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< title > Control in the Frame of the Legs applied on the Simscape Model< / title >
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< / div > < div id = "content" >
< h1 class = "title" > Control in the Frame of the Legs 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 = "#org1a08332" > 1. Decentralized Control< / a >
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< ul >
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< li > < a href = "#org88b6ca3" > 1.1. Control Schematic< / a > < / li >
< li > < a href = "#org9041934" > 1.2. Initialize the Simscape Model< / a > < / li >
< li > < a href = "#org78bce32" > 1.3. Identification of the plant< / a > < / li >
< li > < a href = "#org3a56a98" > 1.4. Plant Analysis< / a > < / li >
< li > < a href = "#org36df689" > 1.5. Controller Design< / a > < / li >
< li > < a href = "#orgac5ea1c" > 1.6. Simulation< / a > < / li >
< li > < a href = "#orga044079" > 1.7. Results< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#orgeeaa041" > 2. HAC-LAC (IFF) Decentralized Control< / a >
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< ul >
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< li > < a href = "#orge42dfda" > 2.1. Control Schematic< / a > < / li >
< li > < a href = "#org790d1db" > 2.2. Initialize the Simscape Model< / a > < / li >
< li > < a href = "#org110a4e9" > 2.3. Initialization< / a > < / li >
< li > < a href = "#org8f68ab2" > 2.4. Identification for IFF< / a > < / li >
< li > < a href = "#orgbe68cd0" > 2.5. Integral Force Feedback Controller< / a > < / li >
< li > < a href = "#orgca29231" > 2.6. Identification of the damped plant< / a > < / li >
< li > < a href = "#org95df29b" > 2.7. Controller Design< / a > < / li >
< li > < a href = "#org8b5710f" > 2.8. Simulation< / a > < / li >
< li > < a href = "#org791c2a5" > 2.9. Results< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#orgf9b95b3" > 3. Conclusion< / a > < / li >
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< / ul >
< / div >
< / div >
< p >
In this document, we apply some decentralized control to the NASS and see what level of performance can be obtained.
< / p >
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< div id = "outline-container-org1a08332" class = "outline-2" >
< h2 id = "org1a08332" > < span class = "section-number-2" > 1< / span > Decentralized Control< / h2 >
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< div class = "outline-text-2" id = "text-1" >
< / div >
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< div id = "outline-container-org88b6ca3" class = "outline-3" >
< h3 id = "org88b6ca3" > < span class = "section-number-3" > 1.1< / span > Control Schematic< / h3 >
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< div class = "outline-text-3" id = "text-1-1" >
< p >
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The control architecture is shown in Figure < a href = "#orgd4d73cb" > 1< / a > .
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< / p >
< p >
The signals are:
< / p >
< ul class = "org-ul" >
< li > \(\bm{r}_\mathcal{X}\): wanted position of the sample with respect to the granite< / li >
< li > \(\bm{r}_{\mathcal{X}_n}\): wanted position of the sample with respect to the nano-hexapod< / li >
< li > \(\bm{r}_\mathcal{L}\): wanted length of each of the nano-hexapod’ s legs< / li >
< li > \(\bm{\tau}\): forces applied in each actuator< / li >
< li > \(\bm{\mathcal{L}}\): measured displacement of each leg< / li >
< li > \(\bm{\mathcal{X}}\): measured position of the sample with respect to the granite< / li >
< / ul >
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< div id = "orgd4d73cb" class = "figure" >
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< p > < img src = "figs/decentralized_reference_tracking_L.png" alt = "decentralized_reference_tracking_L.png" / >
< / p >
< p > < span class = "figure-number" > Figure 1: < / span > Decentralized control for reference tracking< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org9041934" class = "outline-3" >
< h3 id = "org9041934" > < span class = "section-number-3" > 1.2< / span > Initialize the Simscape Model< / h3 >
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< div class = "outline-text-3" id = "text-1-2" >
< p >
We initialize all the stages with the default parameters.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
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< / pre >
< / div >
< p >
The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
< / p >
< div class = "org-src-container" >
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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 > , 1);
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< / pre >
< / div >
< p >
We set the references that corresponds to a tomography experiment.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > initializeReferences(< span class = "org-string" > 'Rz_type'< / span > , < span class = "org-string" > 'rotating'< / span > , < span class = "org-string" > 'Rz_period'< / span > , 1);
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< / pre >
< / div >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > initializeDisturbances();
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< / pre >
< / div >
< p >
Open Loop.
< / 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" > 'ref-track-L'< / span > );
Kl = tf(zeros(6));
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< / pre >
< / div >
< p >
And we put some gravity.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > initializeSimscapeConfiguration(< span class = "org-string" > 'gravity'< / span > , < span class = "org-constant" > true< / span > );
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< / pre >
< / div >
< p >
We log the signals.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > initializeLoggingConfiguration(< span class = "org-string" > 'log'< / span > , < span class = "org-string" > 'all'< / span > );
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< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org78bce32" class = "outline-3" >
< h3 id = "org78bce32" > < span class = "section-number-3" > 1.3< / span > Identification of the plant< / h3 >
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< div class = "outline-text-3" id = "text-1-3" >
< p >
Let’ s identify the transfer function from \(\bm{\tau}\) to \(\bm{\mathcal{L}}\).
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Name of the Simulink File< / span > < / span >
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;
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" > '/Controller/Reference-Tracking-L/Sum'< / span > ], 1, < span class = "org-string" > 'openoutput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1; < span class = "org-comment" > % Leg length error< / span >
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< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Run the linearization< / span > < / span >
G = linearize(mdl, io, 0);
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" > 'El1'< / span > , < span class = "org-string" > 'El2'< / span > , < span class = "org-string" > 'El3'< / span > , < span class = "org-string" > 'El4'< / span > , < span class = "org-string" > 'El5'< / span > , < span class = "org-string" > 'El6'< / span > };
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< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org3a56a98" class = "outline-3" >
< h3 id = "org3a56a98" > < span class = "section-number-3" > 1.4< / span > Plant Analysis< / h3 >
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< div class = "outline-text-3" id = "text-1-4" >
< p >
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The diagonal and off-diagonal terms of the plant are shown in Figure < a href = "#orgbc5977b" > 2< / a > .
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< / p >
< p >
We can see that:
< / p >
< ul class = "org-ul" >
< li > the diagonal terms have similar dynamics< / li >
< li > the plant is decoupled at low frequency< / li >
< / ul >
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< div id = "orgbc5977b" class = "figure" >
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< p > < img src = "figs/decentralized_control_plant_L.png" alt = "decentralized_control_plant_L.png" / >
< / p >
< p > < span class = "figure-number" > Figure 2: < / span > Transfer Functions from forces applied in each actuator \(\tau_i\) to the relative motion of each leg \(d\mathcal{L}_i\) (< a href = "./figs/decentralized_control_plant_L.png" > png< / a > , < a href = "./figs/decentralized_control_plant_L.pdf" > pdf< / a > )< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org36df689" class = "outline-3" >
< h3 id = "org36df689" > < span class = "section-number-3" > 1.5< / span > Controller Design< / h3 >
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< div class = "outline-text-3" id = "text-1-5" >
< p >
The controller consists of:
< / p >
< ul class = "org-ul" >
< li > A pure integrator< / li >
< li > An integrator up to little before the crossover< / li >
< li > A lead around the crossover< / li >
< li > A low pass filter with a cut-off frequency 3 times the crossover to increase the gain margin< / li >
< / ul >
< p >
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The obtained loop gains corresponding to the diagonal elements are shown in Figure < a href = "#org0e9c3e8" > 3< / a > .
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > wc = 2< span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > 20;
h = 1.5;
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Kl = diag(1< span class = "org-type" > ./< / span > diag(abs(freqresp(G, wc)))) < span class = "org-type" > *< / span > ...
wc< span class = "org-type" > /< / span > s < span class = "org-type" > *< / span > ...< span class = "org-comment" > % Pure Integrator< / span >
((s< span class = "org-type" > /< / span > wc< span class = "org-type" > *< / span > 2 < span class = "org-type" > +< / span > 1)< span class = "org-type" > /< / span > (s< span class = "org-type" > /< / span > wc< span class = "org-type" > *< / span > 2)) < span class = "org-type" > *< / span > ...< span class = "org-comment" > % Integrator up to wc/2< / span >
1< span class = "org-type" > /< / span > h < span class = "org-type" > *< / span > (1 < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > wc< span class = "org-type" > *< / span > h)< span class = "org-type" > /< / span > (1 < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > wc< span class = "org-type" > /< / span > h) < span class = "org-type" > *< / span > ...< span class = "org-comment" > % Lead< / span >
1< span class = "org-type" > /< / span > (1 < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > 3< span class = "org-type" > /< / span > wc) < span class = "org-type" > *< / span > ...< span class = "org-comment" > % Low pass Filter< / span >
1< span class = "org-type" > /< / span > (1 < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > 3< span class = "org-type" > /< / span > wc);
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< / pre >
< / div >
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< div id = "org0e9c3e8" class = "figure" >
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< p > < img src = "figs/decentralized_control_L_loop_gain.png" alt = "decentralized_control_L_loop_gain.png" / >
< / p >
< p > < span class = "figure-number" > Figure 3: < / span > Obtained Loop Gain (< a href = "./figs/decentralized_control_L_loop_gain.png" > png< / a > , < a href = "./figs/decentralized_control_L_loop_gain.pdf" > pdf< / a > )< / p >
< / div >
< p >
We add a minus sign to the controller as it is not included in the Simscape model.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > Kl = < span class = "org-type" > -< / span > Kl;
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< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgac5ea1c" class = "outline-3" >
< h3 id = "orgac5ea1c" > < span class = "section-number-3" > 1.6< / span > Simulation< / h3 >
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< div class = "outline-text-3" id = "text-1-6" >
< 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" > 'ref-track-L'< / span > );
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< / pre >
< / div >
< div class = "org-src-container" >
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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" > '2'< / span > );
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< / pre >
< / div >
< div class = "org-src-container" >
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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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< / pre >
< / div >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > decentralized_L = simout;
save(< span class = "org-string" > './mat/tomo_exp_decentalized.mat'< / span > , < span class = "org-string" > 'decentralized_L'< / span > , < span class = "org-string" > '-append'< / span > );
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< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-orga044079" class = "outline-3" >
< h3 id = "orga044079" > < span class = "section-number-3" > 1.7< / span > Results< / h3 >
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< div class = "outline-text-3" id = "text-1-7" >
< p >
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The reference path and the position of the mobile platform are shown in Figure < a href = "#org5b1621d" > 4< / a > .
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > load(< span class = "org-string" > './mat/experiment_tomography.mat'< / span > , < span class = "org-string" > 'tomo_align_dist'< / span > );
load(< span class = "org-string" > './mat/tomo_exp_decentalized.mat'< / span > , < span class = "org-string" > 'decentralized_L'< / span > );
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< / pre >
< / div >
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< div id = "org5b1621d" class = "figure" >
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< p > < img src = "figs/decentralized_L_position_errors.png" alt = "decentralized_L_position_errors.png" / >
< / p >
< p > < span class = "figure-number" > Figure 4: < / span > Position Errors when using the Decentralized Control Architecture (< a href = "./figs/decentralized_L_position_errors.png" > png< / a > , < a href = "./figs/decentralized_L_position_errors.pdf" > pdf< / a > )< / p >
< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgeeaa041" class = "outline-2" >
< h2 id = "orgeeaa041" > < span class = "section-number-2" > 2< / span > HAC-LAC (IFF) Decentralized Control< / h2 >
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< div class = "outline-text-2" id = "text-2" >
< p >
We here add an Active Damping Loop (Integral Force Feedback) prior to using the Decentralized control architecture using \(\bm{\mathcal{L}}\).
< / p >
< / div >
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< div id = "outline-container-orge42dfda" class = "outline-3" >
< h3 id = "orge42dfda" > < span class = "section-number-3" > 2.1< / span > Control Schematic< / h3 >
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< div class = "outline-text-3" id = "text-2-1" >
< p >
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The control architecture is shown in Figure < a href = "#orgd4d73cb" > 1< / a > .
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< / p >
< p >
The signals are:
< / p >
< ul class = "org-ul" >
< li > \(\bm{r}_\mathcal{X}\): wanted position of the sample with respect to the granite< / li >
< li > \(\bm{r}_{\mathcal{X}_n}\): wanted position of the sample with respect to the nano-hexapod< / li >
< li > \(\bm{r}_\mathcal{L}\): wanted length of each of the nano-hexapod’ s legs< / li >
< li > \(\bm{\tau}\): forces applied in each actuator< / li >
< li > \(\bm{\mathcal{L}}\): measured displacement of each leg< / li >
< li > \(\bm{\mathcal{X}}\): measured position of the sample with respect to the granite< / li >
< / ul >
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< div id = "org9b33c60" class = "figure" >
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< p > < img src = "figs/decentralized_reference_tracking_L.png" alt = "decentralized_reference_tracking_L.png" / >
< / p >
< p > < span class = "figure-number" > Figure 5: < / span > Decentralized control for reference tracking< / p >
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< div id = "outline-container-org790d1db" class = "outline-3" >
< h3 id = "org790d1db" > < span class = "section-number-3" > 2.2< / span > Initialize the Simscape Model< / h3 >
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< div class = "outline-text-3" id = "text-2-2" >
< p >
We initialize all the stages with the default parameters.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
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< / pre >
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< p >
The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
< / p >
< div class = "org-src-container" >
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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 > , 1);
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< p >
We set the references that corresponds to a tomography experiment.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > initializeReferences(< span class = "org-string" > 'Rz_type'< / span > , < span class = "org-string" > 'rotating'< / span > , < span class = "org-string" > 'Rz_period'< / span > , 1);
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< / pre >
< / div >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > initializeDisturbances();
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< p >
Open Loop.
< / 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" > 'ref-track-L'< / span > );
Kl = tf(zeros(6));
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< p >
And we put some gravity.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > initializeSimscapeConfiguration(< span class = "org-string" > 'gravity'< / span > , < span class = "org-constant" > true< / span > );
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< p >
We log the signals.
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > initializeLoggingConfiguration(< span class = "org-string" > 'log'< / span > , < span class = "org-string" > 'all'< / span > );
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< / pre >
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< div id = "outline-container-org110a4e9" class = "outline-3" >
< h3 id = "org110a4e9" > < span class = "section-number-3" > 2.3< / span > Initialization< / h3 >
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< div class = "outline-text-3" id = "text-2-3" >
< 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" > 'ref-track-iff-L'< / span > );
K_iff = tf(zeros(6));
Kl = tf(zeros(6));
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< / div >
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< div id = "outline-container-org8f68ab2" class = "outline-3" >
< h3 id = "org8f68ab2" > < span class = "section-number-3" > 2.4< / span > Identification for IFF< / h3 >
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< div class = "outline-text-3" id = "text-2-4" >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Name of the Simulink File< / span > < / span >
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;
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" > '/Micro-Station'< / span > ], 3, < span class = "org-string" > 'openoutput'< / span > , [], < span class = "org-string" > 'Fnlm'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1; < span class = "org-comment" > % Force Sensors< / span >
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< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Run the linearization< / span > < / span >
G_iff = linearize(mdl, io, 0);
G_iff.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_iff.OutputName = {< span class = "org-string" > 'Fnlm1'< / span > , < span class = "org-string" > 'Fnlm2'< / span > , < span class = "org-string" > 'Fnlm3'< / span > , < span class = "org-string" > 'Fnlm4'< / span > , < span class = "org-string" > 'Fnlm5'< / span > , < span class = "org-string" > 'Fnlm6'< / span > };
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< div id = "outline-container-orgbe68cd0" class = "outline-3" >
< h3 id = "orgbe68cd0" > < span class = "section-number-3" > 2.5< / span > Integral Force Feedback Controller< / h3 >
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< div class = "outline-text-3" id = "text-2-5" >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > w0 = 2< span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > 50;
K_iff = < span class = "org-type" > -< / span > 5000< span class = "org-type" > /< / span > s < span class = "org-type" > *< / span > (s< span class = "org-type" > /< / span > w0)< span class = "org-type" > /< / span > (1 < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > w0) < span class = "org-type" > *< / span > eye(6);
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< / pre >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > K_iff = < span class = "org-type" > -< / span > K_iff;
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< div id = "outline-container-orgca29231" class = "outline-3" >
< h3 id = "orgca29231" > < span class = "section-number-3" > 2.6< / span > Identification of the damped plant< / h3 >
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< div class = "outline-text-3" id = "text-2-6" >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Name of the Simulink DehaezeFile< / span > < / span >
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;
io(io_i) = linio([mdl, < span class = "org-string" > '/Controller'< / span > ], 1, < span class = "org-string" > 'input'< / 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" > '/Controller/Reference-Tracking-IFF-L/Sum'< / span > ], 1, < span class = "org-string" > 'openoutput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1; < span class = "org-comment" > % Leg length error< / span >
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< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Run the linearization< / span > < / span >
Gd = linearize(mdl, io, 0);
Gd.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 > };
Gd.OutputName = {< span class = "org-string" > 'El1'< / span > , < span class = "org-string" > 'El2'< / span > , < span class = "org-string" > 'El3'< / span > , < span class = "org-string" > 'El4'< / span > , < span class = "org-string" > 'El5'< / span > , < span class = "org-string" > 'El6'< / span > };
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< div id = "outline-container-org95df29b" class = "outline-3" >
< h3 id = "org95df29b" > < span class = "section-number-3" > 2.7< / span > Controller Design< / h3 >
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< div class = "outline-text-3" id = "text-2-7" >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > wc = 2< span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > 300;
h = 3;
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Kl = diag(1< span class = "org-type" > ./< / span > diag(abs(freqresp(Gd, wc)))) < span class = "org-type" > *< / span > ...
((s< span class = "org-type" > /< / span > (2< span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > 20) < span class = "org-type" > +< / span > 1)< span class = "org-type" > /< / span > (s< span class = "org-type" > /< / span > (2< span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > 20))) < span class = "org-type" > *< / span > ...< span class = "org-comment" > % Pure Integrator< / span >
((s< span class = "org-type" > /< / span > (2< span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > 50) < span class = "org-type" > +< / span > 1)< span class = "org-type" > /< / span > (s< span class = "org-type" > /< / span > (2< span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > 50))) < span class = "org-type" > *< / span > ...< span class = "org-comment" > % Integrator up to wc/2< / span >
1< span class = "org-type" > /< / span > h < span class = "org-type" > *< / span > (1 < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > wc< span class = "org-type" > *< / span > h)< span class = "org-type" > /< / span > (1 < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > wc< span class = "org-type" > /< / span > h) < span class = "org-type" > *< / span > ...
1< span class = "org-type" > /< / span > (1 < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > (2< span class = "org-type" > *< / span > wc)) < span class = "org-type" > *< / span > ...
1< span class = "org-type" > /< / span > (1 < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > (3< span class = "org-type" > *< / span > wc));
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< / pre >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > isstable(feedback(Gd< span class = "org-type" > *< / span > Kl, eye(6), < span class = "org-type" > -< / span > 1))
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< / pre >
< / div >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > Kl = < span class = "org-type" > -< / span > Kl;
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< div id = "outline-container-org8b5710f" class = "outline-3" >
< h3 id = "org8b5710f" > < span class = "section-number-3" > 2.8< / span > Simulation< / h3 >
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< div class = "outline-text-3" id = "text-2-8" >
< 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" > 'ref-track-iff-L'< / span > );
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< / pre >
< / div >
< div class = "org-src-container" >
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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" > '2'< / span > );
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< / pre >
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< div class = "org-src-container" >
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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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< / pre >
< / div >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > decentralized_iff_L = simout;
save(< span class = "org-string" > './mat/tomo_exp_decentalized.mat'< / span > , < span class = "org-string" > 'decentralized_iff_L'< / span > , < span class = "org-string" > '-append'< / span > );
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< div id = "outline-container-org791c2a5" class = "outline-3" >
< h3 id = "org791c2a5" > < span class = "section-number-3" > 2.9< / span > Results< / h3 >
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< div id = "outline-container-orgf9b95b3" class = "outline-2" >
< h2 id = "orgf9b95b3" > < span class = "section-number-2" > 3< / span > Conclusion< / h2 >
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< / div >
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< div id = "postamble" class = "status" >
< p class = "author" > Author: Dehaeze Thomas< / p >
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< p class = "date" > Created: 2021-02-20 sam. 23:08< / p >
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