Analysis of IFF with amplified actuators

org/amplified_piezoelectric_stack.org

@@ -657,8 +657,8 @@ Finally, we use the following controller for the Decentralized Direct Velocity F
 
 *** Identification of the undamped plant                            :ignore:
 #+begin_src matlab :exports none
-  Kdvf_backup = Kdvf;
-  Kdvf = tf(zeros(6));
+  Kiff_backup = Kiff;
+  Kiff = tf(zeros(6));
 #+end_src
 
 #+begin_src matlab :exports none
@@ -687,7 +687,7 @@ Finally, we use the following controller for the Decentralized Direct Velocity F
 #+end_src
 
 #+begin_src matlab :exports none
-  Kdvf = Kdvf_backup;
+  Kiff = Kiff_backup;
 #+end_src
 
 *** Identification of the damped plant                              :ignore:
@@ -790,6 +790,16 @@ Finally, we use the following controller for the Decentralized Direct Velocity F
   linkaxes([ax1,ax2,ax3,ax4],'x');
 #+end_src
 
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/amplified_piezo_iff_plant_damped_X.pdf', 'width', 'full', 'height', 'full');
+#+end_src
+
+#+name: fig:amplified_piezo_iff_plant_damped_X
+#+caption: Primary plant in the task space with (dashed) and without (solid) IFF
+#+RESULTS:
+[[file:figs/amplified_piezo_iff_plant_damped_X.png]]
+
+
 #+begin_src matlab :exports none
   freqs = logspace(0, 3, 5000);
 
@@ -827,6 +837,16 @@ Finally, we use the following controller for the Decentralized Direct Velocity F
   linkaxes([ax1,ax2],'x');
 #+end_src
 
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/amplified_piezo_iff_damped_plant_L.pdf', 'width', 'full', 'height', 'full');
+#+end_src
+
+#+name: fig:amplified_piezo_iff_damped_plant_L
+#+caption: Primary plant in the space of the legs with (dashed) and without (solid) IFF
+#+RESULTS:
+[[file:figs/amplified_piezo_iff_damped_plant_L.png]]
+
+
 *** Effect of the Damping on the coupling dynamics                  :ignore:
 #+begin_src matlab :exports none
   freqs = logspace(0, 3, 1000);
@@ -849,6 +869,16 @@ Finally, we use the following controller for the Decentralized Direct Velocity F
   ylim([1e-12, inf]);
 #+end_src
 
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/amplified_piezo_iff_damped_coupling_X.pdf', 'width', 'full', 'height', 'full');
+#+end_src
+
+#+name: fig:amplified_piezo_iff_damped_coupling_X
+#+caption: Coupling in the primary plant in the task with (dashed) and without (solid) IFF
+#+RESULTS:
+[[file:figs/amplified_piezo_iff_damped_coupling_X.png]]
+
+
 #+begin_src matlab :exports none
   freqs = logspace(0, 3, 1000);
 
@@ -869,3 +899,145 @@ Finally, we use the following controller for the Decentralized Direct Velocity F
   ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
   ylim([1e-9, inf]);
 #+end_src
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/amplified_piezo_iff_damped_coupling_L.pdf', 'width', 'full', 'height', 'full');
+#+end_src
+
+#+name: fig:amplified_piezo_iff_damped_coupling_L
+#+caption: Coupling in the primary plant in the space of the legs with (dashed) and without (solid) IFF
+#+RESULTS:
+[[file:figs/amplified_piezo_iff_damped_coupling_L.png]]
+
+** Effect of the Low Authority Control on the Sensibility to Disturbances
+*** Introduction                                                    :ignore:
+
+*** Identification                                                  :ignore:
+#+begin_src matlab :exports none
+  %% Name of the Simulink File
+  mdl = 'nass_model';
+
+  %% Micro-Hexapod
+  clear io; io_i = 1;
+  io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Dwz');   io_i = io_i + 1; % Z Ground motion
+  io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Fty_z'); io_i = io_i + 1; % Parasitic force Ty - Z
+  io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Frz_z'); io_i = io_i + 1; % Parasitic force Rz - Z
+  io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Fd');    io_i = io_i + 1; % Direct forces
+
+  io(io_i) = linio([mdl, '/Tracking Error'], 1, 'output', [], 'En'); io_i = io_i + 1; % Position Errror
+#+end_src
+
+#+begin_src matlab :exports none
+  Kiff_backup = Kiff;
+  Kiff = tf(zeros(6));
+#+end_src
+
+#+begin_src matlab :exports none
+  Gd = {zeros(length(Ms), 1)};
+
+  for i = 1:length(Ms)
+      initializeSample('mass', Ms(i), 'freq', sqrt(Kp/Ms(i))/2/pi*ones(6,1));
+      initializeReferences('Rz_type', 'rotating-not-filtered', 'Rz_period', Ms(i));
+
+      %% Run the linearization
+      G = linearize(mdl, io);
+      G.InputName  = {'Dwz', 'Fty_z', 'Frz_z', 'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'};
+      G.OutputName = {'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'};
+
+      Gd(i) = {G};
+  end
+#+end_src
+
+#+begin_src matlab :exports none
+  Kiff = Kiff_backup;
+#+end_src
+
+#+begin_src matlab :exports none
+  Gd_iff = {zeros(length(Ms), 1)};
+
+  for i = 1:length(Ms)
+      initializeSample('mass', Ms(i), 'freq', sqrt(Kp/Ms(i))/2/pi*ones(6,1));
+      initializeReferences('Rz_type', 'rotating-not-filtered', 'Rz_period', Ms(i));
+
+      %% Run the linearization
+      G = linearize(mdl, io);
+      G.InputName  = {'Dwz', 'Fty_z', 'Frz_z', 'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'};
+      G.OutputName = {'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'};
+
+      Gd_iff(i) = {G};
+  end
+#+end_src
+
+*** Results                                                         :ignore:
+#+begin_src matlab :exports none
+  freqs = logspace(0, 3, 5000);
+
+  figure;
+
+  subplot(2, 2, 1);
+  title('$D_{w,z}$ to $E_z$');
+  hold on;
+  for i = 1:length(Ms)
+      set(gca,'ColorOrderIndex',i);
+      plot(freqs, abs(squeeze(freqresp(Gd{i}('Ez', 'Dwz'), freqs, 'Hz'))), ...
+           'DisplayName', sprintf('$m_p = %.0f [kg]$', Ms(i)));
+      set(gca,'ColorOrderIndex',i);
+      plot(freqs, abs(squeeze(freqresp(Gd_iff{i}('Ez', 'Dwz'), freqs, 'Hz'))), '--', ...
+           'HandleVisibility', 'off');
+  end
+  hold off;
+  set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+  ylabel('Amplitude [m/m]'); set(gca, 'XTickLabel',[]);
+  legend('location', 'southeast');
+
+  subplot(2, 2, 2);
+  title('$F_{dz}$ to $E_z$');
+  hold on;
+  for i = 1:length(Ms)
+      set(gca,'ColorOrderIndex',i);
+      plot(freqs, abs(squeeze(freqresp(Gd{i}('Ez', 'Fdz'), freqs, 'Hz'))));
+      set(gca,'ColorOrderIndex',i);
+      plot(freqs, abs(squeeze(freqresp(Gd_iff{i}('Ez', 'Fdz'), freqs, 'Hz'))), '--');
+  end
+  hold off;
+  set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+  set(gca, 'XTickLabel',[]); ylabel('Amplitude [m/N]');
+
+  subplot(2, 2, 3);
+  title('$F_{T_y,z}$ to $E_z$');
+  hold on;
+  for i = 1:length(Ms)
+      set(gca,'ColorOrderIndex',i);
+      plot(freqs, abs(squeeze(freqresp(Gd{i}('Ez', 'Fty_z'), freqs, 'Hz'))));
+      set(gca,'ColorOrderIndex',i);
+      plot(freqs, abs(squeeze(freqresp(Gd_iff{i}('Ez', 'Fty_z'), freqs, 'Hz'))), '--');
+  end
+  hold off;
+  set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+  xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
+
+  subplot(2, 2, 4);
+  title('$F_{R_z,z}$ to $E_z$');
+  hold on;
+  for i = 1:length(Ms)
+      set(gca,'ColorOrderIndex',i);
+      plot(freqs, abs(squeeze(freqresp(Gd{i}('Ez', 'Frz_z'), freqs, 'Hz'))));
+      set(gca,'ColorOrderIndex',i);
+      plot(freqs, abs(squeeze(freqresp(Gd_iff{i}('Ez', 'Frz_z'), freqs, 'Hz'))), '--');
+  end
+  hold off;
+  set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+  xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/amplified_piezo_iff_disturbances.pdf', 'width', 'full', 'height', 'full');
+#+end_src
+
+#+name: fig:amplified_piezo_iff_disturbances
+#+caption: Norm of the transfer function from vertical disturbances to vertical position error with (dashed) and without (solid) Integral Force Feedback applied
+#+RESULTS:
+[[file:figs/amplified_piezo_iff_disturbances.png]]
+
+*** Conclusion                                                      :ignore:
+#+begin_important
+#+end_important