Analysis of active damping techniques with simscape model
Some flexibility is added to the sample
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@ -25,7 +25,7 @@
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#+PROPERTY: header-args:matlab+ :exports both
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#+PROPERTY: header-args:matlab+ :exports both
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#+PROPERTY: header-args:matlab+ :eval no-export
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#+PROPERTY: header-args:matlab+ :eval no-export
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#+PROPERTY: header-args:matlab+ :output-dir figs
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#+PROPERTY: header-args:matlab+ :output-dir figs
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#+PROPERTY: header-args:matlab+ :tangle matlab/modal_frf_coh.m
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#+PROPERTY: header-args:matlab+ :tangle no
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#+PROPERTY: header-args:matlab+ :mkdirp yes
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#+PROPERTY: header-args:matlab+ :mkdirp yes
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#+PROPERTY: header-args:shell :eval no-export
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#+PROPERTY: header-args:shell :eval no-export
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@ -41,79 +41,8 @@
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#+PROPERTY: header-args:latex+ :output-dir figs
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#+PROPERTY: header-args:latex+ :output-dir figs
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:END:
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:END:
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* Analysis of the nano-hexapod transfer functions :noexport:
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** Introduction :ignore:
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** Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init>>
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#+end_src
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#+begin_src matlab :tangle no
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simulinkproject('../');
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#+end_src
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** Init
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#+begin_src matlab
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%% Initialize Ground
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initializeGround();
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%% Initialize Granite
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initializeGranite(struct('rigid', false));
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%% Initialize Translation stage
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initializeTy(struct('rigid', false));
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%% Initialize Tilt Stage
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initializeRy(struct('rigid', false));
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%% Initialize Spindle
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initializeRz(struct('rigid', false));
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%% Initialize Hexapod Symétrie
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initializeMicroHexapod(struct('rigid', false));
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%% Initialize Center of gravity compensation
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initializeAxisc();
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%% Initialize the mirror
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initializeMirror();
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%% Initialize the Nano Hexapod
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initializeNanoHexapod(struct('actuator', 'piezo'));
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%% Initialize the Sample
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initializeSample(struct('mass', 50));
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#+end_src
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#+begin_src matlab
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K = tf(zeros(6));
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save('./mat/controllers.mat', 'K', '-append');
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K_iff = tf(zeros(6));
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save('./mat/controllers.mat', 'K_iff', '-append');
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#+end_src
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** Identification
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#+begin_src matlab
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G = identifyPlant();
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#+end_src
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** Force Sensor
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#+begin_src matlab
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figure;
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hold on;
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for i=1:6
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plot(freqs, abs(squeeze(freqresp(G.G_iff(['Fm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
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end
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [N/N]'); xlabel('Frequency [Hz]');
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#+end_src
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* Introduction :ignore:
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* Introduction :ignore:
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First, in section [[sec:undamped]], we will looked at the undamped system.
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First, in section [[sec:undamped_system]], we will looked at the undamped system.
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Then, we will compare three active damping techniques:
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Then, we will compare three active damping techniques:
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- In section [[sec:iff]]: the integral force feedback is used
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- In section [[sec:iff]]: the integral force feedback is used
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@ -130,7 +59,26 @@ The disturbances are:
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- Motion errors of all the stages
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- Motion errors of all the stages
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* Undamped System
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* Undamped System
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<<sec:undamped>>
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:PROPERTIES:
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:header-args:matlab+: :tangle matlab/undamped_system.m
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:header-args:matlab+: :comments org :mkdirp yes
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:END:
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<<sec:undamped_system>>
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** ZIP file containing the data and matlab files :ignore:
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#+begin_src bash :exports none :results none
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if [ matlab/undamped_system.m -nt data/undamped_system.zip ]; then
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cp matlab/undamped_system.m undamped_system.m;
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zip data/undamped_system \
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undamped_system.m
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rm undamped_system.m;
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fi
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#+end_src
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#+begin_note
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All the files (data and Matlab scripts) are accessible [[file:data/undamped_system.zip][here]].
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#+end_note
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** Introduction :ignore:
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** Introduction :ignore:
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We first look at the undamped system.
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We first look at the undamped system.
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The performance of this undamped system will be compared with the damped system using various techniques.
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The performance of this undamped system will be compared with the damped system using various techniques.
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@ -157,6 +105,7 @@ We initialize all the stages with the default parameters.
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The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
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The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
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#+begin_src matlab
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#+begin_src matlab
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initializeInputs();
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initializeGround();
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initializeGround();
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initializeGranite();
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initializeGranite();
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initializeTy();
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initializeTy();
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@ -187,6 +136,11 @@ We identify the various transfer functions of the system
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G = identifyPlant();
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G = identifyPlant();
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#+end_src
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#+end_src
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And we save it for further analysis.
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#+begin_src matlab
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save('./active_damping/mat/plants.mat', 'G', '-append');
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#+end_src
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** Sensitivity to disturbances
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** Sensitivity to disturbances
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The sensitivity to disturbances are shown on figure [[fig:sensitivity_dist_undamped]].
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The sensitivity to disturbances are shown on figure [[fig:sensitivity_dist_undamped]].
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@ -225,6 +179,28 @@ The sensitivity to disturbances are shown on figure [[fig:sensitivity_dist_undam
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#+CAPTION: Undamped sensitivity to disturbances ([[./figs/sensitivity_dist_undamped.png][png]], [[./figs/sensitivity_dist_undamped.pdf][pdf]])
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#+CAPTION: Undamped sensitivity to disturbances ([[./figs/sensitivity_dist_undamped.png][png]], [[./figs/sensitivity_dist_undamped.pdf][pdf]])
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[[file:figs/sensitivity_dist_undamped.png]]
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[[file:figs/sensitivity_dist_undamped.png]]
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#+begin_src matlab :exports none
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freqs = logspace(0, 3, 1000);
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figure;
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hold on;
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plot(freqs, abs(squeeze(freqresp(G.G_dist('Dz', 'Frzz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{rz, z}\right|$');
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plot(freqs, abs(squeeze(freqresp(G.G_dist('Dz', 'Ftyz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{ty, z}\right|$');
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plot(freqs, abs(squeeze(freqresp(G.G_dist('Dx', 'Ftyx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / F_{ty, x}\right|$');
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
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legend('location', 'northeast');
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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/sensitivity_dist_stages.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:sensitivity_dist_stages
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#+CAPTION: Sensitivity to force disturbances in various stages ([[./figs/sensitivity_dist_stages.png][png]], [[./figs/sensitivity_dist_stages.pdf][pdf]])
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[[file:figs/sensitivity_dist_stages.png]]
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** Undamped Plant
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** Undamped Plant
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The "plant" (transfer function from forces applied by the nano-hexapod to the measured displacement of the sample with respect to the granite) bode plot is shown on figure [[fig:sensitivity_dist_undamped]].
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The "plant" (transfer function from forces applied by the nano-hexapod to the measured displacement of the sample with respect to the granite) bode plot is shown on figure [[fig:sensitivity_dist_undamped]].
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@ -266,19 +242,37 @@ The "plant" (transfer function from forces applied by the nano-hexapod to the me
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#+CAPTION: Transfer Function from cartesian forces to displacement for the undamped plant ([[./figs/plant_undamped.png][png]], [[./figs/plant_undamped.pdf][pdf]])
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#+CAPTION: Transfer Function from cartesian forces to displacement for the undamped plant ([[./figs/plant_undamped.png][png]], [[./figs/plant_undamped.pdf][pdf]])
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[[file:figs/plant_undamped.png]]
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[[file:figs/plant_undamped.png]]
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** Save
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* Integral Force Feedback
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#+begin_src matlab
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:PROPERTIES:
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save('./active_damping/mat/plants.mat', 'G', '-append');
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:header-args:matlab+: :tangle matlab/iff.m
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:header-args:matlab+: :comments org :mkdirp yes
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:END:
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<<sec:iff>>
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** ZIP file containing the data and matlab files :ignore:
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#+begin_src bash :exports none :results none
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if [ matlab/iff.m -nt data/iff.zip ]; then
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cp matlab/iff.m iff.m;
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zip data/iff \
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mat/plant.mat \
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iff.m
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rm iff.m;
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fi
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#+end_src
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#+end_src
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* Integral Force Feedback
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#+begin_note
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<<sec:iff>>
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All the files (data and Matlab scripts) are accessible [[file:data/iff.zip][here]].
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#+end_note
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** Introduction :ignore:
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** Introduction :ignore:
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Integral Force Feedback is applied.
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Integral Force Feedback is applied.
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In section [[sec:iff_1dof]], IFF is applied on a uni-axial system to understand its behavior.
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In section [[sec:iff_1dof]], IFF is applied on a uni-axial system to understand its behavior.
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Then, it is applied on the simscape model.
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Then, it is applied on the simscape model.
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** One degree-of-freedom example
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** One degree-of-freedom example
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:PROPERTIES:
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:header-args:matlab+: :tangle no
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:END:
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<<sec:iff_1dof>>
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<<sec:iff_1dof>>
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*** Equations
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*** Equations
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#+begin_src latex :file iff_1dof.pdf :post pdf2svg(file=*this*, ext="png") :exports results
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#+begin_src latex :file iff_1dof.pdf :post pdf2svg(file=*this*, ext="png") :exports results
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@ -560,9 +554,10 @@ The corresponding loop gains are shown in figure [[fig:iff_open_loop]].
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#+CAPTION: Loop Gain for the Integral Force Feedback ([[./figs/iff_open_loop.png][png]], [[./figs/iff_open_loop.pdf][pdf]])
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#+CAPTION: Loop Gain for the Integral Force Feedback ([[./figs/iff_open_loop.png][png]], [[./figs/iff_open_loop.pdf][pdf]])
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[[file:figs/iff_open_loop.png]]
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[[file:figs/iff_open_loop.png]]
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** Sensitivity to disturbances
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** Identification of the damped plant
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Let's initialize the system prior to identification.
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Let's initialize the system prior to identification.
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#+begin_src matlab
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#+begin_src matlab
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initializeInputs();
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initializeGround();
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initializeGround();
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initializeGranite();
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initializeGranite();
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initializeTy();
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initializeTy();
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@ -592,6 +587,12 @@ We identify the system dynamics now that the IFF controller is ON.
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G_iff = identifyPlant();
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G_iff = identifyPlant();
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#+end_src
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#+end_src
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And we save the damped plant for further analysis
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#+begin_src matlab
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save('./active_damping/mat/plants.mat', 'G_iff', '-append');
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#+end_src
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** Sensitivity to disturbances
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As shown on figure [[fig:sensitivity_dist_iff]]:
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As shown on figure [[fig:sensitivity_dist_iff]]:
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- The top platform of the nano-hexapod how behaves as a "free-mass".
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- The top platform of the nano-hexapod how behaves as a "free-mass".
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- The transfer function from direct forces $F_s$ to the relative displacement $D$ is equivalent to the one of an isolated mass.
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- The transfer function from direct forces $F_s$ to the relative displacement $D$ is equivalent to the one of an isolated mass.
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@ -664,7 +665,7 @@ As shown on figure [[fig:sensitivity_dist_iff]]:
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#+end_src
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#+end_src
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#+HEADER: :tangle no :exports results :results none :noweb yes
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#+HEADER: :tangle no :exports results :results none :noweb yes
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#+begin_src matlab :var filepath="figs/sensitivity_dist_stages_iff.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
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#+begin_src matlab :var filepath="figs/sensitivity_dist_stages_iff.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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<<plt-matlab>>
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#+end_src
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#+end_src
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@ -777,11 +778,6 @@ However, it increases coupling at low frequency (figure [[fig:plant_iff_coupling
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#+CAPTION: Coupling induced by IFF ([[./figs/plant_iff_coupling.png][png]], [[./figs/plant_iff_coupling.pdf][pdf]])
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#+CAPTION: Coupling induced by IFF ([[./figs/plant_iff_coupling.png][png]], [[./figs/plant_iff_coupling.pdf][pdf]])
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[[file:figs/plant_iff_coupling.png]]
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[[file:figs/plant_iff_coupling.png]]
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** Save
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#+begin_src matlab
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save('./active_damping/mat/plants.mat', 'G_iff', '-append');
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#+end_src
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** Conclusion
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** Conclusion
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#+begin_important
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#+begin_important
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Integral Force Feedback:
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Integral Force Feedback:
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@ -791,11 +787,34 @@ Integral Force Feedback:
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#+end_important
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#+end_important
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* Relative Motion Control
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* Relative Motion Control
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:PROPERTIES:
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:header-args:matlab+: :tangle matlab/rmc.m
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:header-args:matlab+: :comments org :mkdirp yes
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:END:
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<<sec:rmc>>
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<<sec:rmc>>
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** ZIP file containing the data and matlab files :ignore:
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#+begin_src bash :exports none :results none
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if [ matlab/rmc.m -nt data/rmc.zip ]; then
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cp matlab/rmc.m rmc.m;
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zip data/rmc \
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mat/plant.mat \
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rmc.m
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rm rmc.m;
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fi
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#+end_src
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#+begin_note
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All the files (data and Matlab scripts) are accessible [[file:data/rmc.zip][here]].
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#+end_note
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** Introduction :ignore:
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** Introduction :ignore:
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In the Relative Motion Control (RMC), a derivative feedback is applied between the measured actuator displacement to the actuator force input.
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In the Relative Motion Control (RMC), a derivative feedback is applied between the measured actuator displacement to the actuator force input.
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** One degree-of-freedom example
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** One degree-of-freedom example
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:PROPERTIES:
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:header-args:matlab+: :tangle no
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:END:
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<<sec:rmc_1dof>>
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<<sec:rmc_1dof>>
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*** Equations
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*** Equations
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#+begin_src latex :file rmc_1dof.pdf :post pdf2svg(file=*this*, ext="png") :exports results
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#+begin_src latex :file rmc_1dof.pdf :post pdf2svg(file=*this*, ext="png") :exports results
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@ -1075,9 +1094,10 @@ The obtained loop gains are shown in figure [[fig:rmc_open_loop]].
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#+CAPTION: Loop Gain for the Integral Force Feedback ([[./figs/rmc_open_loop.png][png]], [[./figs/rmc_open_loop.pdf][pdf]])
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#+CAPTION: Loop Gain for the Integral Force Feedback ([[./figs/rmc_open_loop.png][png]], [[./figs/rmc_open_loop.pdf][pdf]])
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[[file:figs/rmc_open_loop.png]]
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[[file:figs/rmc_open_loop.png]]
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** Sensitivity to disturbances
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** Identification of the damped plant
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Let's initialize the system prior to identification.
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Let's initialize the system prior to identification.
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#+begin_src matlab
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#+begin_src matlab
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initializeInputs();
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initializeGround();
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initializeGround();
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initializeGranite();
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initializeGranite();
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initializeTy();
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initializeTy();
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@ -1107,6 +1127,12 @@ We identify the system dynamics now that the RMC controller is ON.
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G_rmc = identifyPlant();
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G_rmc = identifyPlant();
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#+end_src
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#+end_src
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And we save the damped plant for further analysis.
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#+begin_src matlab
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||||||
|
save('./active_damping/mat/plants.mat', 'G_rmc', '-append');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
** Sensitivity to disturbances
|
||||||
As shown in figure [[fig:sensitivity_dist_rmc]], RMC control succeed in lowering the sensitivity to disturbances near resonance of the system.
|
As shown in figure [[fig:sensitivity_dist_rmc]], RMC control succeed in lowering the sensitivity to disturbances near resonance of the system.
|
||||||
|
|
||||||
#+begin_src matlab :exports none
|
#+begin_src matlab :exports none
|
||||||
@ -1126,7 +1152,7 @@ As shown in figure [[fig:sensitivity_dist_rmc]], RMC control succeed in lowering
|
|||||||
plot(freqs, abs(squeeze(freqresp(G_rmc.G_gm('Dz', 'Dgz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_gm('Dz', 'Dgz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]');
|
ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]');
|
||||||
legend('location', 'northeast');
|
legend('location', 'southeast');
|
||||||
|
|
||||||
subplot(2, 1, 2);
|
subplot(2, 1, 2);
|
||||||
title('$F_s$ to $D$');
|
title('$F_s$ to $D$');
|
||||||
@ -1170,7 +1196,7 @@ As shown in figure [[fig:sensitivity_dist_rmc]], RMC control succeed in lowering
|
|||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||||
#+begin_src matlab :var filepath="figs/sensitivity_dist_stages_rmc.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
|
#+begin_src matlab :var filepath="figs/sensitivity_dist_stages_rmc.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||||
<<plt-matlab>>
|
<<plt-matlab>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
@ -1252,11 +1278,6 @@ As shown in figure [[fig:sensitivity_dist_rmc]], RMC control succeed in lowering
|
|||||||
#+CAPTION: Damped Plant after RMC is applied ([[./figs/plant_rmc_damped.png][png]], [[./figs/plant_rmc_damped.pdf][pdf]])
|
#+CAPTION: Damped Plant after RMC is applied ([[./figs/plant_rmc_damped.png][png]], [[./figs/plant_rmc_damped.pdf][pdf]])
|
||||||
[[file:figs/plant_rmc_damped.png]]
|
[[file:figs/plant_rmc_damped.png]]
|
||||||
|
|
||||||
** Save
|
|
||||||
#+begin_src matlab
|
|
||||||
save('./active_damping/mat/plants.mat', 'G_rmc', '-append');
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
** Conclusion
|
** Conclusion
|
||||||
#+begin_important
|
#+begin_important
|
||||||
Relative Motion Control:
|
Relative Motion Control:
|
||||||
@ -1264,11 +1285,34 @@ Relative Motion Control:
|
|||||||
#+end_important
|
#+end_important
|
||||||
|
|
||||||
* Direct Velocity Feedback
|
* Direct Velocity Feedback
|
||||||
|
:PROPERTIES:
|
||||||
|
:header-args:matlab+: :tangle matlab/dvf.m
|
||||||
|
:header-args:matlab+: :comments org :mkdirp yes
|
||||||
|
:END:
|
||||||
<<sec:dvf>>
|
<<sec:dvf>>
|
||||||
|
|
||||||
|
** ZIP file containing the data and matlab files :ignore:
|
||||||
|
#+begin_src bash :exports none :results none
|
||||||
|
if [ matlab/dvf.m -nt data/dvf.zip ]; then
|
||||||
|
cp matlab/dvf.m dvf.m;
|
||||||
|
zip data/dvf \
|
||||||
|
mat/plant.mat \
|
||||||
|
dvf.m
|
||||||
|
rm dvf.m;
|
||||||
|
fi
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_note
|
||||||
|
All the files (data and Matlab scripts) are accessible [[file:data/dvf.zip][here]].
|
||||||
|
#+end_note
|
||||||
|
|
||||||
** Introduction :ignore:
|
** Introduction :ignore:
|
||||||
In the Relative Motion Control (RMC), a feedback is applied between the measured velocity of the platform to the actuator force input.
|
In the Relative Motion Control (RMC), a feedback is applied between the measured velocity of the platform to the actuator force input.
|
||||||
|
|
||||||
** One degree-of-freedom example
|
** One degree-of-freedom example
|
||||||
|
:PROPERTIES:
|
||||||
|
:header-args:matlab+: :tangle no
|
||||||
|
:END:
|
||||||
<<sec:dvf_1dof>>
|
<<sec:dvf_1dof>>
|
||||||
*** Equations
|
*** Equations
|
||||||
#+begin_src latex :file dvf_1dof.pdf :post pdf2svg(file=*this*, ext="png") :exports results
|
#+begin_src latex :file dvf_1dof.pdf :post pdf2svg(file=*this*, ext="png") :exports results
|
||||||
@ -1481,8 +1525,6 @@ Let's load the undamped plant:
|
|||||||
|
|
||||||
Let's look at the transfer function from actuator forces in the nano-hexapod to the measured velocity of the nano-hexapod platform in the direction of the corresponding actuator for all 6 pairs of actuator/sensor (figure [[fig:dvf_plant]]).
|
Let's look at the transfer function from actuator forces in the nano-hexapod to the measured velocity of the nano-hexapod platform in the direction of the corresponding actuator for all 6 pairs of actuator/sensor (figure [[fig:dvf_plant]]).
|
||||||
|
|
||||||
The plant looks to complicated to be reasonably controlled.
|
|
||||||
|
|
||||||
#+begin_src matlab :exports none
|
#+begin_src matlab :exports none
|
||||||
freqs = logspace(0, 3, 1000);
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
@ -1520,15 +1562,241 @@ The plant looks to complicated to be reasonably controlled.
|
|||||||
#+CAPTION: Transfer function from forces applied in the legs to leg velocity sensor ([[./figs/dvf_plant.png][png]], [[./figs/dvf_plant.pdf][pdf]])
|
#+CAPTION: Transfer function from forces applied in the legs to leg velocity sensor ([[./figs/dvf_plant.png][png]], [[./figs/dvf_plant.pdf][pdf]])
|
||||||
[[file:figs/dvf_plant.png]]
|
[[file:figs/dvf_plant.png]]
|
||||||
|
|
||||||
|
The controller is defined below and the obtained loop gain is shown in figure [[fig:dvf_open_loop_gain]].
|
||||||
|
|
||||||
|
#+begin_src matlab
|
||||||
|
K_dvf = tf(3e4);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
|
||||||
|
ax1 = subplot(2, 1, 1);
|
||||||
|
hold on;
|
||||||
|
for i=1:6
|
||||||
|
plot(freqs, abs(squeeze(freqresp(K_dvf*G.G_geoph(['Vm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
|
||||||
|
end
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||||
|
|
||||||
|
ax2 = subplot(2, 1, 2);
|
||||||
|
hold on;
|
||||||
|
for i=1:6
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(K_dvf*G.G_geoph(['Vm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
|
||||||
|
end
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||||
|
ylim([-180, 180]);
|
||||||
|
yticks([-180, -90, 0, 90, 180]);
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||||
|
#+begin_src matlab :var filepath="figs/dvf_open_loop_gain.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||||
|
<<plt-matlab>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+NAME: fig:dvf_open_loop_gain
|
||||||
|
#+CAPTION: Loop Gain for DVF ([[./figs/dvf_open_loop_gain.png][png]], [[./figs/dvf_open_loop_gain.pdf][pdf]])
|
||||||
|
[[file:figs/dvf_open_loop_gain.png]]
|
||||||
|
|
||||||
|
** Identification of the damped plant
|
||||||
|
Let's initialize the system prior to identification.
|
||||||
|
#+begin_src matlab
|
||||||
|
initializeInputs();
|
||||||
|
initializeGround();
|
||||||
|
initializeGranite();
|
||||||
|
initializeTy();
|
||||||
|
initializeRy();
|
||||||
|
initializeRz();
|
||||||
|
initializeMicroHexapod();
|
||||||
|
initializeAxisc();
|
||||||
|
initializeMirror();
|
||||||
|
initializeNanoHexapod(struct('actuator', 'piezo'));
|
||||||
|
initializeSample(struct('mass', 50));
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
And initialize the controllers.
|
||||||
|
#+begin_src matlab
|
||||||
|
K = tf(zeros(6));
|
||||||
|
save('./mat/controllers.mat', 'K', '-append');
|
||||||
|
K_iff = tf(zeros(6));
|
||||||
|
save('./mat/controllers.mat', 'K_iff', '-append');
|
||||||
|
K_rmc = tf(zeros(6));
|
||||||
|
save('./mat/controllers.mat', 'K_rmc', '-append');
|
||||||
|
K_dvf = -K_dvf*eye(6);
|
||||||
|
save('./mat/controllers.mat', 'K_dvf', '-append');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
We identify the system dynamics now that the RMC controller is ON.
|
||||||
|
#+begin_src matlab
|
||||||
|
G_dvf = identifyPlant();
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
And we save the damped plant for further analysis.
|
||||||
|
#+begin_src matlab
|
||||||
|
save('./active_damping/mat/plants.mat', 'G_dvf', '-append');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
** Sensitivity to disturbances
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
|
||||||
|
subplot(2, 1, 1);
|
||||||
|
title('$D_g$ to $D$');
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_gm('Dx', 'Dgx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / D_{g,x}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_gm('Dy', 'Dgy'), freqs, 'Hz'))), 'DisplayName', '$\left|D_y / D_{g,y}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_gm('Dz', 'Dgz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / D_{g,z}\right|$');
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_gm('Dx', 'Dgx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_gm('Dy', 'Dgy'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_gm('Dz', 'Dgz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]');
|
||||||
|
legend('location', 'northeast');
|
||||||
|
|
||||||
|
subplot(2, 1, 2);
|
||||||
|
title('$F_s$ to $D$');
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_fs('Dx', 'Fsx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / F_{s,x}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_fs('Dy', 'Fsy'), freqs, 'Hz'))), 'DisplayName', '$\left|D_y / F_{s,y}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_fs('Dz', 'Fsz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{s,z}\right|$');
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_fs('Dx', 'Fsx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_fs('Dy', 'Fsy'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_fs('Dz', 'Fsz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||||
|
legend('location', 'northeast');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||||
|
#+begin_src matlab :var filepath="figs/sensitivity_dist_dvf.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||||
|
<<plt-matlab>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+NAME: fig:sensitivity_dist_dvf
|
||||||
|
#+CAPTION: Sensitivity to disturbance once the DVF controller is applied to the system ([[./figs/sensitivity_dist_dvf.png][png]], [[./figs/sensitivity_dist_dvf.pdf][pdf]])
|
||||||
|
[[file:figs/sensitivity_dist_dvf.png]]
|
||||||
|
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_dist('Dz', 'Frzz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{rz, z}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_dist('Dz', 'Ftyz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{ty, z}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_dist('Dx', 'Ftyx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / F_{ty, x}\right|$');
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_dist('Dz', 'Frzz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_dist('Dz', 'Ftyz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_dist('Dx', 'Ftyx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||||
|
legend('location', 'northeast');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||||
|
#+begin_src matlab :var filepath="figs/sensitivity_dist_stages_dvf.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||||
|
<<plt-matlab>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+NAME: fig:sensitivity_dist_stages_dvf
|
||||||
|
#+CAPTION: Sensitivity to force disturbances in various stages when DVF is applied ([[./figs/sensitivity_dist_stages_dvf.png][png]], [[./figs/sensitivity_dist_stages_dvf.pdf][pdf]])
|
||||||
|
[[file:figs/sensitivity_dist_stages_dvf.png]]
|
||||||
|
|
||||||
|
** Damped Plant
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
|
||||||
|
ax1 = subplot(2, 2, 1);
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Dx', 'Fnx'), freqs, 'Hz'))));
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Dy', 'Fny'), freqs, 'Hz'))));
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Dz', 'Fnz'), freqs, 'Hz'))));
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), '--');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_cart('Dy', 'Fny'), freqs, 'Hz'))), '--');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), '--');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||||
|
|
||||||
|
ax2 = subplot(2, 2, 2);
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Rx', 'Mnx'), freqs, 'Hz'))));
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Ry', 'Mny'), freqs, 'Hz'))));
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Rz', 'Mnz'), freqs, 'Hz'))));
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_cart('Rx', 'Mnx'), freqs, 'Hz'))), '--');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_cart('Ry', 'Mny'), freqs, 'Hz'))), '--');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_cart('Rz', 'Mnz'), freqs, 'Hz'))), '--');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [rad/(Nm)]'); xlabel('Frequency [Hz]');
|
||||||
|
|
||||||
|
ax3 = subplot(2, 2, 3);
|
||||||
|
hold on;
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / F_{n,x}\right|$');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Dy', 'Fny'), freqs, 'Hz'))), 'DisplayName', '$\left|D_y / F_{n,y}\right|$');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{n,z}\right|$');
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf.G_cart('Dy', 'Fny'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||||
|
ylim([-180, 180]);
|
||||||
|
yticks([-180, -90, 0, 90, 180]);
|
||||||
|
legend('location', 'northwest');
|
||||||
|
|
||||||
|
ax4 = subplot(2, 2, 4);
|
||||||
|
hold on;
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Rx', 'Mnx'), freqs, 'Hz'))), 'DisplayName', '$\left|R_x / M_{n,x}\right|$');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Ry', 'Mny'), freqs, 'Hz'))), 'DisplayName', '$\left|R_y / M_{n,y}\right|$');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Rz', 'Mnz'), freqs, 'Hz'))), 'DisplayName', '$\left|R_z / M_{n,z}\right|$');
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf.G_cart('Rx', 'Mnx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf.G_cart('Ry', 'Mny'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf.G_cart('Rz', 'Mnz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||||
|
ylim([-180, 180]);
|
||||||
|
yticks([-180, -90, 0, 90, 180]);
|
||||||
|
legend('location', 'northwest');
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2,ax3,ax4],'x');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||||
|
#+begin_src matlab :var filepath="figs/plant_dvf_damped.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||||
|
<<plt-matlab>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+NAME: fig:plant_dvf_damped
|
||||||
|
#+CAPTION: Damped Plant after DVF is applied ([[./figs/plant_dvf_damped.png][png]], [[./figs/plant_dvf_damped.pdf][pdf]])
|
||||||
|
[[file:figs/plant_dvf_damped.png]]
|
||||||
|
|
||||||
** Conclusion
|
** Conclusion
|
||||||
#+begin_important
|
#+begin_important
|
||||||
Direct Velocity Feedback:
|
Direct Velocity Feedback:
|
||||||
- Not usable
|
|
||||||
#+end_important
|
#+end_important
|
||||||
|
|
||||||
* Comparison
|
* Comparison
|
||||||
<<sec:comparison>>
|
<<sec:comparison>>
|
||||||
|
** Introduction :ignore:
|
||||||
** Matlab Init :noexport:ignore:
|
** Matlab Init :noexport:ignore:
|
||||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||||
<<matlab-dir>>
|
<<matlab-dir>>
|
||||||
@ -1542,36 +1810,254 @@ Direct Velocity Feedback:
|
|||||||
cd('../');
|
cd('../');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Comparison
|
** Load the plants
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
load('./active_damping/mat/plants.mat', 'G', 'G_iff', 'G_rmc');
|
load('./active_damping/mat/plants.mat', 'G', 'G_iff', 'G_rmc', 'G_dvf');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
|
** Sensitivity to Disturbance
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
title('$D_{g,z}$ to $D_z$');
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_gm( 'Dz', 'Dgz'), freqs, 'Hz'))), 'k-' , 'DisplayName', 'Undamped');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_iff.G_gm('Dz', 'Dgz'), freqs, 'Hz'))), 'k:' , 'DisplayName', 'IFF');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_gm('Dz', 'Dgz'), freqs, 'Hz'))), 'k--', 'DisplayName', 'RMC');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_gm('Dz', 'Dgz'), freqs, 'Hz'))), 'k-.', 'DisplayName', 'DVF');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]');
|
||||||
|
legend('location', 'northeast');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||||
|
#+begin_src matlab :var filepath="figs/sensitivity_comp_ground_motion_z.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||||
|
<<plt-matlab>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+NAME: fig:sensitivity_comp_ground_motion_z
|
||||||
|
#+CAPTION: caption ([[./figs/sensitivity_comp_ground_motion_z.png][png]], [[./figs/sensitivity_comp_ground_motion_z.pdf][pdf]])
|
||||||
|
[[file:figs/sensitivity_comp_ground_motion_z.png]]
|
||||||
|
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
title('$F_{s,z}$ to $D_z$');
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_fs( 'Dz', 'Fsz'), freqs, 'Hz'))), 'k-' , 'DisplayName', 'Undamped');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_iff.G_fs('Dz', 'Fsz'), freqs, 'Hz'))), 'k:' , 'DisplayName', 'IFF');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_fs('Dz', 'Fsz'), freqs, 'Hz'))), 'k--', 'DisplayName', 'RMC');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_fs('Dz', 'Fsz'), freqs, 'Hz'))), 'k-.', 'DisplayName', 'DVF');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||||
|
legend('location', 'northeast');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||||
|
#+begin_src matlab :var filepath="figs/sensitivity_comp_direct_forces_z.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||||
|
<<plt-matlab>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+NAME: fig:sensitivity_comp_direct_forces_z
|
||||||
|
#+CAPTION: caption ([[./figs/sensitivity_comp_direct_forces_z.png][png]], [[./figs/sensitivity_comp_direct_forces_z.pdf][pdf]])
|
||||||
|
[[file:figs/sensitivity_comp_direct_forces_z.png]]
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
title('$F_{rz,z}$ to $D_z$');
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_dist( 'Dz', 'Frzz'), freqs, 'Hz'))), 'k-' , 'DisplayName', 'Undamped');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_iff.G_dist('Dz', 'Frzz'), freqs, 'Hz'))), 'k:' , 'DisplayName', 'IFF');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_dist('Dz', 'Frzz'), freqs, 'Hz'))), 'k--', 'DisplayName', 'RMC');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_dist('Dz', 'Frzz'), freqs, 'Hz'))), 'k-.', 'DisplayName', 'DVF');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||||
|
legend('location', 'northeast');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||||
|
#+begin_src matlab :var filepath="figs/sensitivity_comp_spindle_z.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||||
|
<<plt-matlab>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+NAME: fig:sensitivity_comp_spindle_z
|
||||||
|
#+CAPTION: caption ([[./figs/sensitivity_comp_spindle_z.png][png]], [[./figs/sensitivity_comp_spindle_z.pdf][pdf]])
|
||||||
|
[[file:figs/sensitivity_comp_spindle_z.png]]
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
title('$F_{ty,z}$ to $D_z$');
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_dist( 'Dz', 'Ftyz'), freqs, 'Hz'))), 'k-' , 'DisplayName', 'Undamped');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_iff.G_dist('Dz', 'Ftyz'), freqs, 'Hz'))), 'k:' , 'DisplayName', 'IFF');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_dist('Dz', 'Ftyz'), freqs, 'Hz'))), 'k--', 'DisplayName', 'RMC');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_dist('Dz', 'Ftyz'), freqs, 'Hz'))), 'k-.', 'DisplayName', 'DVF');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||||
|
legend('location', 'northeast');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||||
|
#+begin_src matlab :var filepath="figs/sensitivity_comp_ty_z.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||||
|
<<plt-matlab>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+NAME: fig:sensitivity_comp_ty_z
|
||||||
|
#+CAPTION: caption ([[./figs/sensitivity_comp_ty_z.png][png]], [[./figs/sensitivity_comp_ty_z.pdf][pdf]])
|
||||||
|
[[file:figs/sensitivity_comp_ty_z.png]]
|
||||||
|
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
title('$F_{ty,x}$ to $D_x$');
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_dist( 'Dx', 'Ftyx'), freqs, 'Hz'))), 'k-' , 'DisplayName', 'Undamped');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_iff.G_dist('Dx', 'Ftyx'), freqs, 'Hz'))), 'k:' , 'DisplayName', 'IFF');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_dist('Dx', 'Ftyx'), freqs, 'Hz'))), 'k--', 'DisplayName', 'RMC');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_dist('Dx', 'Ftyx'), freqs, 'Hz'))), 'k-.', 'DisplayName', 'DVF');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||||
|
legend('location', 'northeast');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||||
|
#+begin_src matlab :var filepath="figs/sensitivity_comp_ty_x.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||||
|
<<plt-matlab>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+NAME: fig:sensitivity_comp_ty_x
|
||||||
|
#+CAPTION: caption ([[./figs/sensitivity_comp_ty_x.png][png]], [[./figs/sensitivity_comp_ty_x.pdf][pdf]])
|
||||||
|
[[file:figs/sensitivity_comp_ty_x.png]]
|
||||||
|
|
||||||
|
** Damped Plant
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
|
||||||
|
title('$F_{n,z}$ to $D_z$');
|
||||||
|
ax1 = subplot(2, 1, 1);
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart( 'Dz', 'Fnz'), freqs, 'Hz'))), 'k-' , 'DisplayName', 'Undamped');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_iff.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), 'k:' , 'DisplayName', 'IFF');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), 'k--', 'DisplayName', 'RMC');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), 'k-.', 'DisplayName', 'DVF');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||||
|
legend('location', 'northeast');
|
||||||
|
|
||||||
|
ax2 = subplot(2, 1, 2);
|
||||||
|
hold on;
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart ('Dz', 'Fnz'), freqs, 'Hz'))), 'k-');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_iff.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), 'k:');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_rmc.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), 'k--');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), 'k-.');
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||||
|
ylim([-180, 180]);
|
||||||
|
yticks([-180, -90, 0, 90, 180]);
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||||
|
#+begin_src matlab :var filepath="figs/plant_comp_damping_z.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||||
|
<<plt-matlab>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+NAME: fig:plant_comp_damping_z
|
||||||
|
#+CAPTION: Plant for the $z$ direction for different active damping technique used ([[./figs/plant_comp_damping_z.png][png]], [[./figs/plant_comp_damping_z.pdf][pdf]])
|
||||||
|
[[file:figs/plant_comp_damping_z.png]]
|
||||||
|
|
||||||
#+begin_src matlab :exports none
|
#+begin_src matlab :exports none
|
||||||
freqs = logspace(0, 3, 1000);
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
figure;
|
figure;
|
||||||
|
|
||||||
subplot(2, 1, 1);
|
title('$F_{n,z}$ to $D_z$');
|
||||||
title('$D_g$ to $D$');
|
ax1 = subplot(2, 1, 1);
|
||||||
hold on;
|
hold on;
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_gm( 'Dx', 'Dgx'), freqs, 'Hz'))), 'DisplayName', 'Undamped');
|
plot(freqs, abs(squeeze(freqresp(G.G_cart( 'Dx', 'Fnx'), freqs, 'Hz'))), 'k-' , 'DisplayName', 'Undamped');
|
||||||
plot(freqs, abs(squeeze(freqresp(G_iff.G_gm('Dx', 'Dgx'), freqs, 'Hz'))), 'DisplayName', 'IFF');
|
plot(freqs, abs(squeeze(freqresp(G_iff.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), 'k:' , 'DisplayName', 'IFF');
|
||||||
plot(freqs, abs(squeeze(freqresp(G_rmc.G_gm('Dx', 'Dgx'), freqs, 'Hz'))), 'DisplayName', 'RMC');
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), 'k--', 'DisplayName', 'RMC');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), 'k-.', 'DisplayName', 'DVF');
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]');
|
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||||
legend('location', 'northeast');
|
legend('location', 'northeast');
|
||||||
|
|
||||||
subplot(2, 1, 2);
|
ax2 = subplot(2, 1, 2);
|
||||||
title('$F_s$ to $D$');
|
|
||||||
hold on;
|
hold on;
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_fs( 'Dx', 'Fsx'), freqs, 'Hz'))), 'DisplayName', 'Undamped');
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart ('Dx', 'Fnx'), freqs, 'Hz'))), 'k-');
|
||||||
plot(freqs, abs(squeeze(freqresp(G_iff.G_fs('Dx', 'Fsx'), freqs, 'Hz'))), 'DisplayName', 'IFF');
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_iff.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), 'k:');
|
||||||
plot(freqs, abs(squeeze(freqresp(G_rmc.G_fs('Dx', 'Fsx'), freqs, 'Hz'))), 'DisplayName', 'RMC');
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_rmc.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), 'k--');
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), 'k-.');
|
||||||
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
hold off;
|
||||||
legend('location', 'northeast');
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||||
|
ylim([-180, 180]);
|
||||||
|
yticks([-180, -90, 0, 90, 180]);
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||||
|
#+begin_src matlab :var filepath="figs/plant_comp_damping_x.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||||
|
<<plt-matlab>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+NAME: fig:plant_comp_damping_x
|
||||||
|
#+CAPTION: Plant for the $x$ direction for different active damping technique used ([[./figs/plant_comp_damping_x.png][png]], [[./figs/plant_comp_damping_x.pdf][pdf]])
|
||||||
|
[[file:figs/plant_comp_damping_x.png]]
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
|
||||||
|
title('$F_{n,x}$ to $R_z$');
|
||||||
|
ax1 = subplot(2, 1, 1);
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart( 'Rz', 'Fnx'), freqs, 'Hz'))), 'k-' , 'DisplayName', 'Undamped');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_iff.G_cart('Rz', 'Fnx'), freqs, 'Hz'))), 'k:' , 'DisplayName', 'IFF');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_cart('Rz', 'Fnx'), freqs, 'Hz'))), 'k--', 'DisplayName', 'RMC');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_cart('Rz', 'Fnx'), freqs, 'Hz'))), 'k-.', 'DisplayName', 'DVF');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||||
|
legend('location', 'northeast');
|
||||||
|
|
||||||
|
ax2 = subplot(2, 1, 2);
|
||||||
|
hold on;
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart ('Ry', 'Fnx'), freqs, 'Hz'))), 'k-');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_iff.G_cart('Ry', 'Fnx'), freqs, 'Hz'))), 'k:');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_rmc.G_cart('Ry', 'Fnx'), freqs, 'Hz'))), 'k--');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf.G_cart('Ry', 'Fnx'), freqs, 'Hz'))), 'k-.');
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||||
|
ylim([-180, 180]);
|
||||||
|
yticks([-180, -90, 0, 90, 180]);
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||||
|
#+begin_src matlab :var filepath="figs/plant_comp_damping_coupling.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||||
|
<<plt-matlab>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+NAME: fig:plant_comp_damping_coupling
|
||||||
|
#+CAPTION: Comparison of one off-diagonal plant for different damping technique applied ([[./figs/plant_comp_damping_coupling.png][png]], [[./figs/plant_comp_damping_coupling.pdf][pdf]])
|
||||||
|
[[file:figs/plant_comp_damping_coupling.png]]
|
||||||
|
|
||||||
* Conclusion
|
* Conclusion
|
||||||
<<sec:conclusion>>
|
<<sec:conclusion>>
|
||||||
|
|||||||
241
active_damping/matlab/dvf.m
Normal file
241
active_damping/matlab/dvf.m
Normal file
@ -0,0 +1,241 @@
|
|||||||
|
%% Clear Workspace and Close figures
|
||||||
|
clear; close all; clc;
|
||||||
|
|
||||||
|
%% Intialize Laplace variable
|
||||||
|
s = zpk('s');
|
||||||
|
|
||||||
|
open 'simscape/sim_nano_station_id.slx'
|
||||||
|
|
||||||
|
% Control Design
|
||||||
|
% Let's load the undamped plant:
|
||||||
|
|
||||||
|
load('./active_damping/mat/plants.mat', 'G');
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% Let's look at the transfer function from actuator forces in the nano-hexapod to the measured velocity of the nano-hexapod platform in the direction of the corresponding actuator for all 6 pairs of actuator/sensor (figure [[fig:dvf_plant]]).
|
||||||
|
|
||||||
|
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
|
||||||
|
ax1 = subplot(2, 1, 1);
|
||||||
|
hold on;
|
||||||
|
for i=1:6
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_geoph(['Vm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
|
||||||
|
end
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||||
|
|
||||||
|
ax2 = subplot(2, 1, 2);
|
||||||
|
hold on;
|
||||||
|
for i=1:6
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_geoph(['Vm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
|
||||||
|
end
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||||
|
ylim([-180, 180]);
|
||||||
|
yticks([-180, -90, 0, 90, 180]);
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% #+NAME: fig:dvf_plant
|
||||||
|
% #+CAPTION: Transfer function from forces applied in the legs to leg velocity sensor ([[./figs/dvf_plant.png][png]], [[./figs/dvf_plant.pdf][pdf]])
|
||||||
|
% [[file:figs/dvf_plant.png]]
|
||||||
|
|
||||||
|
% The controller is defined below and the obtained loop gain is shown in figure [[fig:dvf_open_loop_gain]].
|
||||||
|
|
||||||
|
|
||||||
|
K_dvf = tf(3e4);
|
||||||
|
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
|
||||||
|
ax1 = subplot(2, 1, 1);
|
||||||
|
hold on;
|
||||||
|
for i=1:6
|
||||||
|
plot(freqs, abs(squeeze(freqresp(K_dvf*G.G_geoph(['Vm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
|
||||||
|
end
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||||
|
|
||||||
|
ax2 = subplot(2, 1, 2);
|
||||||
|
hold on;
|
||||||
|
for i=1:6
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(K_dvf*G.G_geoph(['Vm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
|
||||||
|
end
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||||
|
ylim([-180, 180]);
|
||||||
|
yticks([-180, -90, 0, 90, 180]);
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
|
||||||
|
% Identification of the damped plant
|
||||||
|
% Let's initialize the system prior to identification.
|
||||||
|
|
||||||
|
initializeGround();
|
||||||
|
initializeGranite();
|
||||||
|
initializeTy();
|
||||||
|
initializeRy();
|
||||||
|
initializeRz();
|
||||||
|
initializeMicroHexapod();
|
||||||
|
initializeAxisc();
|
||||||
|
initializeMirror();
|
||||||
|
initializeNanoHexapod(struct('actuator', 'piezo'));
|
||||||
|
initializeSample(struct('mass', 50));
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% And initialize the controllers.
|
||||||
|
|
||||||
|
K = tf(zeros(6));
|
||||||
|
save('./mat/controllers.mat', 'K', '-append');
|
||||||
|
K_iff = tf(zeros(6));
|
||||||
|
save('./mat/controllers.mat', 'K_iff', '-append');
|
||||||
|
K_rmc = tf(zeros(6));
|
||||||
|
save('./mat/controllers.mat', 'K_rmc', '-append');
|
||||||
|
K_dvf = -K_dvf*eye(6);
|
||||||
|
save('./mat/controllers.mat', 'K_dvf', '-append');
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% We identify the system dynamics now that the RMC controller is ON.
|
||||||
|
|
||||||
|
G_dvf = identifyPlant();
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% And we save the damped plant for further analysis.
|
||||||
|
|
||||||
|
save('./active_damping/mat/plants.mat', 'G_dvf', '-append');
|
||||||
|
|
||||||
|
% Sensitivity to disturbances
|
||||||
|
|
||||||
|
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
|
||||||
|
subplot(2, 1, 1);
|
||||||
|
title('$D_g$ to $D$');
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_gm('Dx', 'Dgx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / D_{g,x}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_gm('Dy', 'Dgy'), freqs, 'Hz'))), 'DisplayName', '$\left|D_y / D_{g,y}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_gm('Dz', 'Dgz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / D_{g,z}\right|$');
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_gm('Dx', 'Dgx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_gm('Dy', 'Dgy'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_gm('Dz', 'Dgz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]');
|
||||||
|
legend('location', 'northeast');
|
||||||
|
|
||||||
|
subplot(2, 1, 2);
|
||||||
|
title('$F_s$ to $D$');
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_fs('Dx', 'Fsx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / F_{s,x}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_fs('Dy', 'Fsy'), freqs, 'Hz'))), 'DisplayName', '$\left|D_y / F_{s,y}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_fs('Dz', 'Fsz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{s,z}\right|$');
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_fs('Dx', 'Fsx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_fs('Dy', 'Fsy'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_fs('Dz', 'Fsz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||||
|
legend('location', 'northeast');
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% #+NAME: fig:sensitivity_dist_dvf
|
||||||
|
% #+CAPTION: Sensitivity to disturbance once the DVF controller is applied to the system ([[./figs/sensitivity_dist_dvf.png][png]], [[./figs/sensitivity_dist_dvf.pdf][pdf]])
|
||||||
|
% [[file:figs/sensitivity_dist_dvf.png]]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_dist('Dz', 'Frzz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{rz, z}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_dist('Dz', 'Ftyz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{ty, z}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_dist('Dx', 'Ftyx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / F_{ty, x}\right|$');
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_dist('Dz', 'Frzz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_dist('Dz', 'Ftyz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_dist('Dx', 'Ftyx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||||
|
legend('location', 'northeast');
|
||||||
|
|
||||||
|
% Damped Plant
|
||||||
|
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
|
||||||
|
ax1 = subplot(2, 2, 1);
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Dx', 'Fnx'), freqs, 'Hz'))));
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Dy', 'Fny'), freqs, 'Hz'))));
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Dz', 'Fnz'), freqs, 'Hz'))));
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), '--');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_cart('Dy', 'Fny'), freqs, 'Hz'))), '--');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), '--');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||||
|
|
||||||
|
ax2 = subplot(2, 2, 2);
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Rx', 'Mnx'), freqs, 'Hz'))));
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Ry', 'Mny'), freqs, 'Hz'))));
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Rz', 'Mnz'), freqs, 'Hz'))));
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_cart('Rx', 'Mnx'), freqs, 'Hz'))), '--');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_cart('Ry', 'Mny'), freqs, 'Hz'))), '--');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_dvf.G_cart('Rz', 'Mnz'), freqs, 'Hz'))), '--');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [rad/(Nm)]'); xlabel('Frequency [Hz]');
|
||||||
|
|
||||||
|
ax3 = subplot(2, 2, 3);
|
||||||
|
hold on;
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / F_{n,x}\right|$');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Dy', 'Fny'), freqs, 'Hz'))), 'DisplayName', '$\left|D_y / F_{n,y}\right|$');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{n,z}\right|$');
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf.G_cart('Dy', 'Fny'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||||
|
ylim([-180, 180]);
|
||||||
|
yticks([-180, -90, 0, 90, 180]);
|
||||||
|
legend('location', 'northwest');
|
||||||
|
|
||||||
|
ax4 = subplot(2, 2, 4);
|
||||||
|
hold on;
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Rx', 'Mnx'), freqs, 'Hz'))), 'DisplayName', '$\left|R_x / M_{n,x}\right|$');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Ry', 'Mny'), freqs, 'Hz'))), 'DisplayName', '$\left|R_y / M_{n,y}\right|$');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Rz', 'Mnz'), freqs, 'Hz'))), 'DisplayName', '$\left|R_z / M_{n,z}\right|$');
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf.G_cart('Rx', 'Mnx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf.G_cart('Ry', 'Mny'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf.G_cart('Rz', 'Mnz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||||
|
ylim([-180, 180]);
|
||||||
|
yticks([-180, -90, 0, 90, 180]);
|
||||||
|
legend('location', 'northwest');
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2,ax3,ax4],'x');
|
||||||
281
active_damping/matlab/iff.m
Normal file
281
active_damping/matlab/iff.m
Normal file
@ -0,0 +1,281 @@
|
|||||||
|
%% Clear Workspace and Close figures
|
||||||
|
clear; close all; clc;
|
||||||
|
|
||||||
|
%% Intialize Laplace variable
|
||||||
|
s = zpk('s');
|
||||||
|
|
||||||
|
open 'simscape/sim_nano_station_id.slx'
|
||||||
|
|
||||||
|
% Control Design
|
||||||
|
% Let's load the undamped plant:
|
||||||
|
|
||||||
|
load('./active_damping/mat/plants.mat', 'G');
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% Let's look at the transfer function from actuator forces in the nano-hexapod to the force sensor in the nano-hexapod legs for all 6 pairs of actuator/sensor (figure [[fig:iff_plant]]).
|
||||||
|
|
||||||
|
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
|
||||||
|
ax1 = subplot(2, 1, 1);
|
||||||
|
hold on;
|
||||||
|
for i=1:6
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_iff(['Fm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
|
||||||
|
end
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
|
||||||
|
|
||||||
|
ax2 = subplot(2, 1, 2);
|
||||||
|
hold on;
|
||||||
|
for i=1:6
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_iff(['Fm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
|
||||||
|
end
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||||
|
ylim([-180, 180]);
|
||||||
|
yticks([-180, -90, 0, 90, 180]);
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% #+NAME: fig:iff_plant
|
||||||
|
% #+CAPTION: Transfer function from forces applied in the legs to force sensor ([[./figs/iff_plant.png][png]], [[./figs/iff_plant.pdf][pdf]])
|
||||||
|
% [[file:figs/iff_plant.png]]
|
||||||
|
|
||||||
|
% The controller for each pair of actuator/sensor is:
|
||||||
|
|
||||||
|
K_iff = -1000/s;
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% The corresponding loop gains are shown in figure [[fig:iff_open_loop]].
|
||||||
|
|
||||||
|
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
|
||||||
|
ax1 = subplot(2, 1, 1);
|
||||||
|
hold on;
|
||||||
|
for i=1:6
|
||||||
|
plot(freqs, abs(squeeze(freqresp(K_iff*G.G_iff(['Fm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
|
||||||
|
end
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
|
||||||
|
|
||||||
|
ax2 = subplot(2, 1, 2);
|
||||||
|
hold on;
|
||||||
|
for i=1:6
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(K_iff*G.G_iff(['Fm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
|
||||||
|
end
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||||
|
ylim([-180, 180]);
|
||||||
|
yticks([-180, -90, 0, 90, 180]);
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
|
||||||
|
% Identification of the damped plant
|
||||||
|
% Let's initialize the system prior to identification.
|
||||||
|
|
||||||
|
initializeGround();
|
||||||
|
initializeGranite();
|
||||||
|
initializeTy();
|
||||||
|
initializeRy();
|
||||||
|
initializeRz();
|
||||||
|
initializeMicroHexapod();
|
||||||
|
initializeAxisc();
|
||||||
|
initializeMirror();
|
||||||
|
initializeNanoHexapod(struct('actuator', 'piezo'));
|
||||||
|
initializeSample(struct('mass', 50));
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% All the controllers are set to 0.
|
||||||
|
|
||||||
|
K = tf(zeros(6));
|
||||||
|
save('./mat/controllers.mat', 'K', '-append');
|
||||||
|
K_iff = -K_iff*eye(6);
|
||||||
|
save('./mat/controllers.mat', 'K_iff', '-append');
|
||||||
|
K_rmc = tf(zeros(6));
|
||||||
|
save('./mat/controllers.mat', 'K_rmc', '-append');
|
||||||
|
K_dvf = tf(zeros(6));
|
||||||
|
save('./mat/controllers.mat', 'K_dvf', '-append');
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% We identify the system dynamics now that the IFF controller is ON.
|
||||||
|
|
||||||
|
G_iff = identifyPlant();
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% And we save the damped plant for further analysis
|
||||||
|
|
||||||
|
save('./active_damping/mat/plants.mat', 'G_iff', '-append');
|
||||||
|
|
||||||
|
% Sensitivity to disturbances
|
||||||
|
% As shown on figure [[fig:sensitivity_dist_iff]]:
|
||||||
|
% - The top platform of the nano-hexapod how behaves as a "free-mass".
|
||||||
|
% - The transfer function from direct forces $F_s$ to the relative displacement $D$ is equivalent to the one of an isolated mass.
|
||||||
|
% - The transfer function from ground motion $D_g$ to the relative displacement $D$ tends to the transfer function from $D_g$ to the displacement of the granite (the sample is being isolated thanks to IFF).
|
||||||
|
% However, as the goal is to make the relative displacement $D$ as small as possible (e.g. to make the sample motion follows the granite motion), this is not a good thing.
|
||||||
|
|
||||||
|
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
|
||||||
|
subplot(2, 1, 1);
|
||||||
|
title('$D_g$ to $D$');
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_gm('Dx', 'Dgx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / D_{g,x}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_gm('Dy', 'Dgy'), freqs, 'Hz'))), 'DisplayName', '$\left|D_y / D_{g,y}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_gm('Dz', 'Dgz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / D_{g,z}\right|$');
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_iff.G_gm('Dx', 'Dgx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_iff.G_gm('Dy', 'Dgy'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_iff.G_gm('Dz', 'Dgz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]');
|
||||||
|
legend('location', 'northeast');
|
||||||
|
|
||||||
|
subplot(2, 1, 2);
|
||||||
|
title('$F_s$ to $D$');
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_fs('Dx', 'Fsx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / F_{s,x}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_fs('Dy', 'Fsy'), freqs, 'Hz'))), 'DisplayName', '$\left|D_y / F_{s,y}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_fs('Dz', 'Fsz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{s,z}\right|$');
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_iff.G_fs('Dx', 'Fsx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_iff.G_fs('Dy', 'Fsy'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_iff.G_fs('Dz', 'Fsz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||||
|
legend('location', 'northeast');
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% #+NAME: fig:sensitivity_dist_iff
|
||||||
|
% #+CAPTION: Sensitivity to disturbance once the IFF controller is applied to the system ([[./figs/sensitivity_dist_iff.png][png]], [[./figs/sensitivity_dist_iff.pdf][pdf]])
|
||||||
|
% [[file:figs/sensitivity_dist_iff.png]]
|
||||||
|
|
||||||
|
% #+begin_warning
|
||||||
|
% The order of the models are very high and thus the plots may be wrong.
|
||||||
|
% For instance, the plots are not the same when using =minreal=.
|
||||||
|
% #+end_warning
|
||||||
|
|
||||||
|
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_dist('Dz', 'Frzz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{rz, z}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_dist('Dz', 'Ftyz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{ty, z}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_dist('Dx', 'Ftyx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / F_{ty, x}\right|$');
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, abs(squeeze(freqresp(minreal(prescale(G_iff.G_dist('Dz', 'Frzz'), {2*pi, 2*pi*1e3})), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(minreal(G_iff.G_dist('Dz', 'Ftyz')), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(minreal(G_iff.G_dist('Dx', 'Ftyx')), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||||
|
legend('location', 'northeast');
|
||||||
|
|
||||||
|
% Damped Plant
|
||||||
|
% Now, look at the new damped plant to control.
|
||||||
|
|
||||||
|
% It damps the plant (resonance of the nano hexapod as well as other resonances) as shown in figure [[fig:plant_iff_damped]].
|
||||||
|
|
||||||
|
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
|
||||||
|
ax1 = subplot(2, 2, 1);
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Dx', 'Fnx'), freqs, 'Hz'))));
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Dy', 'Fny'), freqs, 'Hz'))));
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Dz', 'Fnz'), freqs, 'Hz'))));
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_iff.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), '--');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_iff.G_cart('Dy', 'Fny'), freqs, 'Hz'))), '--');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_iff.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), '--');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||||
|
|
||||||
|
ax2 = subplot(2, 2, 2);
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Rx', 'Mnx'), freqs, 'Hz'))));
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Ry', 'Mny'), freqs, 'Hz'))));
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Rz', 'Mnz'), freqs, 'Hz'))));
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_iff.G_cart('Rx', 'Mnx'), freqs, 'Hz'))), '--');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_iff.G_cart('Ry', 'Mny'), freqs, 'Hz'))), '--');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_iff.G_cart('Rz', 'Mnz'), freqs, 'Hz'))), '--');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [rad/(Nm)]'); xlabel('Frequency [Hz]');
|
||||||
|
|
||||||
|
ax3 = subplot(2, 2, 3);
|
||||||
|
hold on;
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / F_{n,x}\right|$');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Dy', 'Fny'), freqs, 'Hz'))), 'DisplayName', '$\left|D_y / F_{n,y}\right|$');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{n,z}\right|$');
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_iff.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_iff.G_cart('Dy', 'Fny'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_iff.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||||
|
ylim([-180, 180]);
|
||||||
|
yticks([-180, -90, 0, 90, 180]);
|
||||||
|
legend('location', 'northwest');
|
||||||
|
|
||||||
|
ax4 = subplot(2, 2, 4);
|
||||||
|
hold on;
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Rx', 'Mnx'), freqs, 'Hz'))), 'DisplayName', '$\left|R_x / M_{n,x}\right|$');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Ry', 'Mny'), freqs, 'Hz'))), 'DisplayName', '$\left|R_y / M_{n,y}\right|$');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Rz', 'Mnz'), freqs, 'Hz'))), 'DisplayName', '$\left|R_z / M_{n,z}\right|$');
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_iff.G_cart('Rx', 'Mnx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_iff.G_cart('Ry', 'Mny'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_iff.G_cart('Rz', 'Mnz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||||
|
ylim([-180, 180]);
|
||||||
|
yticks([-180, -90, 0, 90, 180]);
|
||||||
|
legend('location', 'northwest');
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2,ax3,ax4],'x');
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% #+NAME: fig:plant_iff_damped
|
||||||
|
% #+CAPTION: Damped Plant after IFF is applied ([[./figs/plant_iff_damped.png][png]], [[./figs/plant_iff_damped.pdf][pdf]])
|
||||||
|
% [[file:figs/plant_iff_damped.png]]
|
||||||
|
|
||||||
|
% However, it increases coupling at low frequency (figure [[fig:plant_iff_coupling]]).
|
||||||
|
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
|
||||||
|
for ix = 1:6
|
||||||
|
for iy = 1:6
|
||||||
|
subplot(6, 6, (ix-1)*6 + iy);
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart(ix, iy), freqs, 'Hz'))), 'k-');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_iff.G_cart(ix, iy), freqs, 'Hz'))), 'k--');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylim([1e-12, 1e-5]);
|
||||||
|
end
|
||||||
|
end
|
||||||
246
active_damping/matlab/rmc.m
Normal file
246
active_damping/matlab/rmc.m
Normal file
@ -0,0 +1,246 @@
|
|||||||
|
%% Clear Workspace and Close figures
|
||||||
|
clear; close all; clc;
|
||||||
|
|
||||||
|
%% Intialize Laplace variable
|
||||||
|
s = zpk('s');
|
||||||
|
|
||||||
|
open 'simscape/sim_nano_station_id.slx'
|
||||||
|
|
||||||
|
% Control Design
|
||||||
|
% Let's load the undamped plant:
|
||||||
|
|
||||||
|
load('./active_damping/mat/plants.mat', 'G');
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% Let's look at the transfer function from actuator forces in the nano-hexapod to the measured displacement of the actuator for all 6 pairs of actuator/sensor (figure [[fig:rmc_plant]]).
|
||||||
|
|
||||||
|
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
|
||||||
|
ax1 = subplot(2, 1, 1);
|
||||||
|
hold on;
|
||||||
|
for i=1:6
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_dleg(['Dm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
|
||||||
|
end
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||||
|
|
||||||
|
ax2 = subplot(2, 1, 2);
|
||||||
|
hold on;
|
||||||
|
for i=1:6
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_dleg(['Dm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
|
||||||
|
end
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||||
|
ylim([-180, 180]);
|
||||||
|
yticks([-180, -90, 0, 90, 180]);
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% #+NAME: fig:rmc_plant
|
||||||
|
% #+CAPTION: Transfer function from forces applied in the legs to leg displacement sensor ([[./figs/rmc_plant.png][png]], [[./figs/rmc_plant.pdf][pdf]])
|
||||||
|
% [[file:figs/rmc_plant.png]]
|
||||||
|
|
||||||
|
% The Relative Motion Controller is defined below.
|
||||||
|
% A Low pass Filter is added to make the controller transfer function proper.
|
||||||
|
|
||||||
|
K_rmc = s*50000/(1 + s/2/pi/10000);
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% The obtained loop gains are shown in figure [[fig:rmc_open_loop]].
|
||||||
|
|
||||||
|
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
|
||||||
|
ax1 = subplot(2, 1, 1);
|
||||||
|
hold on;
|
||||||
|
for i=1:6
|
||||||
|
plot(freqs, abs(squeeze(freqresp(K_rmc*G.G_dleg(['Dm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
|
||||||
|
end
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||||
|
|
||||||
|
ax2 = subplot(2, 1, 2);
|
||||||
|
hold on;
|
||||||
|
for i=1:6
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(K_rmc*G.G_dleg(['Dm', num2str(i)], ['F', num2str(i)]), freqs, 'Hz'))));
|
||||||
|
end
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||||
|
ylim([-180, 180]);
|
||||||
|
yticks([-180, -90, 0, 90, 180]);
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
|
||||||
|
% Identification of the damped plant
|
||||||
|
% Let's initialize the system prior to identification.
|
||||||
|
|
||||||
|
initializeGround();
|
||||||
|
initializeGranite();
|
||||||
|
initializeTy();
|
||||||
|
initializeRy();
|
||||||
|
initializeRz();
|
||||||
|
initializeMicroHexapod();
|
||||||
|
initializeAxisc();
|
||||||
|
initializeMirror();
|
||||||
|
initializeNanoHexapod(struct('actuator', 'piezo'));
|
||||||
|
initializeSample(struct('mass', 50));
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% And initialize the controllers.
|
||||||
|
|
||||||
|
K = tf(zeros(6));
|
||||||
|
save('./mat/controllers.mat', 'K', '-append');
|
||||||
|
K_iff = tf(zeros(6));
|
||||||
|
save('./mat/controllers.mat', 'K_iff', '-append');
|
||||||
|
K_rmc = -K_rmc*eye(6);
|
||||||
|
save('./mat/controllers.mat', 'K_rmc', '-append');
|
||||||
|
K_dvf = tf(zeros(6));
|
||||||
|
save('./mat/controllers.mat', 'K_dvf', '-append');
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% We identify the system dynamics now that the RMC controller is ON.
|
||||||
|
|
||||||
|
G_rmc = identifyPlant();
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% And we save the damped plant for further analysis.
|
||||||
|
|
||||||
|
save('./active_damping/mat/plants.mat', 'G_rmc', '-append');
|
||||||
|
|
||||||
|
% Sensitivity to disturbances
|
||||||
|
% As shown in figure [[fig:sensitivity_dist_rmc]], RMC control succeed in lowering the sensitivity to disturbances near resonance of the system.
|
||||||
|
|
||||||
|
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
|
||||||
|
subplot(2, 1, 1);
|
||||||
|
title('$D_g$ to $D$');
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_gm('Dx', 'Dgx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / D_{g,x}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_gm('Dy', 'Dgy'), freqs, 'Hz'))), 'DisplayName', '$\left|D_y / D_{g,y}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_gm('Dz', 'Dgz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / D_{g,z}\right|$');
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_gm('Dx', 'Dgx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_gm('Dy', 'Dgy'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_gm('Dz', 'Dgz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]');
|
||||||
|
legend('location', 'northeast');
|
||||||
|
|
||||||
|
subplot(2, 1, 2);
|
||||||
|
title('$F_s$ to $D$');
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_fs('Dx', 'Fsx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / F_{s,x}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_fs('Dy', 'Fsy'), freqs, 'Hz'))), 'DisplayName', '$\left|D_y / F_{s,y}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_fs('Dz', 'Fsz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{s,z}\right|$');
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_fs('Dx', 'Fsx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_fs('Dy', 'Fsy'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_fs('Dz', 'Fsz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||||
|
legend('location', 'northeast');
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% #+NAME: fig:sensitivity_dist_rmc
|
||||||
|
% #+CAPTION: Sensitivity to disturbance once the RMC controller is applied to the system ([[./figs/sensitivity_dist_rmc.png][png]], [[./figs/sensitivity_dist_rmc.pdf][pdf]])
|
||||||
|
% [[file:figs/sensitivity_dist_rmc.png]]
|
||||||
|
|
||||||
|
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_dist('Dz', 'Frzz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{rz, z}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_dist('Dz', 'Ftyz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{ty, z}\right|$');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_dist('Dx', 'Ftyx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / F_{ty, x}\right|$');
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_dist('Dz', 'Frzz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_dist('Dz', 'Ftyz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_dist('Dx', 'Ftyx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||||
|
legend('location', 'northeast');
|
||||||
|
|
||||||
|
% Damped Plant
|
||||||
|
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
|
||||||
|
ax1 = subplot(2, 2, 1);
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Dx', 'Fnx'), freqs, 'Hz'))));
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Dy', 'Fny'), freqs, 'Hz'))));
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Dz', 'Fnz'), freqs, 'Hz'))));
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), '--');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_cart('Dy', 'Fny'), freqs, 'Hz'))), '--');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), '--');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||||
|
|
||||||
|
ax2 = subplot(2, 2, 2);
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Rx', 'Mnx'), freqs, 'Hz'))));
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Ry', 'Mny'), freqs, 'Hz'))));
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G.G_cart('Rz', 'Mnz'), freqs, 'Hz'))));
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_cart('Rx', 'Mnx'), freqs, 'Hz'))), '--');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_cart('Ry', 'Mny'), freqs, 'Hz'))), '--');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_rmc.G_cart('Rz', 'Mnz'), freqs, 'Hz'))), '--');
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [rad/(Nm)]'); xlabel('Frequency [Hz]');
|
||||||
|
|
||||||
|
ax3 = subplot(2, 2, 3);
|
||||||
|
hold on;
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), 'DisplayName', '$\left|D_x / F_{n,x}\right|$');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Dy', 'Fny'), freqs, 'Hz'))), 'DisplayName', '$\left|D_y / F_{n,y}\right|$');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), 'DisplayName', '$\left|D_z / F_{n,z}\right|$');
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_rmc.G_cart('Dx', 'Fnx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_rmc.G_cart('Dy', 'Fny'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_rmc.G_cart('Dz', 'Fnz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||||
|
ylim([-180, 180]);
|
||||||
|
yticks([-180, -90, 0, 90, 180]);
|
||||||
|
legend('location', 'northwest');
|
||||||
|
|
||||||
|
ax4 = subplot(2, 2, 4);
|
||||||
|
hold on;
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Rx', 'Mnx'), freqs, 'Hz'))), 'DisplayName', '$\left|R_x / M_{n,x}\right|$');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Ry', 'Mny'), freqs, 'Hz'))), 'DisplayName', '$\left|R_y / M_{n,y}\right|$');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G.G_cart('Rz', 'Mnz'), freqs, 'Hz'))), 'DisplayName', '$\left|R_z / M_{n,z}\right|$');
|
||||||
|
set(gca,'ColorOrderIndex',1);
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_rmc.G_cart('Rx', 'Mnx'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_rmc.G_cart('Ry', 'Mny'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_rmc.G_cart('Rz', 'Mnz'), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||||
|
ylim([-180, 180]);
|
||||||
|
yticks([-180, -90, 0, 90, 180]);
|
||||||
|
legend('location', 'northwest');
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2,ax3,ax4],'x');
|
||||||
BIN
figs/dvf_open_loop_gain.png
Normal file
BIN
figs/dvf_open_loop_gain.png
Normal file
Binary file not shown.
|
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|
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|
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|
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BIN
figs/plant_comp_damping_coupling.png
Normal file
BIN
figs/plant_comp_damping_coupling.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 118 KiB |
BIN
figs/plant_comp_damping_x.png
Normal file
BIN
figs/plant_comp_damping_x.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 118 KiB |
BIN
figs/plant_comp_damping_z.png
Normal file
BIN
figs/plant_comp_damping_z.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 104 KiB |
BIN
figs/plant_dvf_damped.png
Normal file
BIN
figs/plant_dvf_damped.png
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|
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|
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|
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|
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@ -3,7 +3,7 @@
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||||
<head>
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<head>
|
||||||
<!-- 2019-10-25 ven. 12:32 -->
|
<!-- 2019-10-25 ven. 16:02 -->
|
||||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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|
||||||
<title>Simscape Uniaxial Model</title>
|
<title>Simscape Uniaxial Model</title>
|
||||||
@ -280,48 +280,48 @@ for the JavaScript code in this tag.
|
|||||||
<h2>Table of Contents</h2>
|
<h2>Table of Contents</h2>
|
||||||
<div id="text-table-of-contents">
|
<div id="text-table-of-contents">
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#orgd9a890c">1. Simscape Model</a></li>
|
<li><a href="#org119d8dc">1. Simscape Model</a></li>
|
||||||
<li><a href="#orgeafc497">2. Undamped System</a>
|
<li><a href="#org95b633d">2. Undamped System</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org631c716">2.1. Init</a></li>
|
<li><a href="#orga87af67">2.1. Init</a></li>
|
||||||
<li><a href="#orgbbef650">2.2. Identification</a></li>
|
<li><a href="#org2d53583">2.2. Identification</a></li>
|
||||||
<li><a href="#orgb5102fd">2.3. Sensitivity to Disturbances</a></li>
|
<li><a href="#orgc443c0b">2.3. Sensitivity to Disturbances</a></li>
|
||||||
<li><a href="#orgafe8970">2.4. Plant</a></li>
|
<li><a href="#orgdb21910">2.4. Plant</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#orgeab4870">3. Integral Force Feedback</a>
|
<li><a href="#org497a34a">3. Integral Force Feedback</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org6cf62a2">3.1. Control Design</a></li>
|
<li><a href="#org90d6383">3.1. Control Design</a></li>
|
||||||
<li><a href="#orgf9a5f33">3.2. Identification</a></li>
|
<li><a href="#orge5c43d3">3.2. Identification</a></li>
|
||||||
<li><a href="#org7a80859">3.3. Sensitivity to Disturbance</a></li>
|
<li><a href="#orgdc6e62f">3.3. Sensitivity to Disturbance</a></li>
|
||||||
<li><a href="#org7bab9e9">3.4. Damped Plant</a></li>
|
<li><a href="#orgf2883d8">3.4. Damped Plant</a></li>
|
||||||
<li><a href="#orgaac01c0">3.5. Conclusion</a></li>
|
<li><a href="#orgb766da3">3.5. Conclusion</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#org8d9b463">4. Relative Motion Control</a>
|
<li><a href="#org0216063">4. Relative Motion Control</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#orgbf2540a">4.1. Control Design</a></li>
|
<li><a href="#orgda1c98e">4.1. Control Design</a></li>
|
||||||
<li><a href="#org1d106d7">4.2. Identification</a></li>
|
<li><a href="#orge3806a0">4.2. Identification</a></li>
|
||||||
<li><a href="#orgeb7d680">4.3. Sensitivity to Disturbance</a></li>
|
<li><a href="#orge58c47d">4.3. Sensitivity to Disturbance</a></li>
|
||||||
<li><a href="#org573eda0">4.4. Damped Plant</a></li>
|
<li><a href="#org70ec2cf">4.4. Damped Plant</a></li>
|
||||||
<li><a href="#org02ca488">4.5. Conclusion</a></li>
|
<li><a href="#orga845b21">4.5. Conclusion</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#org57948ea">5. Direct Velocity Feedback</a>
|
<li><a href="#org7666422">5. Direct Velocity Feedback</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org4b4d061">5.1. Control Design</a></li>
|
<li><a href="#org58e4d64">5.1. Control Design</a></li>
|
||||||
<li><a href="#orgd4f4973">5.2. Identification</a></li>
|
<li><a href="#org7e8b911">5.2. Identification</a></li>
|
||||||
<li><a href="#org6cfeae5">5.3. Sensitivity to Disturbance</a></li>
|
<li><a href="#org2adcafe">5.3. Sensitivity to Disturbance</a></li>
|
||||||
<li><a href="#org89e0408">5.4. Damped Plant</a></li>
|
<li><a href="#orge8b5bd9">5.4. Damped Plant</a></li>
|
||||||
<li><a href="#orgc27bce5">5.5. Conclusion</a></li>
|
<li><a href="#org22d6515">5.5. Conclusion</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#org6dd07d9">6. Comparison of Active Damping Techniques</a>
|
<li><a href="#org55010b4">6. Comparison of Active Damping Techniques</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#orgd62929a">6.1. Load the plants</a></li>
|
<li><a href="#org5cb1e25">6.1. Load the plants</a></li>
|
||||||
<li><a href="#orgbd35b93">6.2. Sensitivity to Disturbance</a></li>
|
<li><a href="#orgc746216">6.2. Sensitivity to Disturbance</a></li>
|
||||||
<li><a href="#org72ab5fd">6.3. Damped Plant</a></li>
|
<li><a href="#orgcd1790f">6.3. Damped Plant</a></li>
|
||||||
<li><a href="#org2c43078">6.4. Conclusion</a></li>
|
<li><a href="#org9a602cb">6.4. Conclusion</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
</ul>
|
</ul>
|
||||||
@ -336,11 +336,11 @@ The idea is to use the same model as the full Simscape Model but to restrict the
|
|||||||
This is done in order to more easily study the system and evaluate control techniques.
|
This is done in order to more easily study the system and evaluate control techniques.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div id="outline-container-orgd9a890c" class="outline-2">
|
<div id="outline-container-org119d8dc" class="outline-2">
|
||||||
<h2 id="orgd9a890c"><span class="section-number-2">1</span> Simscape Model</h2>
|
<h2 id="org119d8dc"><span class="section-number-2">1</span> Simscape Model</h2>
|
||||||
<div class="outline-text-2" id="text-1">
|
<div class="outline-text-2" id="text-1">
|
||||||
<p>
|
<p>
|
||||||
A schematic of the uniaxial model used for simulations is represented in figure <a href="#org9234e2b">1</a>.
|
A schematic of the uniaxial model used for simulations is represented in figure <a href="#org20bfb11">1</a>.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
@ -384,7 +384,7 @@ The control signal \(u\) is:
|
|||||||
</ul>
|
</ul>
|
||||||
|
|
||||||
|
|
||||||
<div id="org9234e2b" class="figure">
|
<div id="org20bfb11" class="figure">
|
||||||
<p><img src="figs/uniaxial-model-nass-flexible.png" alt="uniaxial-model-nass-flexible.png" />
|
<p><img src="figs/uniaxial-model-nass-flexible.png" alt="uniaxial-model-nass-flexible.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 1: </span>Schematic of the uniaxial model used</p>
|
<p><span class="figure-number">Figure 1: </span>Schematic of the uniaxial model used</p>
|
||||||
@ -393,11 +393,11 @@ The control signal \(u\) is:
|
|||||||
|
|
||||||
<p>
|
<p>
|
||||||
Few active damping techniques will be compared in order to decide which sensor is to be included in the system.
|
Few active damping techniques will be compared in order to decide which sensor is to be included in the system.
|
||||||
Schematics of the active damping techniques are displayed in figure <a href="#org49f5486">2</a>.
|
Schematics of the active damping techniques are displayed in figure <a href="#org2eb3599">2</a>.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<div id="org49f5486" class="figure">
|
<div id="org2eb3599" class="figure">
|
||||||
<p><img src="figs/uniaxial-model-nass-flexible-active-damping.png" alt="uniaxial-model-nass-flexible-active-damping.png" />
|
<p><img src="figs/uniaxial-model-nass-flexible-active-damping.png" alt="uniaxial-model-nass-flexible-active-damping.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 2: </span>Comparison of used active damping techniques</p>
|
<p><span class="figure-number">Figure 2: </span>Comparison of used active damping techniques</p>
|
||||||
@ -405,16 +405,16 @@ Schematics of the active damping techniques are displayed in figure <a href="#or
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgeafc497" class="outline-2">
|
<div id="outline-container-org95b633d" class="outline-2">
|
||||||
<h2 id="orgeafc497"><span class="section-number-2">2</span> Undamped System</h2>
|
<h2 id="org95b633d"><span class="section-number-2">2</span> Undamped System</h2>
|
||||||
<div class="outline-text-2" id="text-2">
|
<div class="outline-text-2" id="text-2">
|
||||||
<p>
|
<p>
|
||||||
Let's start by study the undamped system.
|
Let's start by study the undamped system.
|
||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org631c716" class="outline-3">
|
<div id="outline-container-orga87af67" class="outline-3">
|
||||||
<h3 id="org631c716"><span class="section-number-3">2.1</span> Init</h3>
|
<h3 id="orga87af67"><span class="section-number-3">2.1</span> Init</h3>
|
||||||
<div class="outline-text-3" id="text-2-1">
|
<div class="outline-text-3" id="text-2-1">
|
||||||
<p>
|
<p>
|
||||||
We initialize all the stages with the default parameters.
|
We initialize all the stages with the default parameters.
|
||||||
@ -426,8 +426,8 @@ All the controllers are set to 0 (Open Loop).
|
|||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
<div id="outline-container-orgbbef650" class="outline-3">
|
<div id="outline-container-org2d53583" class="outline-3">
|
||||||
<h3 id="orgbbef650"><span class="section-number-3">2.2</span> Identification</h3>
|
<h3 id="org2d53583"><span class="section-number-3">2.2</span> Identification</h3>
|
||||||
<div class="outline-text-3" id="text-2-2">
|
<div class="outline-text-3" id="text-2-2">
|
||||||
<p>
|
<p>
|
||||||
We identify the dynamics of the system.
|
We identify the dynamics of the system.
|
||||||
@ -490,19 +490,19 @@ Finally, we save the identified system dynamics for further analysis.
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgb5102fd" class="outline-3">
|
<div id="outline-container-orgc443c0b" class="outline-3">
|
||||||
<h3 id="orgb5102fd"><span class="section-number-3">2.3</span> Sensitivity to Disturbances</h3>
|
<h3 id="orgc443c0b"><span class="section-number-3">2.3</span> Sensitivity to Disturbances</h3>
|
||||||
<div class="outline-text-3" id="text-2-3">
|
<div class="outline-text-3" id="text-2-3">
|
||||||
<p>
|
<p>
|
||||||
We show several plots representing the sensitivity to disturbances:
|
We show several plots representing the sensitivity to disturbances:
|
||||||
</p>
|
</p>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>in figure <a href="#orge3abf0f">3</a> the transfer functions from ground motion \(D_w\) to the sample position \(D\) and the transfer function from direct force on the sample \(F_s\) to the sample position \(D\) are shown</li>
|
<li>in figure <a href="#org4d3097e">3</a> the transfer functions from ground motion \(D_w\) to the sample position \(D\) and the transfer function from direct force on the sample \(F_s\) to the sample position \(D\) are shown</li>
|
||||||
<li>in figure <a href="#org25d95cb">4</a>, it is the effect of parasitic forces of the positioning stages (\(F_{ty}\) and \(F_{rz}\)) on the position \(D\) of the sample that are shown</li>
|
<li>in figure <a href="#orgfd7633d">4</a>, it is the effect of parasitic forces of the positioning stages (\(F_{ty}\) and \(F_{rz}\)) on the position \(D\) of the sample that are shown</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|
||||||
|
|
||||||
<div id="orge3abf0f" class="figure">
|
<div id="org4d3097e" class="figure">
|
||||||
<p><img src="figs/uniaxial-sensitivity-disturbances.png" alt="uniaxial-sensitivity-disturbances.png" />
|
<p><img src="figs/uniaxial-sensitivity-disturbances.png" alt="uniaxial-sensitivity-disturbances.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 3: </span>Sensitivity to disturbances (<a href="./figs/uniaxial-sensitivity-disturbances.png">png</a>, <a href="./figs/uniaxial-sensitivity-disturbances.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 3: </span>Sensitivity to disturbances (<a href="./figs/uniaxial-sensitivity-disturbances.png">png</a>, <a href="./figs/uniaxial-sensitivity-disturbances.pdf">pdf</a>)</p>
|
||||||
@ -510,7 +510,7 @@ We show several plots representing the sensitivity to disturbances:
|
|||||||
|
|
||||||
|
|
||||||
|
|
||||||
<div id="org25d95cb" class="figure">
|
<div id="orgfd7633d" class="figure">
|
||||||
<p><img src="figs/uniaxial-sensitivity-force-dist.png" alt="uniaxial-sensitivity-force-dist.png" />
|
<p><img src="figs/uniaxial-sensitivity-force-dist.png" alt="uniaxial-sensitivity-force-dist.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 4: </span>Sensitivity to disturbances (<a href="./figs/uniaxial-sensitivity-force-dist.png">png</a>, <a href="./figs/uniaxial-sensitivity-force-dist.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 4: </span>Sensitivity to disturbances (<a href="./figs/uniaxial-sensitivity-force-dist.png">png</a>, <a href="./figs/uniaxial-sensitivity-force-dist.pdf">pdf</a>)</p>
|
||||||
@ -518,16 +518,16 @@ We show several plots representing the sensitivity to disturbances:
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgafe8970" class="outline-3">
|
<div id="outline-container-orgdb21910" class="outline-3">
|
||||||
<h3 id="orgafe8970"><span class="section-number-3">2.4</span> Plant</h3>
|
<h3 id="orgdb21910"><span class="section-number-3">2.4</span> Plant</h3>
|
||||||
<div class="outline-text-3" id="text-2-4">
|
<div class="outline-text-3" id="text-2-4">
|
||||||
<p>
|
<p>
|
||||||
The transfer function from the force \(F\) applied by the nano-hexapod to the position of the sample \(D\) is shown in figure <a href="#org62d1d12">5</a>.
|
The transfer function from the force \(F\) applied by the nano-hexapod to the position of the sample \(D\) is shown in figure <a href="#orgee21d6a">5</a>.
|
||||||
It corresponds to the plant to control.
|
It corresponds to the plant to control.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<div id="org62d1d12" class="figure">
|
<div id="orgee21d6a" class="figure">
|
||||||
<p><img src="figs/uniaxial-plant.png" alt="uniaxial-plant.png" />
|
<p><img src="figs/uniaxial-plant.png" alt="uniaxial-plant.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 5: </span>Bode plot of the Plant (<a href="./figs/uniaxial-plant.png">png</a>, <a href="./figs/uniaxial-plant.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 5: </span>Bode plot of the Plant (<a href="./figs/uniaxial-plant.png">png</a>, <a href="./figs/uniaxial-plant.pdf">pdf</a>)</p>
|
||||||
@ -536,21 +536,21 @@ It corresponds to the plant to control.
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgeab4870" class="outline-2">
|
<div id="outline-container-org497a34a" class="outline-2">
|
||||||
<h2 id="orgeab4870"><span class="section-number-2">3</span> Integral Force Feedback</h2>
|
<h2 id="org497a34a"><span class="section-number-2">3</span> Integral Force Feedback</h2>
|
||||||
<div class="outline-text-2" id="text-3">
|
<div class="outline-text-2" id="text-3">
|
||||||
<p>
|
<p>
|
||||||
<a id="org04c8f6e"></a>
|
<a id="org61a9736"></a>
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div id="orge50f87e" class="figure">
|
<div id="orgf30b3b3" class="figure">
|
||||||
<p><img src="figs/uniaxial-model-nass-flexible-iff.png" alt="uniaxial-model-nass-flexible-iff.png" />
|
<p><img src="figs/uniaxial-model-nass-flexible-iff.png" alt="uniaxial-model-nass-flexible-iff.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 6: </span>Uniaxial IFF Control Schematic</p>
|
<p><span class="figure-number">Figure 6: </span>Uniaxial IFF Control Schematic</p>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
<div id="outline-container-org6cf62a2" class="outline-3">
|
<div id="outline-container-org90d6383" class="outline-3">
|
||||||
<h3 id="org6cf62a2"><span class="section-number-3">3.1</span> Control Design</h3>
|
<h3 id="org90d6383"><span class="section-number-3">3.1</span> Control Design</h3>
|
||||||
<div class="outline-text-3" id="text-3-1">
|
<div class="outline-text-3" id="text-3-1">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
@ -562,7 +562,7 @@ Let's look at the transfer function from actuator forces in the nano-hexapod to
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<div id="org26ea3c1" class="figure">
|
<div id="org13e2d05" class="figure">
|
||||||
<p><img src="figs/uniaxial_iff_plant.png" alt="uniaxial_iff_plant.png" />
|
<p><img src="figs/uniaxial_iff_plant.png" alt="uniaxial_iff_plant.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 7: </span>Transfer function from forces applied in the legs to force sensor (<a href="./figs/uniaxial_iff_plant.png">png</a>, <a href="./figs/uniaxial_iff_plant.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 7: </span>Transfer function from forces applied in the legs to force sensor (<a href="./figs/uniaxial_iff_plant.png">png</a>, <a href="./figs/uniaxial_iff_plant.pdf">pdf</a>)</p>
|
||||||
@ -577,7 +577,7 @@ The controller for each pair of actuator/sensor is:
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="org27d1bb0" class="figure">
|
<div id="org928425f" class="figure">
|
||||||
<p><img src="figs/uniaxial_iff_open_loop.png" alt="uniaxial_iff_open_loop.png" />
|
<p><img src="figs/uniaxial_iff_open_loop.png" alt="uniaxial_iff_open_loop.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 8: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/uniaxial_iff_open_loop.png">png</a>, <a href="./figs/uniaxial_iff_open_loop.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 8: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/uniaxial_iff_open_loop.png">png</a>, <a href="./figs/uniaxial_iff_open_loop.pdf">pdf</a>)</p>
|
||||||
@ -585,8 +585,8 @@ The controller for each pair of actuator/sensor is:
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgf9a5f33" class="outline-3">
|
<div id="outline-container-orge5c43d3" class="outline-3">
|
||||||
<h3 id="orgf9a5f33"><span class="section-number-3">3.2</span> Identification</h3>
|
<h3 id="orge5c43d3"><span class="section-number-3">3.2</span> Identification</h3>
|
||||||
<div class="outline-text-3" id="text-3-2">
|
<div class="outline-text-3" id="text-3-2">
|
||||||
<p>
|
<p>
|
||||||
Let's initialize the system prior to identification.
|
Let's initialize the system prior to identification.
|
||||||
@ -669,18 +669,18 @@ G_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org7a80859" class="outline-3">
|
<div id="outline-container-orgdc6e62f" class="outline-3">
|
||||||
<h3 id="org7a80859"><span class="section-number-3">3.3</span> Sensitivity to Disturbance</h3>
|
<h3 id="orgdc6e62f"><span class="section-number-3">3.3</span> Sensitivity to Disturbance</h3>
|
||||||
<div class="outline-text-3" id="text-3-3">
|
<div class="outline-text-3" id="text-3-3">
|
||||||
|
|
||||||
<div id="orgca12220" class="figure">
|
<div id="org8df8488" class="figure">
|
||||||
<p><img src="figs/uniaxial_sensitivity_dist_iff.png" alt="uniaxial_sensitivity_dist_iff.png" />
|
<p><img src="figs/uniaxial_sensitivity_dist_iff.png" alt="uniaxial_sensitivity_dist_iff.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 9: </span>Sensitivity to disturbance once the IFF controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_iff.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_iff.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 9: </span>Sensitivity to disturbance once the IFF controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_iff.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_iff.pdf">pdf</a>)</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="org19c25c8" class="figure">
|
<div id="org6003ced" class="figure">
|
||||||
<p><img src="figs/uniaxial_sensitivity_dist_stages_iff.png" alt="uniaxial_sensitivity_dist_stages_iff.png" />
|
<p><img src="figs/uniaxial_sensitivity_dist_stages_iff.png" alt="uniaxial_sensitivity_dist_stages_iff.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 10: </span>Sensitivity to force disturbances in various stages when IFF is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_iff.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_iff.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 10: </span>Sensitivity to force disturbances in various stages when IFF is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_iff.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_iff.pdf">pdf</a>)</p>
|
||||||
@ -688,11 +688,11 @@ G_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org7bab9e9" class="outline-3">
|
<div id="outline-container-orgf2883d8" class="outline-3">
|
||||||
<h3 id="org7bab9e9"><span class="section-number-3">3.4</span> Damped Plant</h3>
|
<h3 id="orgf2883d8"><span class="section-number-3">3.4</span> Damped Plant</h3>
|
||||||
<div class="outline-text-3" id="text-3-4">
|
<div class="outline-text-3" id="text-3-4">
|
||||||
|
|
||||||
<div id="org60ea1f1" class="figure">
|
<div id="org2071f90" class="figure">
|
||||||
<p><img src="figs/uniaxial_plant_iff_damped.png" alt="uniaxial_plant_iff_damped.png" />
|
<p><img src="figs/uniaxial_plant_iff_damped.png" alt="uniaxial_plant_iff_damped.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 11: </span>Damped Plant after IFF is applied (<a href="./figs/uniaxial_plant_iff_damped.png">png</a>, <a href="./figs/uniaxial_plant_iff_damped.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 11: </span>Damped Plant after IFF is applied (<a href="./figs/uniaxial_plant_iff_damped.png">png</a>, <a href="./figs/uniaxial_plant_iff_damped.pdf">pdf</a>)</p>
|
||||||
@ -700,8 +700,8 @@ G_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgaac01c0" class="outline-3">
|
<div id="outline-container-orgb766da3" class="outline-3">
|
||||||
<h3 id="orgaac01c0"><span class="section-number-3">3.5</span> Conclusion</h3>
|
<h3 id="orgb766da3"><span class="section-number-3">3.5</span> Conclusion</h3>
|
||||||
<div class="outline-text-3" id="text-3-5">
|
<div class="outline-text-3" id="text-3-5">
|
||||||
<div class="important">
|
<div class="important">
|
||||||
<p>
|
<p>
|
||||||
@ -713,25 +713,25 @@ Integral Force Feedback:
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org8d9b463" class="outline-2">
|
<div id="outline-container-org0216063" class="outline-2">
|
||||||
<h2 id="org8d9b463"><span class="section-number-2">4</span> Relative Motion Control</h2>
|
<h2 id="org0216063"><span class="section-number-2">4</span> Relative Motion Control</h2>
|
||||||
<div class="outline-text-2" id="text-4">
|
<div class="outline-text-2" id="text-4">
|
||||||
<p>
|
<p>
|
||||||
<a id="orgdc4ae31"></a>
|
<a id="orgcf7a709"></a>
|
||||||
</p>
|
</p>
|
||||||
<p>
|
<p>
|
||||||
In the Relative Motion Control (RMC), a derivative feedback is applied between the measured actuator displacement to the actuator force input.
|
In the Relative Motion Control (RMC), a derivative feedback is applied between the measured actuator displacement to the actuator force input.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<div id="org46f85ef" class="figure">
|
<div id="org8ed07c5" class="figure">
|
||||||
<p><img src="figs/uniaxial-model-nass-flexible-rmc.png" alt="uniaxial-model-nass-flexible-rmc.png" />
|
<p><img src="figs/uniaxial-model-nass-flexible-rmc.png" alt="uniaxial-model-nass-flexible-rmc.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 12: </span>Uniaxial RMC Control Schematic</p>
|
<p><span class="figure-number">Figure 12: </span>Uniaxial RMC Control Schematic</p>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
<div id="outline-container-orgbf2540a" class="outline-3">
|
<div id="outline-container-orgda1c98e" class="outline-3">
|
||||||
<h3 id="orgbf2540a"><span class="section-number-3">4.1</span> Control Design</h3>
|
<h3 id="orgda1c98e"><span class="section-number-3">4.1</span> Control Design</h3>
|
||||||
<div class="outline-text-3" id="text-4-1">
|
<div class="outline-text-3" id="text-4-1">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
@ -743,7 +743,7 @@ Let's look at the transfer function from actuator forces in the nano-hexapod to
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<div id="orgc47e343" class="figure">
|
<div id="org75fbb9f" class="figure">
|
||||||
<p><img src="figs/uniaxial_rmc_plant.png" alt="uniaxial_rmc_plant.png" />
|
<p><img src="figs/uniaxial_rmc_plant.png" alt="uniaxial_rmc_plant.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 13: </span>Transfer function from forces applied in the legs to leg displacement sensor (<a href="./figs/uniaxial_rmc_plant.png">png</a>, <a href="./figs/uniaxial_rmc_plant.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 13: </span>Transfer function from forces applied in the legs to leg displacement sensor (<a href="./figs/uniaxial_rmc_plant.png">png</a>, <a href="./figs/uniaxial_rmc_plant.pdf">pdf</a>)</p>
|
||||||
@ -759,7 +759,7 @@ A Low pass Filter is added to make the controller transfer function proper.
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="org9c157b6" class="figure">
|
<div id="orgc5d2eb6" class="figure">
|
||||||
<p><img src="figs/uniaxial_rmc_open_loop.png" alt="uniaxial_rmc_open_loop.png" />
|
<p><img src="figs/uniaxial_rmc_open_loop.png" alt="uniaxial_rmc_open_loop.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 14: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/uniaxial_rmc_open_loop.png">png</a>, <a href="./figs/uniaxial_rmc_open_loop.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 14: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/uniaxial_rmc_open_loop.png">png</a>, <a href="./figs/uniaxial_rmc_open_loop.pdf">pdf</a>)</p>
|
||||||
@ -767,8 +767,8 @@ A Low pass Filter is added to make the controller transfer function proper.
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org1d106d7" class="outline-3">
|
<div id="outline-container-orge3806a0" class="outline-3">
|
||||||
<h3 id="org1d106d7"><span class="section-number-3">4.2</span> Identification</h3>
|
<h3 id="orge3806a0"><span class="section-number-3">4.2</span> Identification</h3>
|
||||||
<div class="outline-text-3" id="text-4-2">
|
<div class="outline-text-3" id="text-4-2">
|
||||||
<p>
|
<p>
|
||||||
Let's initialize the system prior to identification.
|
Let's initialize the system prior to identification.
|
||||||
@ -852,18 +852,18 @@ G_rmc.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="outline-container-orgeb7d680" class="outline-3">
|
<div id="outline-container-orge58c47d" class="outline-3">
|
||||||
<h3 id="orgeb7d680"><span class="section-number-3">4.3</span> Sensitivity to Disturbance</h3>
|
<h3 id="orge58c47d"><span class="section-number-3">4.3</span> Sensitivity to Disturbance</h3>
|
||||||
<div class="outline-text-3" id="text-4-3">
|
<div class="outline-text-3" id="text-4-3">
|
||||||
|
|
||||||
<div id="org7a8bd68" class="figure">
|
<div id="orgd910119" class="figure">
|
||||||
<p><img src="figs/uniaxial_sensitivity_dist_rmc.png" alt="uniaxial_sensitivity_dist_rmc.png" />
|
<p><img src="figs/uniaxial_sensitivity_dist_rmc.png" alt="uniaxial_sensitivity_dist_rmc.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 15: </span>Sensitivity to disturbance once the RMC controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_rmc.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_rmc.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 15: </span>Sensitivity to disturbance once the RMC controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_rmc.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_rmc.pdf">pdf</a>)</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="orgb8fed93" class="figure">
|
<div id="org6610f06" class="figure">
|
||||||
<p><img src="figs/uniaxial_sensitivity_dist_stages_rmc.png" alt="uniaxial_sensitivity_dist_stages_rmc.png" />
|
<p><img src="figs/uniaxial_sensitivity_dist_stages_rmc.png" alt="uniaxial_sensitivity_dist_stages_rmc.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 16: </span>Sensitivity to force disturbances in various stages when RMC is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_rmc.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_rmc.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 16: </span>Sensitivity to force disturbances in various stages when RMC is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_rmc.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_rmc.pdf">pdf</a>)</p>
|
||||||
@ -871,11 +871,11 @@ G_rmc.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org573eda0" class="outline-3">
|
<div id="outline-container-org70ec2cf" class="outline-3">
|
||||||
<h3 id="org573eda0"><span class="section-number-3">4.4</span> Damped Plant</h3>
|
<h3 id="org70ec2cf"><span class="section-number-3">4.4</span> Damped Plant</h3>
|
||||||
<div class="outline-text-3" id="text-4-4">
|
<div class="outline-text-3" id="text-4-4">
|
||||||
|
|
||||||
<div id="org1f8e935" class="figure">
|
<div id="org7508a42" class="figure">
|
||||||
<p><img src="figs/uniaxial_plant_rmc_damped.png" alt="uniaxial_plant_rmc_damped.png" />
|
<p><img src="figs/uniaxial_plant_rmc_damped.png" alt="uniaxial_plant_rmc_damped.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 17: </span>Damped Plant after RMC is applied (<a href="./figs/uniaxial_plant_rmc_damped.png">png</a>, <a href="./figs/uniaxial_plant_rmc_damped.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 17: </span>Damped Plant after RMC is applied (<a href="./figs/uniaxial_plant_rmc_damped.png">png</a>, <a href="./figs/uniaxial_plant_rmc_damped.pdf">pdf</a>)</p>
|
||||||
@ -883,8 +883,8 @@ G_rmc.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org02ca488" class="outline-3">
|
<div id="outline-container-orga845b21" class="outline-3">
|
||||||
<h3 id="org02ca488"><span class="section-number-3">4.5</span> Conclusion</h3>
|
<h3 id="orga845b21"><span class="section-number-3">4.5</span> Conclusion</h3>
|
||||||
<div class="outline-text-3" id="text-4-5">
|
<div class="outline-text-3" id="text-4-5">
|
||||||
<div class="important">
|
<div class="important">
|
||||||
<p>
|
<p>
|
||||||
@ -896,25 +896,25 @@ Relative Motion Control:
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org57948ea" class="outline-2">
|
<div id="outline-container-org7666422" class="outline-2">
|
||||||
<h2 id="org57948ea"><span class="section-number-2">5</span> Direct Velocity Feedback</h2>
|
<h2 id="org7666422"><span class="section-number-2">5</span> Direct Velocity Feedback</h2>
|
||||||
<div class="outline-text-2" id="text-5">
|
<div class="outline-text-2" id="text-5">
|
||||||
<p>
|
<p>
|
||||||
<a id="orgdd11541"></a>
|
<a id="org6b8afcf"></a>
|
||||||
</p>
|
</p>
|
||||||
<p>
|
<p>
|
||||||
In the Relative Motion Control (RMC), a feedback is applied between the measured velocity of the platform to the actuator force input.
|
In the Relative Motion Control (RMC), a feedback is applied between the measured velocity of the platform to the actuator force input.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<div id="org0fcd7e7" class="figure">
|
<div id="orga86445d" class="figure">
|
||||||
<p><img src="figs/uniaxial-model-nass-flexible-dvf.png" alt="uniaxial-model-nass-flexible-dvf.png" />
|
<p><img src="figs/uniaxial-model-nass-flexible-dvf.png" alt="uniaxial-model-nass-flexible-dvf.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 18: </span>Uniaxial DVF Control Schematic</p>
|
<p><span class="figure-number">Figure 18: </span>Uniaxial DVF Control Schematic</p>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
<div id="outline-container-org4b4d061" class="outline-3">
|
<div id="outline-container-org58e4d64" class="outline-3">
|
||||||
<h3 id="org4b4d061"><span class="section-number-3">5.1</span> Control Design</h3>
|
<h3 id="org58e4d64"><span class="section-number-3">5.1</span> Control Design</h3>
|
||||||
<div class="outline-text-3" id="text-5-1">
|
<div class="outline-text-3" id="text-5-1">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
@ -922,7 +922,7 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="orgbf7145f" class="figure">
|
<div id="orgf4888fb" class="figure">
|
||||||
<p><img src="figs/uniaxial_dvf_plant.png" alt="uniaxial_dvf_plant.png" />
|
<p><img src="figs/uniaxial_dvf_plant.png" alt="uniaxial_dvf_plant.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 19: </span>Transfer function from forces applied in the legs to leg velocity sensor (<a href="./figs/uniaxial_dvf_plant.png">png</a>, <a href="./figs/uniaxial_dvf_plant.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 19: </span>Transfer function from forces applied in the legs to leg velocity sensor (<a href="./figs/uniaxial_dvf_plant.png">png</a>, <a href="./figs/uniaxial_dvf_plant.pdf">pdf</a>)</p>
|
||||||
@ -934,7 +934,7 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="org1b6adf4" class="figure">
|
<div id="org1a62235" class="figure">
|
||||||
<p><img src="figs/uniaxial_dvf_loop_gain.png" alt="uniaxial_dvf_loop_gain.png" />
|
<p><img src="figs/uniaxial_dvf_loop_gain.png" alt="uniaxial_dvf_loop_gain.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 20: </span>Transfer function from forces applied in the legs to leg velocity sensor (<a href="./figs/uniaxial_dvf_loop_gain.png">png</a>, <a href="./figs/uniaxial_dvf_loop_gain.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 20: </span>Transfer function from forces applied in the legs to leg velocity sensor (<a href="./figs/uniaxial_dvf_loop_gain.png">png</a>, <a href="./figs/uniaxial_dvf_loop_gain.pdf">pdf</a>)</p>
|
||||||
@ -942,8 +942,8 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgd4f4973" class="outline-3">
|
<div id="outline-container-org7e8b911" class="outline-3">
|
||||||
<h3 id="orgd4f4973"><span class="section-number-3">5.2</span> Identification</h3>
|
<h3 id="org7e8b911"><span class="section-number-3">5.2</span> Identification</h3>
|
||||||
<div class="outline-text-3" id="text-5-2">
|
<div class="outline-text-3" id="text-5-2">
|
||||||
<p>
|
<p>
|
||||||
Let's initialize the system prior to identification.
|
Let's initialize the system prior to identification.
|
||||||
@ -1026,18 +1026,18 @@ G_dvf.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org6cfeae5" class="outline-3">
|
<div id="outline-container-org2adcafe" class="outline-3">
|
||||||
<h3 id="org6cfeae5"><span class="section-number-3">5.3</span> Sensitivity to Disturbance</h3>
|
<h3 id="org2adcafe"><span class="section-number-3">5.3</span> Sensitivity to Disturbance</h3>
|
||||||
<div class="outline-text-3" id="text-5-3">
|
<div class="outline-text-3" id="text-5-3">
|
||||||
|
|
||||||
<div id="org6fb6e94" class="figure">
|
<div id="org9ca6224" class="figure">
|
||||||
<p><img src="figs/uniaxial_sensitivity_dist_dvf.png" alt="uniaxial_sensitivity_dist_dvf.png" />
|
<p><img src="figs/uniaxial_sensitivity_dist_dvf.png" alt="uniaxial_sensitivity_dist_dvf.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 21: </span>Sensitivity to disturbance once the DVF controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_dvf.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_dvf.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 21: </span>Sensitivity to disturbance once the DVF controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_dvf.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_dvf.pdf">pdf</a>)</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="org6f13385" class="figure">
|
<div id="orgd0ada58" class="figure">
|
||||||
<p><img src="figs/uniaxial_sensitivity_dist_stages_dvf.png" alt="uniaxial_sensitivity_dist_stages_dvf.png" />
|
<p><img src="figs/uniaxial_sensitivity_dist_stages_dvf.png" alt="uniaxial_sensitivity_dist_stages_dvf.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 22: </span>Sensitivity to force disturbances in various stages when DVF is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_dvf.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_dvf.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 22: </span>Sensitivity to force disturbances in various stages when DVF is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_dvf.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_dvf.pdf">pdf</a>)</p>
|
||||||
@ -1045,11 +1045,11 @@ G_dvf.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org89e0408" class="outline-3">
|
<div id="outline-container-orge8b5bd9" class="outline-3">
|
||||||
<h3 id="org89e0408"><span class="section-number-3">5.4</span> Damped Plant</h3>
|
<h3 id="orge8b5bd9"><span class="section-number-3">5.4</span> Damped Plant</h3>
|
||||||
<div class="outline-text-3" id="text-5-4">
|
<div class="outline-text-3" id="text-5-4">
|
||||||
|
|
||||||
<div id="org7051238" class="figure">
|
<div id="org55c6262" class="figure">
|
||||||
<p><img src="figs/uniaxial_plant_dvf_damped.png" alt="uniaxial_plant_dvf_damped.png" />
|
<p><img src="figs/uniaxial_plant_dvf_damped.png" alt="uniaxial_plant_dvf_damped.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 23: </span>Damped Plant after DVF is applied (<a href="./figs/uniaxial_plant_dvf_damped.png">png</a>, <a href="./figs/uniaxial_plant_dvf_damped.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 23: </span>Damped Plant after DVF is applied (<a href="./figs/uniaxial_plant_dvf_damped.png">png</a>, <a href="./figs/uniaxial_plant_dvf_damped.pdf">pdf</a>)</p>
|
||||||
@ -1057,8 +1057,8 @@ G_dvf.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgc27bce5" class="outline-3">
|
<div id="outline-container-org22d6515" class="outline-3">
|
||||||
<h3 id="orgc27bce5"><span class="section-number-3">5.5</span> Conclusion</h3>
|
<h3 id="org22d6515"><span class="section-number-3">5.5</span> Conclusion</h3>
|
||||||
<div class="outline-text-3" id="text-5-5">
|
<div class="outline-text-3" id="text-5-5">
|
||||||
<div class="important">
|
<div class="important">
|
||||||
<p>
|
<p>
|
||||||
@ -1069,15 +1069,15 @@ Direct Velocity Feedback:
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
<div id="outline-container-org6dd07d9" class="outline-2">
|
<div id="outline-container-org55010b4" class="outline-2">
|
||||||
<h2 id="org6dd07d9"><span class="section-number-2">6</span> Comparison of Active Damping Techniques</h2>
|
<h2 id="org55010b4"><span class="section-number-2">6</span> Comparison of Active Damping Techniques</h2>
|
||||||
<div class="outline-text-2" id="text-6">
|
<div class="outline-text-2" id="text-6">
|
||||||
<p>
|
<p>
|
||||||
<a id="org5272a4c"></a>
|
<a id="org9b9c235"></a>
|
||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
<div id="outline-container-orgd62929a" class="outline-3">
|
<div id="outline-container-org5cb1e25" class="outline-3">
|
||||||
<h3 id="orgd62929a"><span class="section-number-3">6.1</span> Load the plants</h3>
|
<h3 id="org5cb1e25"><span class="section-number-3">6.1</span> Load the plants</h3>
|
||||||
<div class="outline-text-3" id="text-6-1">
|
<div class="outline-text-3" id="text-6-1">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span>, <span class="org-string">'G_iff'</span>, <span class="org-string">'G_rmc'</span>, <span class="org-string">'G_dvf'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span>, <span class="org-string">'G_iff'</span>, <span class="org-string">'G_rmc'</span>, <span class="org-string">'G_dvf'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
@ -1086,11 +1086,11 @@ Direct Velocity Feedback:
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgbd35b93" class="outline-3">
|
<div id="outline-container-orgc746216" class="outline-3">
|
||||||
<h3 id="orgbd35b93"><span class="section-number-3">6.2</span> Sensitivity to Disturbance</h3>
|
<h3 id="orgc746216"><span class="section-number-3">6.2</span> Sensitivity to Disturbance</h3>
|
||||||
<div class="outline-text-3" id="text-6-2">
|
<div class="outline-text-3" id="text-6-2">
|
||||||
|
|
||||||
<div id="org5eda09f" class="figure">
|
<div id="orga056e76" class="figure">
|
||||||
<p><img src="figs/uniaxial_sensitivity_ground_motion.png" alt="uniaxial_sensitivity_ground_motion.png" />
|
<p><img src="figs/uniaxial_sensitivity_ground_motion.png" alt="uniaxial_sensitivity_ground_motion.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 24: </span>Sensitivity to Ground Motion - Comparison (<a href="./figs/uniaxial_sensitivity_ground_motion.png">png</a>, <a href="./figs/uniaxial_sensitivity_ground_motion.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 24: </span>Sensitivity to Ground Motion - Comparison (<a href="./figs/uniaxial_sensitivity_ground_motion.png">png</a>, <a href="./figs/uniaxial_sensitivity_ground_motion.pdf">pdf</a>)</p>
|
||||||
@ -1098,21 +1098,21 @@ Direct Velocity Feedback:
|
|||||||
|
|
||||||
|
|
||||||
|
|
||||||
<div id="org1fae0e7" class="figure">
|
<div id="org5bfe138" class="figure">
|
||||||
<p><img src="figs/uniaxial_sensitivity_direct_force.png" alt="uniaxial_sensitivity_direct_force.png" />
|
<p><img src="figs/uniaxial_sensitivity_direct_force.png" alt="uniaxial_sensitivity_direct_force.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 25: </span>Sensitivity to disturbance - Comparison (<a href="./figs/uniaxial_sensitivity_direct_force.png">png</a>, <a href="./figs/uniaxial_sensitivity_direct_force.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 25: </span>Sensitivity to disturbance - Comparison (<a href="./figs/uniaxial_sensitivity_direct_force.png">png</a>, <a href="./figs/uniaxial_sensitivity_direct_force.pdf">pdf</a>)</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="orgb2bd39c" class="figure">
|
<div id="org4e0c629" class="figure">
|
||||||
<p><img src="figs/uniaxial_sensitivity_fty.png" alt="uniaxial_sensitivity_fty.png" />
|
<p><img src="figs/uniaxial_sensitivity_fty.png" alt="uniaxial_sensitivity_fty.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 26: </span>Sensitivity to force disturbances - Comparison (<a href="./figs/uniaxial_sensitivity_fty.png">png</a>, <a href="./figs/uniaxial_sensitivity_fty.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 26: </span>Sensitivity to force disturbances - Comparison (<a href="./figs/uniaxial_sensitivity_fty.png">png</a>, <a href="./figs/uniaxial_sensitivity_fty.pdf">pdf</a>)</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="org1f00826" class="figure">
|
<div id="orgae22af6" class="figure">
|
||||||
<p><img src="figs/uniaxial_sensitivity_frz.png" alt="uniaxial_sensitivity_frz.png" />
|
<p><img src="figs/uniaxial_sensitivity_frz.png" alt="uniaxial_sensitivity_frz.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 27: </span>Sensitivity to force disturbances - Comparison (<a href="./figs/uniaxial_sensitivity_frz.png">png</a>, <a href="./figs/uniaxial_sensitivity_frz.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 27: </span>Sensitivity to force disturbances - Comparison (<a href="./figs/uniaxial_sensitivity_frz.png">png</a>, <a href="./figs/uniaxial_sensitivity_frz.pdf">pdf</a>)</p>
|
||||||
@ -1120,11 +1120,11 @@ Direct Velocity Feedback:
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org72ab5fd" class="outline-3">
|
<div id="outline-container-orgcd1790f" class="outline-3">
|
||||||
<h3 id="org72ab5fd"><span class="section-number-3">6.3</span> Damped Plant</h3>
|
<h3 id="orgcd1790f"><span class="section-number-3">6.3</span> Damped Plant</h3>
|
||||||
<div class="outline-text-3" id="text-6-3">
|
<div class="outline-text-3" id="text-6-3">
|
||||||
|
|
||||||
<div id="org0296cfa" class="figure">
|
<div id="org38fbe3d" class="figure">
|
||||||
<p><img src="figs/uniaxial_plant_damped_comp.png" alt="uniaxial_plant_damped_comp.png" />
|
<p><img src="figs/uniaxial_plant_damped_comp.png" alt="uniaxial_plant_damped_comp.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 28: </span>Damped Plant - Comparison (<a href="./figs/uniaxial_plant_damped_comp.png">png</a>, <a href="./figs/uniaxial_plant_damped_comp.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 28: </span>Damped Plant - Comparison (<a href="./figs/uniaxial_plant_damped_comp.png">png</a>, <a href="./figs/uniaxial_plant_damped_comp.pdf">pdf</a>)</p>
|
||||||
@ -1132,10 +1132,10 @@ Direct Velocity Feedback:
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org2c43078" class="outline-3">
|
<div id="outline-container-org9a602cb" class="outline-3">
|
||||||
<h3 id="org2c43078"><span class="section-number-3">6.4</span> Conclusion</h3>
|
<h3 id="org9a602cb"><span class="section-number-3">6.4</span> Conclusion</h3>
|
||||||
<div class="outline-text-3" id="text-6-4">
|
<div class="outline-text-3" id="text-6-4">
|
||||||
<table id="orga82a170" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
<table id="orgf039db4" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||||
<caption class="t-above"><span class="table-number">Table 1:</span> Comparison of proposed active damping techniques</caption>
|
<caption class="t-above"><span class="table-number">Table 1:</span> Comparison of proposed active damping techniques</caption>
|
||||||
|
|
||||||
<colgroup>
|
<colgroup>
|
||||||
@ -1205,7 +1205,7 @@ The next step is to take into account the power spectral density of each disturb
|
|||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Dehaeze Thomas</p>
|
<p class="author">Author: Dehaeze Thomas</p>
|
||||||
<p class="date">Created: 2019-10-25 ven. 12:32</p>
|
<p class="date">Created: 2019-10-25 ven. 16:02</p>
|
||||||
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
</body>
|
</body>
|
||||||
|
|||||||
@ -2217,7 +2217,7 @@ Direct Velocity Feedback:
|
|||||||
title('$F_{rz}$ to $D$');
|
title('$F_{rz}$ to $D$');
|
||||||
hold on;
|
hold on;
|
||||||
plot(freqs, abs(squeeze(freqresp(G ('D', 'Frz'), freqs, 'Hz'))), 'k-' , 'DisplayName', 'OL');
|
plot(freqs, abs(squeeze(freqresp(G ('D', 'Frz'), freqs, 'Hz'))), 'k-' , 'DisplayName', 'OL');
|
||||||
plot(freqs, abs(squeeze(freqresp(G_iff('D', 'Frz'), freqs, 'Hz'))), 'k' , 'DisplayName', 'IFF');
|
plot(freqs, abs(squeeze(freqresp(G_iff('D', 'Frz'), freqs, 'Hz'))), 'k:' , 'DisplayName', 'IFF');
|
||||||
plot(freqs, abs(squeeze(freqresp(G_rmc('D', 'Frz'), freqs, 'Hz'))), 'k--', 'DisplayName', 'RMC');
|
plot(freqs, abs(squeeze(freqresp(G_rmc('D', 'Frz'), freqs, 'Hz'))), 'k--', 'DisplayName', 'RMC');
|
||||||
plot(freqs, abs(squeeze(freqresp(G_dvf('D', 'Frz'), freqs, 'Hz'))), 'k-.', 'DisplayName', 'DVF');
|
plot(freqs, abs(squeeze(freqresp(G_dvf('D', 'Frz'), freqs, 'Hz'))), 'k-.', 'DisplayName', 'DVF');
|
||||||
hold off;
|
hold off;
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user