Add compliance analysis of the micro-station

org/identification.org

@@ -80,10 +80,6 @@ Some of the springs and dampers values can be estimated from the joints/stages s
 #+end_src
 
 ** Prepare the Simulation
-#+begin_src matlab
-  open('nass_model.slx')
-#+end_src
-
 We load the configuration.
 #+begin_src matlab
   load('mat/conf_simulink.mat');
@@ -393,6 +389,96 @@ We then compare the measurements with the identified transfer functions using th
 [[file:figs/identification_comp_top_stages.png]]
 
 
+* Obtained Compliance of the Micro-Station
+** Matlab Init                                              :noexport:ignore:
+#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
+  <<matlab-dir>>
+#+end_src
+
+#+begin_src matlab :exports none :results silent :noweb yes
+  <<matlab-init>>
+#+end_src
+
+#+begin_src matlab :tangle no
+  simulinkproject('../');
+#+end_src
+
+#+begin_src matlab
+  open('nass_model.slx')
+#+end_src
+
+** Initialization
+We initialize all the stages with the default parameters.
+#+begin_src matlab
+  initializeGround();
+  initializeGranite();
+  initializeTy();
+  initializeRy();
+  initializeRz();
+  initializeMicroHexapod('type', 'compliance');
+#+end_src
+
+We put nothing on top of the micro-hexapod.
+#+begin_src matlab
+  initializeAxisc('type', 'none');
+  initializeMirror('type', 'none');
+  initializeNanoHexapod('type', 'none');
+  initializeSample('type', 'none');
+#+end_src
+
+#+begin_src matlab
+  initializeReferences();
+  initializeDisturbances();
+  initializeController();
+  initializeSimscapeConfiguration();
+  initializeLoggingConfiguration();
+#+end_src
+
+And we identify the dynamics from forces/torques applied on the micro-hexapod top platform to the motion of the micro-hexapod top platform at the same point.
+
+The obtained compliance is shown in Figure [[fig:compliance_micro_station]].
+#+begin_src matlab
+  %% Name of the Simulink File
+  mdl = 'nass_model';
+
+  %% Input/Output definition
+  clear io; io_i = 1;
+  io(io_i) = linio([mdl, '/Micro-Station/Micro Hexapod/Compliance/Fm'], 1, 'openinput');       io_i = io_i + 1; % Direct Forces/Torques applied on the micro-hexapod top platform
+  io(io_i) = linio([mdl, '/Micro-Station/Micro Hexapod/Compliance/Dm'], 1, 'output'); io_i = io_i + 1; % Absolute displacement of the top platform
+
+  %% Run the linearization
+  Gm = linearize(mdl, io, 0);
+  Gm.InputName  = {'Fmx', 'Fmy', 'Fmz', 'Mmx', 'Mmy', 'Mmz'};
+  Gm.OutputName = {'Dx', 'Dy', 'Dz', 'Drx', 'Dry', 'Drz'};
+#+end_src
+
+#+begin_src matlab :exports none
+  labels = {'$D_x/F_{x}$', '$D_y/F_{y}$', '$D_z/F_{z}$', '$R_{x}/M_{x}$', '$R_{y}/M_{y}$', '$R_{R}/M_{z}$'};
+
+  freqs = logspace(1, 3, 1000);
+
+  figure;
+
+  hold on;
+  for i = 1:6
+    plot(freqs, abs(squeeze(freqresp(Gm(i, i), freqs, 'Hz'))), 'DisplayName', labels{i});
+  end
+  hold off;
+  set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+  xlabel('Frequency [Hz]');
+  ylabel('Compliance');
+  legend('location', 'northwest');
+#+end_src
+
+#+header: :tangle no :exports results :results none :noweb yes
+#+begin_src matlab :var filepath="figs/compliance_micro_station.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
+<<plt-matlab>>
+#+end_src
+
+#+name: fig:compliance_micro_station
+#+caption: Obtained compliance of the Micro-Station ([[./figs/compliance_micro_station.png][png]], [[./figs/compliance_micro_station.pdf][pdf]])
+[[file:figs/compliance_micro_station.png]]
+
 * Conclusion
 #+begin_important
   For such a complex system, we believe that the Simscape Model represents the dynamics of the system with enough fidelity.

org/simscape_subsystems.org

@@ -859,7 +859,7 @@ The =rz= structure is saved.
 :END:
 #+begin_src matlab
   arguments
-      args.type      char   {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init'})} = 'flexible'
+      args.type      char   {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init', 'compliance'})} = 'flexible'
       % initializeFramesPositions
       args.H    (1,1) double {mustBeNumeric, mustBePositive} = 350e-3
       args.MO_B (1,1) double {mustBeNumeric} = 270e-3
@@ -938,6 +938,8 @@ Equilibrium position of the each joint.
       micro_hexapod.type = 3;
     case 'init'
       micro_hexapod.type = 4;
+    case 'compliance'
+      micro_hexapod.type = 5;
   end
 #+end_src
 

src/initializeMicroHexapod.m

@@ -1,7 +1,7 @@
 function [micro_hexapod] = initializeMicroHexapod(args)
 
 arguments
-    args.type      char   {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init'})} = 'flexible'
+    args.type      char   {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init', 'compliance'})} = 'flexible'
     % initializeFramesPositions
     args.H    (1,1) double {mustBeNumeric, mustBePositive} = 350e-3
     args.MO_B (1,1) double {mustBeNumeric} = 270e-3
@@ -65,6 +65,8 @@ switch args.type
     micro_hexapod.type = 3;
   case 'init'
     micro_hexapod.type = 4;
+  case 'compliance'
+    micro_hexapod.type = 5;
 end
 
 save('./mat/stages.mat', 'micro_hexapod', '-append');