312 lines
10 KiB
Org Mode
312 lines
10 KiB
Org Mode
#+TITLE: Stewart Platform - Dynamics Study
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:DRAWER:
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#+HTML_LINK_HOME: ./index.html
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#+HTML_LINK_UP: ./index.html
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
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#+HTML_HEAD: <script src="./js/jquery.min.js"></script>
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#+HTML_HEAD: <script src="./js/bootstrap.min.js"></script>
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#+HTML_HEAD: <script src="./js/jquery.stickytableheaders.min.js"></script>
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#+HTML_HEAD: <script src="./js/readtheorg.js"></script>
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#+PROPERTY: header-args:matlab :session *MATLAB*
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#+PROPERTY: header-args:matlab+ :comments org
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#+PROPERTY: header-args:matlab+ :exports both
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#+PROPERTY: header-args:matlab+ :results none
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#+PROPERTY: header-args:matlab+ :eval no-export
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#+PROPERTY: header-args:matlab+ :noweb yes
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#+PROPERTY: header-args:matlab+ :mkdirp yes
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#+PROPERTY: header-args:matlab+ :output-dir figs
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#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/}{config.tex}")
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#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
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#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
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#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
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#+PROPERTY: header-args:latex+ :results raw replace :buffer no
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#+PROPERTY: header-args:latex+ :eval no-export
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#+PROPERTY: header-args:latex+ :exports both
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#+PROPERTY: header-args:latex+ :mkdirp yes
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#+PROPERTY: header-args:latex+ :output-dir figs
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:END:
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* Some tests
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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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** Simscape Model
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#+begin_src matlab
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open('stewart_platform_dynamics.slx')
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#+end_src
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** test
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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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#+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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%% 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, '/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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%% 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 = {'Edx', 'Edy', 'Edz', 'Erx', 'Ery', 'Erz'};
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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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#+end_src
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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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%% Run the linearization
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Gd = linearize(mdl, io, options);
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Gd.InputName = {'Fex', 'Fey', 'Fez', 'Mex', 'Mey', 'Mez'};
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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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figure;
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bode(Gd, G)
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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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#+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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#+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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%% 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, '/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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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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%% 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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%% Run the linearization
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Gd = linearize(mdl, io, options);
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Gd.InputName = {'Fex', 'Fey', 'Fez', 'Mex', 'Mey', 'Mez'};
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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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figure;
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bode(Gd, G, freqs)
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#+end_src
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#+begin_important
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Seems quite similar.
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#+end_important
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** Comparison of the static transfer function and the Compliance matrix
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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 = 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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#+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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%% 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, '/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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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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#+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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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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#+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 |
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| 1.7e-05 | 2.5e-21 | 2.0e-21 | -2.8e-20 | 1.9e-04 | 1.3e-36 |
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| 3.7e-23 | 3.1e-22 | -6.0e-39 | -1.0e-20 | 3.1e-22 | 4.6e-05 |
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#+begin_important
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The low frequency transfer function matrix from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}$ corresponds to the compliance matrix of the Stewart platform.
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#+end_important
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** Transfer function from forces applied in the legs to the displacement of the legs
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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 = 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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#+end_src
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Estimation of the transfer function from $\bm{\tau}$ to $\bm{L}$:
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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, '/L'], 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 = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
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G.OutputName = {'L1', 'L2', 'L3', 'L4', 'L5', 'L6'};
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#+end_src
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#+begin_src matlab
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freqs = logspace(1, 3, 1000);
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figure; bode(G, 2*pi*freqs)
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#+end_src
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#+begin_src matlab
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bodeFig({G(1,1), G(1,2)}, freqs, struct('phase', true));
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#+end_src
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