Rework - New simscape file
This commit is contained in:
@@ -38,8 +38,9 @@
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#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
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:END:
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* Some tests
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** Matlab Init :noexport:ignore:
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* Compare external forces and forces applied by the actuators
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** Introduction :ignore:
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** Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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@@ -52,57 +53,43 @@
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simulinkproject('../');
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#+end_src
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** Simscape Model
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#+begin_src matlab
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open('stewart_platform_dynamics.slx')
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open('stewart_platform_model.slx')
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#+end_src
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** test
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** Comparison with fixed support
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#+begin_src matlab
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stewart = initializeStewartPlatform();
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stewart = initializeFramesPositions(stewart);
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stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
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stewart = generateGeneralConfiguration(stewart);
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stewart = computeJointsPose(stewart);
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stewart = initializeStrutDynamics(stewart);
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stewart = initializeJointDynamics(stewart, 'type_F', 'universal_p', 'type_M', 'spherical_p');
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stewart = initializeCylindricalPlatforms(stewart);
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stewart = initializeCylindricalStruts(stewart);
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stewart = computeJacobian(stewart);
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stewart = initializeStewartPose(stewart);
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stewart = initializeInertialSensor(stewart, 'type', 'none');
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#+end_src
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Estimation of the transfer function from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}$:
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#+begin_src matlab
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ground = initializeGround('type', 'none');
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payload = initializePayload('type', 'none');
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#+end_src
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Estimation of the transfer function from $\bm{\tau}$ to $\mathcal{\bm{X}}$:
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#+begin_src matlab
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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_dynamics';
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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, '/F'], 1, 'openinput'); io_i = io_i + 1;
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io(io_i) = linio([mdl, '/X'], 1, 'openoutput'); io_i = io_i + 1;
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%% Run the linearization
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G = linearize(mdl, io, options);
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G.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
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G.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
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#+end_src
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#+begin_src matlab
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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_dynamics';
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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, '/J-T'], 1, 'openinput'); io_i = io_i + 1;
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io(io_i) = linio([mdl, '/X'], 1, 'openoutput'); io_i = 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, '/Relative Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Position/Orientation of {B} w.r.t. {A}
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%% Run the linearization
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G = linearize(mdl, io, options);
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@@ -111,26 +98,16 @@ Estimation of the transfer function from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}
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#+end_src
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#+begin_src matlab
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G_cart = minreal(G*inv(stewart.J'));
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G_cart.InputName = {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz'};
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Gc = minreal(G*inv(stewart.kinematics.J'));
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Gc.InputName = {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz'};
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#+end_src
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Estimation of the transfer function from $\bm{\mathcal{F}}_{\text{ext}}$ to $\mathcal{\bm{X}}$:
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#+begin_src matlab
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figure; bode(G, G_cart)
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#+end_src
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#+begin_src matlab
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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_dynamics';
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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, '/Fext'], 1, 'openinput'); io_i = io_i + 1;
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io(io_i) = linio([mdl, '/X'], 1, 'openoutput'); io_i = io_i + 1;
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io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'F_ext'); io_i = io_i + 1; % External forces/torques applied on {B}
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io(io_i) = linio([mdl, '/Relative Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Position/Orientation of {B} w.r.t. {A}
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%% Run the linearization
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Gd = linearize(mdl, io, options);
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@@ -138,60 +115,70 @@ Estimation of the transfer function from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}
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Gd.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
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#+end_src
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#+begin_src matlab
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freqs = logspace(0, 3, 1000);
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#+begin_src matlab :exports none
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freqs = logspace(1, 4, 1000);
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figure;
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bode(Gd, G)
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ax1 = subplot(2, 1, 1);
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hold on;
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plot(freqs, abs(squeeze(freqresp(Gc(1,1), freqs, 'Hz'))), '-');
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plot(freqs, abs(squeeze(freqresp(Gd(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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ax2 = subplot(2, 1, 2);
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hold on;
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gc(1,1), freqs, 'Hz'))), '-');
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gd(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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linkaxes([ax1,ax2],'x');
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#+end_src
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** Compare external forces and forces applied by the actuators
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Initialization of the Stewart platform.
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** Comparison with a flexible support
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We redo the identification for when the Stewart platform is on a flexible support.
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#+begin_src matlab
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stewart = initializeStewartPlatform();
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stewart = initializeFramesPositions(stewart);
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stewart = generateGeneralConfiguration(stewart);
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stewart = computeJointsPose(stewart);
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stewart = initializeStrutDynamics(stewart);
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stewart = initializeCylindricalPlatforms(stewart);
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stewart = initializeCylindricalStruts(stewart);
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stewart = computeJacobian(stewart);
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stewart = initializeStewartPose(stewart);
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ground = initializeGround('type', 'flexible');
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#+end_src
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Estimation of the transfer function from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}$:
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Estimation of the transfer function from $\bm{\tau}$ to $\mathcal{\bm{X}}$:
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#+begin_src matlab
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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_dynamics';
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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, '/F'], 1, 'openinput'); io_i = io_i + 1;
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io(io_i) = linio([mdl, '/X'], 1, 'openoutput'); io_i = 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, '/Relative Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Position/Orientation of {B} w.r.t. {A}
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%% Run the linearization
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G = linearize(mdl, io, options);
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G.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
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G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
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G.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
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#+end_src
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Estimation of the transfer function from $\mathcal{\bm{F}}_{d}$ to $\mathcal{\bm{X}}$:
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#+begin_src matlab
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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_dynamics';
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Gc = minreal(G*inv(stewart.kinematics.J'));
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Gc.InputName = {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz'};
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#+end_src
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Estimation of the transfer function from $\bm{\mathcal{F}}_{\text{ext}}$ to $\mathcal{\bm{X}}$:
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#+begin_src matlab
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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, '/Fext'], 1, 'openinput'); io_i = io_i + 1;
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io(io_i) = linio([mdl, '/X'], 1, 'openoutput'); io_i = io_i + 1;
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io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'F_ext'); io_i = io_i + 1; % External forces/torques applied on {B}
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io(io_i) = linio([mdl, '/Relative Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Position/Orientation of {B} w.r.t. {A}
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%% Run the linearization
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Gd = linearize(mdl, io, options);
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@@ -199,30 +186,75 @@ Estimation of the transfer function from $\mathcal{\bm{F}}_{d}$ to $\mathcal{\bm
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Gd.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
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#+end_src
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Comparison of the two transfer function matrices.
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#+begin_src matlab
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freqs = logspace(0, 4, 1000);
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#+begin_src matlab :exports none
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freqs = logspace(1, 4, 1000);
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figure;
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bode(Gd, G, freqs)
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ax1 = subplot(2, 1, 1);
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hold on;
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plot(freqs, abs(squeeze(freqresp(Gc(1,1), freqs, 'Hz'))), '-');
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plot(freqs, abs(squeeze(freqresp(Gd(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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ax2 = subplot(2, 1, 2);
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hold on;
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gc(1,1), freqs, 'Hz'))), '-');
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gd(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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linkaxes([ax1,ax2],'x');
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#+end_src
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** Conclusion
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#+begin_important
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Seems quite similar.
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The transfer function from forces/torques applied by the actuators on the payload $\bm{\mathcal{F}} = \bm{J}^T \bm{\tau}$ to the pose of the mobile platform $\bm{\mathcal{X}}$ is the same as the transfer function from external forces/torques to $\bm{\mathcal{X}}$ as long as the Stewart platform's base is fixed.
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#+end_important
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** Comparison of the static transfer function and the Compliance matrix
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* Comparison of the static transfer function and the Compliance matrix
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** Introduction :ignore:
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** Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init>>
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#+end_src
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#+begin_src matlab
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simulinkproject('../');
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#+end_src
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#+begin_src matlab
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open('stewart_platform_model.slx')
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#+end_src
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** Analysis
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Initialization of the Stewart platform.
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#+begin_src matlab
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stewart = initializeStewartPlatform();
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stewart = initializeFramesPositions(stewart);
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stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
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stewart = generateGeneralConfiguration(stewart);
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stewart = computeJointsPose(stewart);
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stewart = initializeStrutDynamics(stewart);
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stewart = initializeJointDynamics(stewart, 'type_F', 'universal_p', 'type_M', 'spherical_p');
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stewart = initializeCylindricalPlatforms(stewart);
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stewart = initializeCylindricalStruts(stewart);
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stewart = computeJacobian(stewart);
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stewart = initializeStewartPose(stewart);
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stewart = initializeInertialSensor(stewart, 'type', 'none');
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#+end_src
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#+begin_src matlab
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ground = initializeGround('type', 'none');
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payload = initializePayload('type', 'none');
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#+end_src
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Estimation of the transfer function from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}$:
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@@ -232,88 +264,56 @@ Estimation of the transfer function from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}
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options.SampleTime = 0;
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%% Name of the Simulink File
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mdl = 'stewart_platform_dynamics';
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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, '/F'], 1, 'openinput'); io_i = io_i + 1;
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io(io_i) = linio([mdl, '/X'], 1, 'openoutput'); io_i = io_i + 1;
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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, '/Relative Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Position/Orientation of {B} w.r.t. {A}
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%% Run the linearization
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G = linearize(mdl, io, options);
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G.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
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G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
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G.OutputName = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
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#+end_src
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#+begin_src matlab
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Gc = minreal(G*inv(stewart.kinematics.J'));
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Gc.InputName = {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz'};
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#+end_src
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Let's first look at the low frequency transfer function matrix from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}$.
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#+begin_src matlab :exports results :results value table replace :tangle no
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data2orgtable(real(freqresp(G, 0.1)), {}, {}, ' %.1e ');
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data2orgtable(real(freqresp(Gd, 0.1)), {}, {}, ' %.1e ');
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#+end_src
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#+RESULTS:
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| 2.0e-06 | -9.1e-19 | -5.3e-12 | 7.3e-18 | 1.7e-05 | 1.3e-18 |
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| -1.7e-18 | 2.0e-06 | 8.6e-19 | -1.7e-05 | -1.5e-17 | 6.7e-12 |
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| 3.6e-13 | 3.2e-19 | 5.0e-07 | -2.5e-18 | 8.1e-12 | -1.5e-19 |
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| 1.0e-17 | -1.7e-05 | -5.0e-18 | 1.9e-04 | 9.1e-17 | -3.5e-11 |
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| 1.7e-05 | -6.9e-19 | -5.3e-11 | 6.9e-18 | 1.9e-04 | 4.8e-18 |
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| -3.5e-18 | -4.5e-12 | 1.5e-18 | 7.1e-11 | -3.4e-17 | 4.6e-05 |
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| 4.7e-08 | -7.2e-19 | 5.0e-18 | -8.9e-18 | 3.2e-07 | 9.9e-18 |
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| 4.7e-18 | 4.7e-08 | -5.7e-18 | -3.2e-07 | -1.6e-17 | -1.7e-17 |
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| 3.3e-18 | -6.3e-18 | 2.1e-08 | 4.4e-17 | 6.6e-18 | 7.4e-18 |
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| -3.2e-17 | -3.2e-07 | 6.2e-18 | 5.2e-06 | -3.5e-16 | 6.3e-17 |
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| 3.2e-07 | 2.7e-17 | 4.8e-17 | -4.5e-16 | 5.2e-06 | -1.2e-19 |
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| 4.0e-17 | -9.5e-17 | 8.4e-18 | 4.3e-16 | 5.8e-16 | 1.7e-06 |
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And now at the Compliance matrix.
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#+begin_src matlab :exports results :results value table replace :tangle no
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data2orgtable(stewart.C, {}, {}, ' %.1e ');
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data2orgtable(stewart.kinematics.C, {}, {}, ' %.1e ');
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#+end_src
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#+RESULTS:
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| 2.0e-06 | 2.9e-22 | 2.8e-22 | -3.2e-21 | 1.7e-05 | 1.5e-37 |
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| -2.1e-22 | 2.0e-06 | -1.8e-23 | -1.7e-05 | -2.3e-21 | 1.1e-22 |
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| 3.1e-22 | -1.6e-23 | 5.0e-07 | 1.7e-22 | 2.2e-21 | -8.1e-39 |
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| 2.1e-21 | -1.7e-05 | 2.0e-22 | 1.9e-04 | 2.3e-20 | -8.7e-21 |
|
||||
| 1.7e-05 | 2.5e-21 | 2.0e-21 | -2.8e-20 | 1.9e-04 | 1.3e-36 |
|
||||
| 3.7e-23 | 3.1e-22 | -6.0e-39 | -1.0e-20 | 3.1e-22 | 4.6e-05 |
|
||||
| 4.7e-08 | -2.0e-24 | 7.4e-25 | 5.9e-23 | 3.2e-07 | 5.9e-24 |
|
||||
| -7.1e-25 | 4.7e-08 | 2.9e-25 | -3.2e-07 | -5.4e-24 | -3.3e-23 |
|
||||
| 7.9e-26 | -6.4e-25 | 2.1e-08 | 1.9e-23 | 5.3e-25 | -6.5e-40 |
|
||||
| 1.4e-23 | -3.2e-07 | 1.3e-23 | 5.2e-06 | 4.9e-22 | -3.8e-24 |
|
||||
| 3.2e-07 | 7.6e-24 | 1.2e-23 | 6.9e-22 | 5.2e-06 | -2.6e-22 |
|
||||
| 7.3e-24 | -3.2e-23 | -1.6e-39 | 9.9e-23 | -3.3e-22 | 1.7e-06 |
|
||||
|
||||
** Conclusion
|
||||
#+begin_important
|
||||
The low frequency transfer function matrix from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}$ corresponds to the compliance matrix of the Stewart platform.
|
||||
#+end_important
|
||||
|
||||
** Transfer function from forces applied in the legs to the displacement of the legs
|
||||
Initialization of the Stewart platform.
|
||||
#+begin_src matlab
|
||||
stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStrutDynamics(stewart);
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
#+end_src
|
||||
|
||||
Estimation of the transfer function from $\bm{\tau}$ to $\bm{L}$:
|
||||
#+begin_src matlab
|
||||
%% Options for Linearized
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
%% Name of the Simulink File
|
||||
mdl = 'stewart_platform_dynamics';
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/J-T'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/L'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
|
||||
%% Run the linearization
|
||||
G = linearize(mdl, io, options);
|
||||
G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
|
||||
G.OutputName = {'L1', 'L2', 'L3', 'L4', 'L5', 'L6'};
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
freqs = logspace(1, 3, 1000);
|
||||
figure; bode(G, 2*pi*freqs)
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
bodeFig({G(1,1), G(1,2)}, freqs, struct('phase', true));
|
||||
#+end_src
|
||||
|
||||
Reference in New Issue
Block a user