Compliance comparison VC and PZ
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docs/figs/compliance_comp_pz_vc_cascade.pdf
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docs/figs/compliance_comp_pz_vc_cascade.pdf
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docs/figs/compliance_comp_pz_vc_cascade.png
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docs/figs/compliance_comp_pz_vc_cascade.png
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@ -1087,6 +1087,64 @@ Finally with the primary controller
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#+caption: Evolution of the NASS compliance with each control loop added ([[./figs/compliance_evolution_vc_cascade_control.png][png]], [[./figs/compliance_evolution_vc_cascade_control.pdf][pdf]])
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[[file:figs/compliance_evolution_vc_cascade_control.png]]
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*** Comparison with Piezo
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Let's initialize a nano-hexapod with piezoelectric actuators.
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#+begin_src matlab
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initializeNanoHexapod('actuator', 'piezo');
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#+end_src
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We don't use any controller.
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#+begin_src matlab
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Kp = tf(zeros(6));
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Kl = tf(zeros(6));
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Kiff = tf(zeros(6));
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#+end_src
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#+begin_src matlab
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%% Run the linearization
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Gc_pz = linearize(mdl, io, 0);
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Gc_pz.InputName = {'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'};
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Gc_pz.OutputName = {'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'};
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#+end_src
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#+begin_src matlab :exports none
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freqs = logspace(-1, 3, 1000);
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figure;
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ax1 = subplot(1, 2, 1);
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hold on;
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plot(freqs, abs(squeeze(freqresp(Gc_pri(1, 1), freqs, 'Hz'))), 'DisplayName', 'PRI');
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plot(freqs, abs(squeeze(freqresp(Gc_pz( 1, 1), freqs, 'Hz'))), 'DisplayName', 'PZ - OL');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Compliance [m/N]');
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xlabel('Frequency [Hz]');
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legend('location', 'northeast');
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ax2 = subplot(1, 2, 2);
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hold on;
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plot(freqs, abs(squeeze(freqresp(Gc_pri(4, 4), freqs, 'Hz'))), 'DisplayName', 'PRI');
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plot(freqs, abs(squeeze(freqresp(Gc_pz( 4, 4), freqs, 'Hz'))), 'DisplayName', 'PZ - OL');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Compliance [$\frac{rad}{Nm}$]');
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xlabel('Frequency [Hz]');
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legend('location', 'northeast');
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linkaxes([ax1,ax2],'x');
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#+end_src
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#+header: :tangle no :exports results :results none :noweb yes
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#+begin_src matlab :var filepath="figs/compliance_comp_pz_vc_cascade.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+name: fig:compliance_comp_pz_vc_cascade
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#+caption: Comparison of the compliance using the open-loop piezo-nano hexapod and the voice coil nano-hexapod with the cascade control topology ([[./figs/compliance_comp_pz_vc_cascade.png][png]], [[./figs/compliance_comp_pz_vc_cascade.pdf][pdf]])
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[[file:figs/compliance_comp_pz_vc_cascade.png]]
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** Robustness to Payload Variability
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*** Initialization
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Let's change the payload mass, and see if the controller design for a payload mass of 1 still gives good performance.
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