{B\}$ are coincident.
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H = 200e-3; % height of the Stewart platform [m]
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MO_B = -10e-3; % Position {B} with respect to {M} [m]
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Hc = 2.5*H; % Size of the useful part of the cube [m]
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FOc = H + MO_B; % Center of the cube with respect to {F}
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stewart = initializeStewartPlatform();
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stewart = initializeFramesPositions(stewart, 'H', H, 'MO_B', MO_B);
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stewart = generateCubicConfiguration(stewart, 'Hc', Hc, 'FOc', FOc, 'FHa', 25e-3, 'MHb', 25e-3);
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stewart = computeJointsPose(stewart);
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stewart = initializeStrutDynamics(stewart, 'K', 1e6*ones(6,1), 'C', 1e1*ones(6,1));
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stewart = initializeJointDynamics(stewart, 'type_F', 'universal', 'type_M', 'spherical');
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stewart = computeJacobian(stewart);
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stewart = initializeStewartPose(stewart);
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stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 1.2*max(vecnorm(stewart.platform_F.Fa)), ...
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'Mpm', 10, ...
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'Mph', 20e-3, ...
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'Mpr', 1.2*max(vecnorm(stewart.platform_M.Mb)));
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stewart = initializeCylindricalStruts(stewart, 'Fsm', 1e-3, 'Msm', 1e-3);
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stewart = initializeInertialSensor(stewart);
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% No flexibility below the Stewart platform and no payload.
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ground = initializeGround('type', 'none');
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payload = initializePayload('type', 'none');
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displayArchitecture(stewart, 'labels', false, 'view', 'all');
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% #+name: fig:stewart_architecture_coupling_struts_cubic
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% #+caption: Geometry of the generated Stewart platform ([[./figs/stewart_architecture_coupling_struts_cubic.png][png]], [[./figs/stewart_architecture_coupling_struts_cubic.pdf][pdf]])
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% [[file:figs/stewart_architecture_coupling_struts_cubic.png]]
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% And we identify the dynamics from the actuator forces $\tau_{i}$ to the relative motion sensors $\delta \mathcal{L}_{i}$ (Figure [[fig:coupling_struts_relative_sensor_cubic]]) and to the force sensors $\tau_{m,i}$ (Figure [[fig:coupling_struts_force_sensor_cubic]]).
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open('stewart_platform_model.slx')
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%% Options for Linearized
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options = linearizeOptions;
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options.SampleTime = 0;
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%% Name of the Simulink File
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mdl = 'stewart_platform_model';
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%% Input/Output definition
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clear io; io_i = 1;
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io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
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io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'dLm'); io_i = io_i + 1; % Relative Displacement Outputs [m]
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%% Run the linearization
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G = linearize(mdl, io, options);
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G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
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G.OutputName = {'Dm1', 'Dm2', 'Dm3', 'Dm4', 'Dm5', 'Dm6'};
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freqs = logspace(1, 3, 1000);
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figure;
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ax1 = subplot(2, 1, 1);
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hold on;
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for i = 1:6
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for j = i+1:6
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plot(freqs, abs(squeeze(freqresp(G(i, j), freqs, 'Hz'))), 'k-');
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end
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end
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set(gca,'ColorOrderIndex',1);
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plot(freqs, abs(squeeze(freqresp(G(1, 1), freqs, 'Hz'))));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
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ax3 = subplot(2, 1, 2);
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hold on;
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for i = 1:6
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for j = i+1:6
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p2 = plot(freqs, 180/pi*angle(squeeze(freqresp(G(i, j), freqs, 'Hz'))), 'k-');
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end
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end
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set(gca,'ColorOrderIndex',1);
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p1 = plot(freqs, 180/pi*angle(squeeze(freqresp(G(1, 1), freqs, 'Hz'))));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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legend([p1, p2], {'$L_i/\tau_i$', '$L_i/\tau_j$'})
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linkaxes([ax1,ax2],'x');
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% #+name: fig:coupling_struts_relative_sensor_cubic
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% #+caption: Dynamics from the force actuators to the relative motion sensors ([[./figs/coupling_struts_relative_sensor_cubic.png][png]], [[./figs/coupling_struts_relative_sensor_cubic.pdf][pdf]])
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% [[file:figs/coupling_struts_relative_sensor_cubic.png]]
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%% Input/Output definition
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clear io; io_i = 1;
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io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
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io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'Taum'); io_i = io_i + 1; % Force Sensor Outputs [N]
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%% Run the linearization
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G = linearize(mdl, io, options);
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G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
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G.OutputName = {'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6'};
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freqs = logspace(1, 3, 500);
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figure;
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ax1 = subplot(2, 1, 1);
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hold on;
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for i = 1:6
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for j = i+1:6
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plot(freqs, abs(squeeze(freqresp(G(i, j), freqs, 'Hz'))), 'k-');
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end
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end
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set(gca,'ColorOrderIndex',1);
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plot(freqs, abs(squeeze(freqresp(G(1, 1), freqs, 'Hz'))));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
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ax3 = subplot(2, 1, 2);
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hold on;
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for i = 1:6
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for j = i+1:6
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p2 = plot(freqs, 180/pi*angle(squeeze(freqresp(G(i, j), freqs, 'Hz'))), 'k-');
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end
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end
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set(gca,'ColorOrderIndex',1);
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p1 = plot(freqs, 180/pi*angle(squeeze(freqresp(G(1, 1), freqs, 'Hz'))));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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legend([p1, p2], {'$F_{m,i}/\tau_i$', '$F_{m,i}/\tau_j$'})
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linkaxes([ax1,ax2],'x');
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% Coupling between the actuators and sensors - Non-Cubic Architecture
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% Now we generate a Stewart platform which is not cubic but with approximately the same size as the previous cubic architecture.
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H = 200e-3; % height of the Stewart platform [m]
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MO_B = -10e-3; % Position {B} with respect to {M} [m]
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stewart = initializeStewartPlatform();
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stewart = initializeFramesPositions(stewart, 'H', H, 'MO_B', MO_B);
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stewart = generateGeneralConfiguration(stewart, 'FR', 250e-3, 'MR', 150e-3);
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stewart = computeJointsPose(stewart);
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stewart = initializeStrutDynamics(stewart, 'K', 1e6*ones(6,1), 'C', 1e1*ones(6,1));
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stewart = initializeJointDynamics(stewart, 'type_F', 'universal', 'type_M', 'spherical');
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stewart = computeJacobian(stewart);
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stewart = initializeStewartPose(stewart);
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stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 1.2*max(vecnorm(stewart.platform_F.Fa)), ...
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'Mpm', 10, ...
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'Mph', 20e-3, ...
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'Mpr', 1.2*max(vecnorm(stewart.platform_M.Mb)));
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stewart = initializeCylindricalStruts(stewart, 'Fsm', 1e-3, 'Msm', 1e-3);
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stewart = initializeInertialSensor(stewart);
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% No flexibility below the Stewart platform and no payload.
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ground = initializeGround('type', 'none');
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payload = initializePayload('type', 'none');
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displayArchitecture(stewart, 'labels', false, 'view', 'all');
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% #+name: fig:stewart_architecture_coupling_struts_non_cubic
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% #+caption: Geometry of the generated Stewart platform ([[./figs/stewart_architecture_coupling_struts_non_cubic.png][png]], [[./figs/stewart_architecture_coupling_struts_non_cubic.pdf][pdf]])
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% [[file:figs/stewart_architecture_coupling_struts_non_cubic.png]]
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% And we identify the dynamics from the actuator forces $\tau_{i}$ to the relative motion sensors $\delta \mathcal{L}_{i}$ (Figure [[fig:coupling_struts_relative_sensor_non_cubic]]) and to the force sensors $\tau_{m,i}$ (Figure [[fig:coupling_struts_force_sensor_non_cubic]]).
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open('stewart_platform_model.slx')
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%% Options for Linearized
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options = linearizeOptions;
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options.SampleTime = 0;
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%% Name of the Simulink File
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mdl = 'stewart_platform_model';
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%% Input/Output definition
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clear io; io_i = 1;
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io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
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io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'dLm'); io_i = io_i + 1; % Relative Displacement Outputs [m]
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%% Run the linearization
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G = linearize(mdl, io, options);
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G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
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G.OutputName = {'Dm1', 'Dm2', 'Dm3', 'Dm4', 'Dm5', 'Dm6'};
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freqs = logspace(1, 3, 1000);
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figure;
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ax1 = subplot(2, 1, 1);
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hold on;
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for i = 1:6
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for j = i+1:6
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plot(freqs, abs(squeeze(freqresp(G(i, j), freqs, 'Hz'))), 'k-');
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end
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end
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set(gca,'ColorOrderIndex',1);
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plot(freqs, abs(squeeze(freqresp(G(1, 1), freqs, 'Hz'))));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
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ax3 = subplot(2, 1, 2);
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hold on;
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for i = 1:6
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for j = i+1:6
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p2 = plot(freqs, 180/pi*angle(squeeze(freqresp(G(i, j), freqs, 'Hz'))), 'k-');
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end
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end
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set(gca,'ColorOrderIndex',1);
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p1 = plot(freqs, 180/pi*angle(squeeze(freqresp(G(1, 1), freqs, 'Hz'))));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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legend([p1, p2], {'$L_i/\tau_i$', '$L_i/\tau_j$'})
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linkaxes([ax1,ax2],'x');
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% #+name: fig:coupling_struts_relative_sensor_non_cubic
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% #+caption: Dynamics from the force actuators to the relative motion sensors ([[./figs/coupling_struts_relative_sensor_non_cubic.png][png]], [[./figs/coupling_struts_relative_sensor_non_cubic.pdf][pdf]])
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% [[file:figs/coupling_struts_relative_sensor_non_cubic.png]]
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%% Input/Output definition
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clear io; io_i = 1;
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io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
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io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'Taum'); io_i = io_i + 1; % Force Sensor Outputs [N]
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%% Run the linearization
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G = linearize(mdl, io, options);
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G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
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G.OutputName = {'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6'};
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freqs = logspace(1, 3, 500);
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figure;
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ax1 = subplot(2, 1, 1);
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hold on;
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for i = 1:6
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for j = i+1:6
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plot(freqs, abs(squeeze(freqresp(G(i, j), freqs, 'Hz'))), 'k-');
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end
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end
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set(gca,'ColorOrderIndex',1);
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plot(freqs, abs(squeeze(freqresp(G(1, 1), freqs, 'Hz'))));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
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ax3 = subplot(2, 1, 2);
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hold on;
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for i = 1:6
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for j = i+1:6
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p2 = plot(freqs, 180/pi*angle(squeeze(freqresp(G(i, j), freqs, 'Hz'))), 'k-');
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end
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end
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set(gca,'ColorOrderIndex',1);
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p1 = plot(freqs, 180/pi*angle(squeeze(freqresp(G(1, 1), freqs, 'Hz'))));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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legend([p1, p2], {'$F_{m,i}/\tau_i$', '$F_{m,i}/\tau_j$'})
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linkaxes([ax1,ax2],'x');
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