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< title > HAC-LAC applied on the Simscape Model< / title >
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< a accesskey = "h" href = "./index.html" > UP < / a >
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< / div > < div id = "content" >
< h1 class = "title" > HAC-LAC applied on the Simscape Model< / h1 >
< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
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< li > < a href = "#org68eabc2" > 1. Undamped System< / a >
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< ul >
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< li > < a href = "#org05b902d" > 1.1. Identification of the plant< / a >
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< ul >
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< li > < a href = "#orga716982" > 1.1.1. Initialize the Simulation< / a > < / li >
< li > < a href = "#org2a3d76d" > 1.1.2. Identification< / a > < / li >
< li > < a href = "#org86a6b3a" > 1.1.3. Display TF< / a > < / li >
< li > < a href = "#org51e23f6" > 1.1.4. Obtained Plants for Active Damping< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#orgaf40de5" > 1.2. Tomography Experiment< / a >
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< ul >
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< li > < a href = "#org5a1507e" > 1.2.1. Simulation< / a > < / li >
< li > < a href = "#org9498b7b" > 1.2.2. Results< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#orgdcbab01" > 1.3. Verification of the transfer function from nano hexapod to metrology< / a >
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< ul >
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< li > < a href = "#org9edf24c" > 1.3.1. Initialize the Simulation< / a > < / li >
< li > < a href = "#org9ff767e" > 1.3.2. Identification< / a > < / li >
< li > < a href = "#org5c0b9bf" > 1.3.3. Display TF< / a > < / li >
< li > < a href = "#org6288fb1" > 1.3.4. Obtained Plants for Active Damping< / a > < / li >
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< / ul >
< / li >
< / ul >
< / li >
< / ul >
< / div >
< / div >
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< div id = "outline-container-org68eabc2" class = "outline-2" >
< h2 id = "org68eabc2" > < span class = "section-number-2" > 1< / span > Undamped System< / h2 >
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< div class = "outline-text-2" id = "text-1" >
< p >
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< a id = "org632e852" > < / a >
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< / p >
< / div >
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< div id = "outline-container-org05b902d" class = "outline-3" >
< h3 id = "org05b902d" > < span class = "section-number-3" > 1.1< / span > Identification of the plant< / h3 >
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< div class = "outline-text-3" id = "text-1-1" >
< / div >
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< div id = "outline-container-orga716982" class = "outline-4" >
< h4 id = "orga716982" > < span class = "section-number-4" > 1.1.1< / span > Initialize the Simulation< / h4 >
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< div class = "outline-text-4" id = "text-1-1-1" >
< p >
We initialize all the stages with the default parameters.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
< / pre >
< / div >
< p >
The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > initializeNanoHexapod(< span class = "org-string" > 'actuator'< / span > , < span class = "org-string" > 'piezo'< / span > );
initializeSample(< span class = "org-string" > 'mass'< / span > , 50);
< / pre >
< / div >
< p >
No disturbances.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > initializeDisturbances(< span class = "org-string" > 'enable'< / span > , < span class = "org-constant" > false< / span > );
< / pre >
< / div >
< p >
We set the references to zero.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > initializeReferences();
< / pre >
< / div >
< p >
And all the controllers are set to 0.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > initializeController(< span class = "org-string" > 'type'< / span > , < span class = "org-string" > 'open-loop'< / span > );
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< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org2a3d76d" class = "outline-4" >
< h4 id = "org2a3d76d" > < span class = "section-number-4" > 1.1.2< / span > Identification< / h4 >
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< div class = "outline-text-4" id = "text-1-1-2" >
< p >
First, we identify the dynamics of the system using the < code > linearize< / code > function.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Options for Linearized< / span > < / span >
options = linearizeOptions;
options.SampleTime = 0;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Name of the Simulink File< / span > < / span >
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mdl = < span class = "org-string" > 'nass_model'< / span > ;
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< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Input/Output definition< / span > < / span >
clear io; io_i = 1;
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io(io_i) = linio([mdl, < span class = "org-string" > '/Controller'< / span > ], 1, < span class = "org-string" > 'openinput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1; < span class = "org-comment" > % Actuator Inputs< / span >
io(io_i) = linio([mdl, < span class = "org-string" > '/Tracking Error'< / span > ], 1, < span class = "org-string" > 'openoutput'< / span > , [], < span class = "org-string" > 'En'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1; < span class = "org-comment" > % Metrology Outputs< / span >
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< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Run the linearization< / span > < / span >
G = linearize(mdl, io, options);
G.InputName = {< span class = "org-string" > 'Fnl1'< / span > , < span class = "org-string" > 'Fnl2'< / span > , < span class = "org-string" > 'Fnl3'< / span > , < span class = "org-string" > 'Fnl4'< / span > , < span class = "org-string" > 'Fnl5'< / span > , < span class = "org-string" > 'Fnl6'< / span > };
G.OutputName = {< span class = "org-string" > 'Edx'< / span > , < span class = "org-string" > 'Edy'< / span > , < span class = "org-string" > 'Edz'< / span > , < span class = "org-string" > 'Erx'< / span > , < span class = "org-string" > 'Ery'< / span > , < span class = "org-string" > 'Erz'< / span > };
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > load(< span class = "org-string" > 'mat/stages.mat'< / span > , < span class = "org-string" > 'nano_hexapod'< / span > );
G_cart = minreal(G< span class = "org-type" > *< / span > inv(nano_hexapod.J< span class = "org-type" > '< / span > ));
G_cart.InputName = {< span class = "org-string" > 'Fnx'< / span > , < span class = "org-string" > 'Fny'< / span > , < span class = "org-string" > 'Fnz'< / span > , < span class = "org-string" > 'Mnx'< / span > , < span class = "org-string" > 'Mny'< / span > , < span class = "org-string" > 'Mnz'< / span > };
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > G_legs = minreal(inv(nano_hexapod.J)< span class = "org-type" > *< / span > G);
G_legs.OutputName = {< span class = "org-string" > 'e1'< / span > , < span class = "org-string" > 'e2'< / span > , < span class = "org-string" > 'e3'< / span > , < span class = "org-string" > 'e4'< / span > , < span class = "org-string" > 'e5'< / span > , < span class = "org-string" > 'e6'< / span > };
< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org86a6b3a" class = "outline-4" >
< h4 id = "org86a6b3a" > < span class = "section-number-4" > 1.1.3< / span > Display TF< / h4 >
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< div class = "outline-text-4" id = "text-1-1-3" >
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< div id = "org37e58f3" class = "figure" >
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< p > < img src = "figs/plant_G_cart.png" alt = "plant_G_cart.png" / >
< / p >
< p > < span class = "figure-number" > Figure 1: < / span > Transfer Function from forces applied by the nano-hexapod to position error (< a href = "./figs/plant_G_cart.png" > png< / a > , < a href = "./figs/plant_G_cart.pdf" > pdf< / a > )< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org51e23f6" class = "outline-4" >
< h4 id = "org51e23f6" > < span class = "section-number-4" > 1.1.4< / span > Obtained Plants for Active Damping< / h4 >
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< div class = "outline-text-4" id = "text-1-1-4" >
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< div id = "orga98bcf7" class = "figure" >
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< p > < img src = "figs/nass_active_damping_iff_plant.png" alt = "nass_active_damping_iff_plant.png" / >
< / p >
< p > < span class = "figure-number" > Figure 2: < / span > < code > G_iff< / code > : IFF Plant (< a href = "./figs/nass_active_damping_iff_plant.png" > png< / a > , < a href = "./figs/nass_active_damping_iff_plant.pdf" > pdf< / a > )< / p >
< / div >
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< div id = "orgf5e6d6e" class = "figure" >
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< p > < img src = "figs/nass_active_damping_ine_plant.png" alt = "nass_active_damping_ine_plant.png" / >
< / p >
< p > < span class = "figure-number" > Figure 3: < / span > < code > G_dvf< / code > : Plant for Direct Velocity Feedback (< a href = "./figs/nass_active_damping_dvf_plant.png" > png< / a > , < a href = "./figs/nass_active_damping_dvf_plant.pdf" > pdf< / a > )< / p >
< / div >
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< div id = "orgfe31dcc" class = "figure" >
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< p > < img src = "figs/nass_active_damping_inertial_plant.png" alt = "nass_active_damping_inertial_plant.png" / >
< / p >
< p > < span class = "figure-number" > Figure 4: < / span > Inertial Feedback Plant (< a href = "./figs/nass_active_damping_inertial_plant.png" > png< / a > , < a href = "./figs/nass_active_damping_inertial_plant.pdf" > pdf< / a > )< / p >
< / div >
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< div id = "outline-container-orgaf40de5" class = "outline-3" >
< h3 id = "orgaf40de5" > < span class = "section-number-3" > 1.2< / span > Tomography Experiment< / h3 >
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< div id = "outline-container-org5a1507e" class = "outline-4" >
< h4 id = "org5a1507e" > < span class = "section-number-4" > 1.2.1< / span > Simulation< / h4 >
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< p >
We initialize elements for the tomography experiment.
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< div class = "org-src-container" >
< pre class = "src src-matlab" > prepareTomographyExperiment();
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< p >
We change the simulation stop time.
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< pre class = "src src-matlab" > load(< span class = "org-string" > 'mat/conf_simulink.mat'< / span > );
< span class = "org-matlab-simulink-keyword" > set_param< / span > (< span class = "org-variable-name" > conf_simulink< / span > , < span class = "org-string" > 'StopTime'< / span > , < span class = "org-string" > '3'< / span > );
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< p >
And we simulate the system.
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< pre class = "src src-matlab" > < span class = "org-matlab-simulink-keyword" > sim< / span > (< span class = "org-string" > 'nass_model'< / span > );
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< p >
Finally, we save the simulation results for further analysis
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< pre class = "src src-matlab" > save(< span class = "org-string" > './active_damping/mat/tomo_exp.mat'< / span > , < span class = "org-string" > 'En'< / span > , < span class = "org-string" > 'Eg'< / span > , < span class = "org-string" > '-append'< / span > );
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< div id = "outline-container-org9498b7b" class = "outline-4" >
< h4 id = "org9498b7b" > < span class = "section-number-4" > 1.2.2< / span > Results< / h4 >
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< div class = "outline-text-4" id = "text-1-2-2" >
< p >
We load the results of tomography experiments.
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< pre class = "src src-matlab" > load(< span class = "org-string" > './active_damping/mat/tomo_exp.mat'< / span > , < span class = "org-string" > 'En'< / span > );
t = linspace(0, 3, length(En(< span class = "org-type" > :< / span > ,1)));
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< div id = "org5746ec3" class = "figure" >
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< p > < img src = "figs/nass_act_damp_undamped_sim_tomo_trans.png" alt = "nass_act_damp_undamped_sim_tomo_trans.png" / >
< / p >
< p > < span class = "figure-number" > Figure 5: < / span > Position Error during tomography experiment - Translations (< a href = "./figs/nass_act_damp_undamped_sim_tomo_trans.png" > png< / a > , < a href = "./figs/nass_act_damp_undamped_sim_tomo_trans.pdf" > pdf< / a > )< / p >
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< div id = "orgb29225c" class = "figure" >
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< p > < img src = "figs/nass_act_damp_undamped_sim_tomo_rot.png" alt = "nass_act_damp_undamped_sim_tomo_rot.png" / >
< / p >
< p > < span class = "figure-number" > Figure 6: < / span > Position Error during tomography experiment - Rotations (< a href = "./figs/nass_act_damp_undamped_sim_tomo_rot.png" > png< / a > , < a href = "./figs/nass_act_damp_undamped_sim_tomo_rot.pdf" > pdf< / a > )< / p >
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< div id = "outline-container-orgdcbab01" class = "outline-3" >
< h3 id = "orgdcbab01" > < span class = "section-number-3" > 1.3< / span > Verification of the transfer function from nano hexapod to metrology< / h3 >
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< div class = "outline-text-3" id = "text-1-3" >
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< div id = "outline-container-org9edf24c" class = "outline-4" >
< h4 id = "org9edf24c" > < span class = "section-number-4" > 1.3.1< / span > Initialize the Simulation< / h4 >
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< div class = "outline-text-4" id = "text-1-3-1" >
< p >
We initialize all the stages with the default parameters.
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< div class = "org-src-container" >
< pre class = "src src-matlab" > initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
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< p >
The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
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< pre class = "src src-matlab" > initializeNanoHexapod(< span class = "org-string" > 'actuator'< / span > , < span class = "org-string" > 'piezo'< / span > );
initializeSample(< span class = "org-string" > 'mass'< / span > , 50);
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< p >
No disturbances.
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< pre class = "src src-matlab" > initializeDisturbances(< span class = "org-string" > 'enable'< / span > , < span class = "org-constant" > false< / span > );
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< p >
We set the references to zero.
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< pre class = "src src-matlab" > initializeReferences();
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< p >
And all the controllers are set to 0.
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > initializeController(< span class = "org-string" > 'type'< / span > , < span class = "org-string" > 'open-loop'< / span > );
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< h4 id = "org9ff767e" > < span class = "section-number-4" > 1.3.2< / span > Identification< / h4 >
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< p >
First, we identify the dynamics of the system using the < code > linearize< / code > function.
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< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Options for Linearized< / span > < / span >
options = linearizeOptions;
options.SampleTime = 0;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Name of the Simulink File< / span > < / span >
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mdl = < span class = "org-string" > 'nass_model'< / span > ;
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< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Input/Output definition< / span > < / span >
clear io; io_i = 1;
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io(io_i) = linio([mdl, < span class = "org-string" > '/Controller'< / span > ], 1, < span class = "org-string" > 'openinput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1; < span class = "org-comment" > % Actuator Inputs< / span >
io(io_i) = linio([mdl, < span class = "org-string" > '/Tracking Error'< / span > ], 1, < span class = "org-string" > 'openoutput'< / span > , [], < span class = "org-string" > 'En'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1; < span class = "org-comment" > % Metrology Outputs< / span >
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< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Run the linearization< / span > < / span >
G = linearize(mdl, io, options);
G.InputName = {< span class = "org-string" > 'Fnl1'< / span > , < span class = "org-string" > 'Fnl2'< / span > , < span class = "org-string" > 'Fnl3'< / span > , < span class = "org-string" > 'Fnl4'< / span > , < span class = "org-string" > 'Fnl5'< / span > , < span class = "org-string" > 'Fnl6'< / span > };
G.OutputName = {< span class = "org-string" > 'Edx'< / span > , < span class = "org-string" > 'Edy'< / span > , < span class = "org-string" > 'Edz'< / span > , < span class = "org-string" > 'Erx'< / span > , < span class = "org-string" > 'Ery'< / span > , < span class = "org-string" > 'Erz'< / span > };
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< div class = "org-src-container" >
< pre class = "src src-matlab" > load(< span class = "org-string" > 'mat/stages.mat'< / span > , < span class = "org-string" > 'nano_hexapod'< / span > );
G_cart = minreal(G< span class = "org-type" > *< / span > inv(nano_hexapod.J< span class = "org-type" > '< / span > ));
G_cart.InputName = {< span class = "org-string" > 'Fnx'< / span > , < span class = "org-string" > 'Fny'< / span > , < span class = "org-string" > 'Fnz'< / span > , < span class = "org-string" > 'Mnx'< / span > , < span class = "org-string" > 'Mny'< / span > , < span class = "org-string" > 'Mnz'< / span > };
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< div class = "org-src-container" >
< pre class = "src src-matlab" > G_legs = minreal(inv(nano_hexapod.J)< span class = "org-type" > *< / span > G);
G_legs.OutputName = {< span class = "org-string" > 'e1'< / span > , < span class = "org-string" > 'e2'< / span > , < span class = "org-string" > 'e3'< / span > , < span class = "org-string" > 'e4'< / span > , < span class = "org-string" > 'e5'< / span > , < span class = "org-string" > 'e6'< / span > };
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< div id = "outline-container-org5c0b9bf" class = "outline-4" >
< h4 id = "org5c0b9bf" > < span class = "section-number-4" > 1.3.3< / span > Display TF< / h4 >
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< div class = "outline-text-4" id = "text-1-3-3" >
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< div id = "org85c36b6" class = "figure" >
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< p > < img src = "figs/plant_G_cart.png" alt = "plant_G_cart.png" / >
< / p >
< p > < span class = "figure-number" > Figure 7: < / span > Transfer Function from forces applied by the nano-hexapod to position error (< a href = "./figs/plant_G_cart.png" > png< / a > , < a href = "./figs/plant_G_cart.pdf" > pdf< / a > )< / p >
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< div id = "outline-container-org6288fb1" class = "outline-4" >
< h4 id = "org6288fb1" > < span class = "section-number-4" > 1.3.4< / span > Obtained Plants for Active Damping< / h4 >
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< div class = "outline-text-4" id = "text-1-3-4" >
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< div id = "org29fb6b2" class = "figure" >
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< p > < img src = "figs/nass_active_damping_iff_plant.png" alt = "nass_active_damping_iff_plant.png" / >
< / p >
< p > < span class = "figure-number" > Figure 8: < / span > < code > G_iff< / code > : IFF Plant (< a href = "./figs/nass_active_damping_iff_plant.png" > png< / a > , < a href = "./figs/nass_active_damping_iff_plant.pdf" > pdf< / a > )< / p >
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< div id = "org9412773" class = "figure" >
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< p > < img src = "figs/nass_active_damping_ine_plant.png" alt = "nass_active_damping_ine_plant.png" / >
< / p >
< p > < span class = "figure-number" > Figure 9: < / span > < code > G_dvf< / code > : Plant for Direct Velocity Feedback (< a href = "./figs/nass_active_damping_dvf_plant.png" > png< / a > , < a href = "./figs/nass_active_damping_dvf_plant.pdf" > pdf< / a > )< / p >
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< div id = "orgea280f2" class = "figure" >
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< p > < img src = "figs/nass_active_damping_inertial_plant.png" alt = "nass_active_damping_inertial_plant.png" / >
< / p >
< p > < span class = "figure-number" > Figure 10: < / span > Inertial Feedback Plant (< a href = "./figs/nass_active_damping_inertial_plant.png" > png< / a > , < a href = "./figs/nass_active_damping_inertial_plant.pdf" > pdf< / a > )< / p >
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< div id = "postamble" class = "status" >
< p class = "author" > Author: Dehaeze Thomas< / p >
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< p class = "date" > Created: 2020-02-25 mar. 18:20< / p >
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