1067 lines
34 KiB
Org Mode
1067 lines
34 KiB
Org Mode
#+TITLE: Determination of the optimal nano-hexapod's stiffness
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:DRAWER:
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#+STARTUP: overview
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#+LANGUAGE: en
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#+EMAIL: dehaeze.thomas@gmail.com
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#+AUTHOR: Dehaeze Thomas
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/zenburn.css"/>
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#+HTML_HEAD: <script type="text/javascript" src="./js/jquery.min.js"></script>
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#+HTML_HEAD: <script type="text/javascript" src="./js/bootstrap.min.js"></script>
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#+HTML_HEAD: <script type="text/javascript" src="./js/jquery.stickytableheaders.min.js"></script>
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#+HTML_HEAD: <script type="text/javascript" src="./js/readtheorg.js"></script>
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#+HTML_MATHJAX: align: center tagside: right font: TeX
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#+PROPERTY: header-args:matlab :session *MATLAB*
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#+PROPERTY: header-args:matlab+ :comments org
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#+PROPERTY: header-args:matlab+ :results none
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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+ :output-dir figs
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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:shell :eval no-export
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#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
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#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
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#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
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#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
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#+PROPERTY: header-args:latex+ :results raw replace :buffer no
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#+PROPERTY: header-args:latex+ :eval no-export
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#+PROPERTY: header-args:latex+ :exports both
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#+PROPERTY: header-args:latex+ :mkdirp yes
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#+PROPERTY: header-args:latex+ :output-dir figs
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:END:
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* Introduction :ignore:
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As shown before, many parameters other than the nano-hexapod itself do influence the plant dynamics:
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- The micro-station compliance (studied [[file:uncertainty_support.org][here]])
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- The payload mass and dynamical properties (studied [[file:uncertainty_payload.org][here]] and [[file:uncertainty_experiment.org][here]])
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- The experimental conditions, mainly the spindle rotation speed (studied [[file:uncertainty_experiment.org][here]])
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As seen before, the stiffness of the nano-hexapod greatly influence the effect of such parameters.
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We wish here to see if we can determine an optimal stiffness of the nano-hexapod such that:
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- Section [[sec:spindle_rotation_speed]]: the change of its dynamics due to the spindle rotation speed is acceptable
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- Section [[sec:micro_station_compliance]]: the support compliance dynamics is not much present in the nano-hexapod dynamics
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- Section [[sec:payload_impedance]]: the change of payload impedance has acceptable effect on the plant dynamics
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The overall goal is to design a nano-hexapod that will allow the highest possible control bandwidth.
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* Spindle Rotation Speed
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<<sec:spindle_rotation_speed>>
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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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#+begin_src matlab
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open('nass_model.slx')
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#+end_src
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** Initialization
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We initialize all the stages with the default parameters.
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#+begin_src matlab
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initializeGround();
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initializeGranite();
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initializeTy();
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initializeRy();
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initializeRz();
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initializeMicroHexapod();
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initializeAxisc();
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initializeMirror();
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#+end_src
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The worst case scenario is a rotation speed of 60rpm with a payload mass of 1Kg.
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#+begin_src matlab
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initializeSample('mass', 10);
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#+end_src
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We don't include gravity nor disturbances in this model as it adds complexity to the simulations and does not alter the obtained dynamics.
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#+begin_src matlab
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initializeSimscapeConfiguration('gravity', false);
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initializeDisturbances('enable', false);
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#+end_src
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We set the controller type to Open-Loop, and we do not need to log any signal.
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#+begin_src matlab
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initializeController('type', 'stabilizing');
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initializeLoggingConfiguration('log', 'none');
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#+end_src
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#+begin_src matlab :exports none
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%% Name of the Simulink File
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mdl = 'nass_model';
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%% Input/Output definition
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clear io; io_i = 1;
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io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1;
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io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Dnlm'); io_i = io_i + 1;
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io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Fnlm'); io_i = io_i + 1;
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io(io_i) = linio([mdl, '/Tracking Error'], 1, 'openoutput', [], 'En'); io_i = io_i + 1;
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#+end_src
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** Identification when not rotating
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We set the range of stiffness that we want to use.
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#+begin_src matlab
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Ks = logspace(3,9,7)
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#+end_src
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#+begin_src matlab
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initializeReferences();
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#+end_src
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#+begin_src matlab
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Gk_iff = {zeros(length(Ks))};
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Gk_dvf = {zeros(length(Ks))};
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Gk_err = {zeros(length(Ks))};
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#+end_src
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#+begin_src matlab
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for i = 1:length(Ks)
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initializeNanoHexapod('k', Ks(i));
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%% Run the linearization
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G = linearize(mdl, io);
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G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
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G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ...
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'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ...
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'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'};
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Gk_iff(i) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
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Gk_dvf(i) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
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Jinvt = tf(inv(nano_hexapod.J)');
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Jinvt.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
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Jinvt.OutputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
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Gk_err(i) = {-minreal(G({'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))*Jinvt};
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end
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#+end_src
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** Identification when rotating at maximum speed
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#+begin_src matlab
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Rz_rpm = 60;
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initializeReferences('Rz_type', 'rotating', ...
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'Rz_period', 60/Rz_rpm, ... % Rotation period [s]
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'Rz_amplitude', -0.2*(2*pi*Rz_rpm/60)); % Angle offset [rad]
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load('mat/nass_references.mat', 'Rz'); % We load the reference for the Spindle
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[~, i_end] = min(abs(Rz.signals.values)); % Obtain the indice where the spindle angle is zero
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t_sim = Rz.time(i_end); % Simulation time before identification [s]
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#+end_src
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#+begin_src matlab
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k_sta = -1e8;
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#+end_src
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#+begin_src matlab
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Gk_wz_iff = {zeros(length(Ks))};
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Gk_wz_dvf = {zeros(length(Ks))};
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Gk_wz_err = {zeros(length(Ks))};
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#+end_src
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#+begin_src matlab
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for i = 1:length(Ks)
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initializeNanoHexapod('k', Ks(i));
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%% Run the linearization
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G = linearize(mdl, io, t_sim);
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G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
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G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ...
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'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ...
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'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'};
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Gk_wz_iff(i) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
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Gk_wz_dvf(i) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
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Jinvt = tf(inv(nano_hexapod.J)');
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Jinvt.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
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Jinvt.OutputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
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Gk_wz_err(i) = {-minreal(G({'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))*Jinvt};
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end
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#+end_src
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#+begin_src matlab
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save('mat/optimal_stiffness_Gk_wz.mat', 'Ks', ...
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'Gk_iff', 'Gk_dvf', 'Gk_err', ...
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'Gk_wz_iff', 'Gk_wz_dvf', 'Gk_wz_err');
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#+end_src
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** Change of dynamics
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#+begin_src matlab :exports none
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load('mat/optimal_stiffness_Gk_wz.mat');
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#+end_src
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Change of dynamics for decentralized IFF control.
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#+begin_src matlab :exports none
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freqs = logspace(-1, 3, 1000);
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figure;
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ax1 = subplot(2, 1, 1);
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hold on;
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for i = 1:length(Gk_iff)
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set(gca,'ColorOrderIndex',i);
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plot(freqs, abs(squeeze(freqresp(Gk_iff{i}( 'Fnlm1', 'Fnl1'), freqs, 'Hz'))), '-');
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set(gca,'ColorOrderIndex',i);
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plot(freqs, abs(squeeze(freqresp(Gk_wz_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), '--');
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
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title('Soft Nano-Hexapod');
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ax2 = subplot(2, 1, 2);
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hold on;
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for i = 1:length(Gk_iff)
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set(gca,'ColorOrderIndex',i);
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gk_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), '-', ...
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'DisplayName', sprintf('$k = %.0g$ [N/m]', Ks(i)));
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set(gca,'ColorOrderIndex',i);
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gk_wz_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), '--', ...
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'HandleVisibility', 'off');
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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legend('location', 'northeast');
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linkaxes([ax1,ax2],'x');
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xlim([freqs(1), freqs(end)]);
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#+end_src
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Change of dynamics from $F_x$ to $D_x$.
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#+begin_src matlab :exports none
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freqs = logspace(-1, 3, 1000);
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figure;
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ax1 = subplot(2, 1, 1);
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hold on;
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for i = 1:length(Gk_err)
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set(gca,'ColorOrderIndex',i);
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plot(freqs, abs(squeeze(freqresp(Gk_err{i}( 'Ex', 'Fx'), freqs, 'Hz'))), '-');
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set(gca,'ColorOrderIndex',i);
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plot(freqs, abs(squeeze(freqresp(Gk_wz_err{i}('Ex', 'Fx'), freqs, 'Hz'))), '--');
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
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ax2 = subplot(2, 1, 2);
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hold on;
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for i = 1:length(Gk_err)
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set(gca,'ColorOrderIndex',i);
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gk_err{i}('Ex', 'Fx'), freqs, 'Hz'))), '-', ...
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'DisplayName', sprintf('$k = %.0g$ [N/m]', Ks(i)));
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set(gca,'ColorOrderIndex',i);
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gk_wz_err{i}('Ex', 'Fx'), freqs, 'Hz'))), '--', ...
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'HandleVisibility', 'off');
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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legend('location', 'northeast');
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linkaxes([ax1,ax2],'x');
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xlim([freqs(1), freqs(end)]);
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#+end_src
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Change of dynamics from $F_z$ to $D_z$.
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#+begin_src matlab :exports none
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freqs = logspace(-1, 3, 1000);
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figure;
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ax1 = subplot(2, 1, 1);
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hold on;
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for i = 1:length(Gk_err)
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set(gca,'ColorOrderIndex',i);
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plot(freqs, abs(squeeze(freqresp(Gk_err{i}( 'Ez', 'Fz'), freqs, 'Hz'))), '-');
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set(gca,'ColorOrderIndex',i);
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plot(freqs, abs(squeeze(freqresp(Gk_wz_err{i}('Ez', 'Fz'), freqs, 'Hz'))), '--');
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
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title('Soft Nano-Hexapod');
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ax2 = subplot(2, 1, 2);
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hold on;
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for i = 1:length(Gk_err)
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set(gca,'ColorOrderIndex',i);
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gk_err{i}('Ez', 'Fz'), freqs, 'Hz'))), '-', ...
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'DisplayName', sprintf('$k = %.0g$ [N/m]', Ks(i)));
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set(gca,'ColorOrderIndex',i);
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gk_wz_err{i}('Ez', 'Fz'), freqs, 'Hz'))), '--', ...
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'HandleVisibility', 'off');
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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legend('location', 'northeast');
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linkaxes([ax1,ax2],'x');
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xlim([freqs(1), freqs(end)]);
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#+end_src
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** Change of coupling
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#+begin_src matlab :exports none
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load('mat/optimal_stiffness_Gk_wz.mat');
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#+end_src
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Change of coupling from $F_x$ to $D_y$ when not rotating and when rotating at 60rpm.
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#+begin_src matlab :exports none
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freqs = logspace(-1, 3, 1000);
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figure;
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hold on;
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for i = 1:length(Gk_err)
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set(gca,'ColorOrderIndex',i);
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plot(freqs, abs(squeeze(freqresp(Gk_err{i}( 'Ey', 'Fx'), freqs, 'Hz'))), '-', ...
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'DisplayName', sprintf('$k = %.0g$ [N/m]', Ks(i)));
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set(gca,'ColorOrderIndex',i);
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plot(freqs, abs(squeeze(freqresp(Gk_wz_err{i}('Ey', 'Fx'), freqs, 'Hz'))), '--', ...
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'HandleVisibility', 'off');
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end
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hold off;
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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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xlim([freqs(1), freqs(end)]);
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legend('location', 'northeast');
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#+end_src
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Comparison of the coupling from $F_x$ to $D_y$ when rotating at 60rpm to the direct term $F_x$ to $D_x$.
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#+begin_src matlab :exports none
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freqs = logspace(-1, 3, 1000);
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figure;
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hold on;
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for i = 1:length(Gk_err)
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set(gca,'ColorOrderIndex',i);
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plot(freqs, abs(squeeze(freqresp(Gk_wz_err{i}('Ex', 'Fx'), freqs, 'Hz'))), '-', ...
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'DisplayName', sprintf('$k = %.0g$ [N/m]', Ks(i)));
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set(gca,'ColorOrderIndex',i);
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plot(freqs, abs(squeeze(freqresp(Gk_wz_err{i}('Ey', 'Fx'), freqs, 'Hz'))), '--', ...
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'HandleVisibility', 'off');
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end
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hold off;
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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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xlim([freqs(1), freqs(end)]);
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legend('location', 'northeast');
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#+end_src
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** Conclusion :ignore:
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#+begin_important
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The leg stiffness should be at higher than $k_i = 10^4\ [N/m]$ such that the main resonance frequency does not shift too much when rotating.
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For the coupling, it is more difficult to conclude about the minimum required leg stiffness.
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#+end_important
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#+begin_notes
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Note that we can use very soft nano-hexapod if we limit the spindle rotating speed.
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#+end_notes
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* Micro-Station Compliance Effect
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<<sec:micro_station_compliance>>
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** Introduction :ignore:
|
|
- take the 6dof compliance of the micro-station
|
|
- simple model + uncertainty
|
|
|
|
** Matlab Init :noexport:ignore:
|
|
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
|
<<matlab-dir>>
|
|
#+end_src
|
|
|
|
#+begin_src matlab :exports none :results silent :noweb yes
|
|
<<matlab-init>>
|
|
#+end_src
|
|
|
|
#+begin_src matlab :tangle no
|
|
simulinkproject('../');
|
|
#+end_src
|
|
|
|
#+begin_src matlab
|
|
open('nass_model.slx')
|
|
#+end_src
|
|
|
|
** Conclusion :ignore:
|
|
* Payload "Impedance" Effect
|
|
<<sec:payload_impedance>>
|
|
|
|
** Introduction :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)
|
|
<<matlab-dir>>
|
|
#+end_src
|
|
|
|
#+begin_src matlab :exports none :results silent :noweb yes
|
|
<<matlab-init>>
|
|
#+end_src
|
|
|
|
#+begin_src matlab :tangle no
|
|
simulinkproject('../');
|
|
#+end_src
|
|
|
|
#+begin_src matlab
|
|
open('nass_model.slx')
|
|
#+end_src
|
|
|
|
** Initialization
|
|
We initialize all the stages with the default parameters.
|
|
#+begin_src matlab
|
|
initializeGround();
|
|
initializeGranite();
|
|
initializeTy();
|
|
initializeRy();
|
|
initializeRz();
|
|
initializeMicroHexapod();
|
|
initializeAxisc();
|
|
initializeMirror();
|
|
#+end_src
|
|
|
|
We don't include gravity nor disturbances in this model as it adds complexity to the simulations and does not alter the obtained dynamics.
|
|
#+begin_src matlab
|
|
initializeSimscapeConfiguration('gravity', false);
|
|
initializeDisturbances('enable', false);
|
|
#+end_src
|
|
|
|
We set the controller type to Open-Loop, and we do not need to log any signal.
|
|
#+begin_src matlab
|
|
initializeController('type', 'stabilizing');
|
|
initializeLoggingConfiguration('log', 'none');
|
|
#+end_src
|
|
|
|
#+begin_src matlab :exports none
|
|
%% Name of the Simulink File
|
|
mdl = 'nass_model';
|
|
|
|
%% Input/Output definition
|
|
clear io; io_i = 1;
|
|
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1;
|
|
io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Dnlm'); io_i = io_i + 1;
|
|
io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Fnlm'); io_i = io_i + 1;
|
|
io(io_i) = linio([mdl, '/Tracking Error'], 1, 'openoutput', [], 'En'); io_i = io_i + 1;
|
|
#+end_src
|
|
|
|
** Change of payload dynamics
|
|
- Change of mass: from 1kg to 50kg
|
|
- Change of resonance frequency: from 50Hz to 500Hz
|
|
- The damping ratio of the payload is fixed to $\xi = 0.2$
|
|
|
|
#+begin_src matlab
|
|
initializeReferences();
|
|
Ks = logspace(3,9,7) % [N/m]
|
|
#+end_src
|
|
|
|
#+begin_src matlab
|
|
Ms = [1, 20, 50]; % [Kg]
|
|
#+end_src
|
|
|
|
#+begin_src matlab
|
|
Gm_iff = {zeros(length(Ks), length(Ms))};
|
|
Gm_dvf = {zeros(length(Ks), length(Ms))};
|
|
Gm_err = {zeros(length(Ks), length(Ms))};
|
|
#+end_src
|
|
|
|
#+begin_src matlab
|
|
for i = 1:length(Ks)
|
|
for j = 1:length(Ms)
|
|
initializeNanoHexapod('k', Ks(i));
|
|
initializeSample('mass', Ms(j), 'freq', 100*ones(6,1));
|
|
|
|
G = linearize(mdl, io);
|
|
G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
|
|
G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ...
|
|
'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ...
|
|
'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'};
|
|
|
|
Gm_iff(i,j) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
|
|
Gm_dvf(i,j) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
|
|
|
|
Jinvt = tf(inv(nano_hexapod.J)');
|
|
Jinvt.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
|
|
Jinvt.OutputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
|
|
Gm_err(i,j) = {-minreal(G({'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))*Jinvt};
|
|
end
|
|
end
|
|
#+end_src
|
|
|
|
#+begin_src matlab
|
|
Fs = [50, 200, 500]; % [Hz]
|
|
#+end_src
|
|
|
|
#+begin_src matlab
|
|
Gf_iff = {zeros(length(Ks), length(Fs))};
|
|
Gf_dvf = {zeros(length(Ks), length(Fs))};
|
|
Gf_err = {zeros(length(Ks), length(Fs))};
|
|
#+end_src
|
|
|
|
#+begin_src matlab
|
|
for i = 1:length(Ks)
|
|
for j = 1:length(Fs)
|
|
initializeNanoHexapod('k', Ks(i));
|
|
initializeSample('mass', 20, 'freq', Fs(j)*ones(6,1));
|
|
|
|
G = linearize(mdl, io);
|
|
G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
|
|
G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ...
|
|
'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ...
|
|
'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'};
|
|
|
|
Gf_iff(i,j) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
|
|
Gf_dvf(i,j) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))};
|
|
|
|
Jinvt = tf(inv(nano_hexapod.J)');
|
|
Jinvt.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
|
|
Jinvt.OutputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
|
|
Gf_err(i,j) = {-minreal(G({'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))*Jinvt};
|
|
end
|
|
end
|
|
#+end_src
|
|
|
|
#+begin_src matlab
|
|
save('mat/optimal_stiffness_Gm_Gf.mat', 'Ks', 'Ms', 'Fs', ...
|
|
'Gm_iff', 'Gm_dvf', 'Gm_err', ...
|
|
'Gf_iff', 'Gf_dvf', 'Gf_err');
|
|
#+end_src
|
|
|
|
** Plots
|
|
** Change of optimal gain for decentralized control
|
|
For each payload, compute the optimal gain for the IFF control.
|
|
The optimal value corresponds to critical damping to *all* the 6 modes of the nano-hexapod.
|
|
|
|
#+begin_src matlab
|
|
load('mat/optimal_stiffness_Gm_Gf.mat');
|
|
#+end_src
|
|
|
|
Change of Mass
|
|
#+begin_src matlab :exports none
|
|
freqs = logspace(-1, 3, 1000);
|
|
|
|
figure;
|
|
|
|
ax1 = subplot(2, 1, 1);
|
|
hold on;
|
|
for i = 1:length(Ks)
|
|
for j = 1:length(Ms)
|
|
set(gca,'ColorOrderIndex',i);
|
|
plot(freqs, abs(squeeze(freqresp(Gm_iff{i,j}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), '-');
|
|
end
|
|
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:length(Ks)
|
|
for j = 1:length(Ms)
|
|
set(gca,'ColorOrderIndex',i);
|
|
if j == 1
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_iff{i,j}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), '-', ...
|
|
'DisplayName', sprintf('$K = %.0e$ [N/m]', Ks(i)));
|
|
else
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_iff{i,j}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), '-', ...
|
|
'HandleVisibility', 'off');
|
|
end
|
|
end
|
|
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]);
|
|
legend('location', 'northeast');
|
|
|
|
linkaxes([ax1,ax2],'x');
|
|
xlim([freqs(1), freqs(end)]);
|
|
#+end_src
|
|
|
|
Change of payload resonance frequency
|
|
#+begin_src matlab :exports none
|
|
freqs = logspace(-1, 3, 1000);
|
|
|
|
figure;
|
|
|
|
ax1 = subplot(2, 1, 1);
|
|
hold on;
|
|
for i = 1:length(Ks)
|
|
for j = 1:length(Fs)
|
|
set(gca,'ColorOrderIndex',i);
|
|
plot(freqs, abs(squeeze(freqresp(Gf_iff{i,j}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), '-');
|
|
end
|
|
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:length(Ks)
|
|
for j = 1:length(Fs)
|
|
set(gca,'ColorOrderIndex',i);
|
|
if j == 1
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf_iff{i,j}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), '-', ...
|
|
'DisplayName', sprintf('$K = %.0e$ [N/m]', Ks(i)));
|
|
else
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf_iff{i,j}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), '-', ...
|
|
'HandleVisibility', 'off');
|
|
end
|
|
end
|
|
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]);
|
|
legend('location', 'northeast');
|
|
|
|
linkaxes([ax1,ax2],'x');
|
|
xlim([freqs(1), freqs(end)]);
|
|
#+end_src
|
|
|
|
** Change of dynamics for the primary controller
|
|
For each stiffness, plot the total spread of dynamics.
|
|
|
|
#+begin_src matlab
|
|
load('mat/optimal_stiffness_Gm_Gf.mat');
|
|
#+end_src
|
|
|
|
*** Frequency variation
|
|
Same payload mass, but different stiffness resulting in different resonance frequency.
|
|
|
|
All curves
|
|
#+begin_src matlab :exports none
|
|
freqs = logspace(-1, 3, 1000);
|
|
|
|
figure;
|
|
|
|
ax1 = subplot(2, 1, 1);
|
|
hold on;
|
|
for i = 1:length(Ks)
|
|
for j = 1:length(Fs)
|
|
set(gca,'ColorOrderIndex',i);
|
|
plot(freqs, abs(squeeze(freqresp(Gf_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), '-');
|
|
end
|
|
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:length(Ks)
|
|
for j = 1:length(Fs)
|
|
set(gca,'ColorOrderIndex',i);
|
|
if j == 1
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), '-', ...
|
|
'DisplayName', sprintf('$K = %.0e$ [N/m]', Ks(i)));
|
|
else
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), '-', ...
|
|
'HandleVisibility', 'off');
|
|
end
|
|
end
|
|
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]);
|
|
legend('location', 'northeast');
|
|
|
|
linkaxes([ax1,ax2],'x');
|
|
xlim([freqs(1), freqs(end)]);
|
|
#+end_src
|
|
|
|
X direction
|
|
#+begin_src matlab :exports none
|
|
i = 1;
|
|
|
|
freqs = logspace(-1, 3, 1000);
|
|
|
|
figure;
|
|
|
|
ax1 = subplot(2, 2, 1);
|
|
hold on;
|
|
for j = 1:length(Fs)
|
|
plot(freqs, abs(squeeze(freqresp(Gf_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), '-');
|
|
end
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
|
title(sprintf('$k = %.0e$ [N/m]', Ks(i)))
|
|
|
|
ax2 = subplot(2, 2, 3);
|
|
hold on;
|
|
for j = 1:length(Fs)
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), '-', ...
|
|
'DisplayName', sprintf('$\\omega_0 = %.0f$ [Hz]', Fs(j)));
|
|
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]);
|
|
legend('location', 'northeast');
|
|
|
|
linkaxes([ax1,ax2],'x');
|
|
xlim([freqs(1), freqs(end)]);
|
|
|
|
i = 7;
|
|
|
|
ax1 = subplot(2, 2, 2);
|
|
hold on;
|
|
for j = 1:length(Fs)
|
|
plot(freqs, abs(squeeze(freqresp(Gf_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), '-');
|
|
end
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
|
title(sprintf('$k = %.0e$ [N/m]', Ks(i)))
|
|
|
|
ax2 = subplot(2, 2, 4);
|
|
hold on;
|
|
for j = 1:length(Fs)
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), '-', ...
|
|
'DisplayName', sprintf('$\\omega_0 = %.0f$ [Hz]', Fs(j)));
|
|
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]);
|
|
legend('location', 'northeast');
|
|
|
|
linkaxes([ax1,ax2],'x');
|
|
xlim([freqs(1), freqs(end)]);
|
|
#+end_src
|
|
|
|
Z direction:
|
|
We can see two mass lines for the soft nano-hexapod:
|
|
- The first mass line corresponds to $\frac{1}{(m_n + m_p)s^2}$ where $m_p = 20\ [kg]$ is the mass of the payload and $m_n = 15\ [Kg]$ is the mass of the nano-hexapod top platform and attached mirror
|
|
- The second mass line corresponds to $\frac{1}{m_n s^2}$
|
|
|
|
#+begin_src matlab :exports none
|
|
i = 1;
|
|
|
|
freqs = logspace(-1, 3, 1000);
|
|
|
|
figure;
|
|
|
|
ax1 = subplot(2, 2, 1);
|
|
hold on;
|
|
for j = 1:length(Fs)
|
|
plot(freqs, abs(squeeze(freqresp(Gf_err{i,j}('Ez', 'Fz'), freqs, 'Hz'))), '-');
|
|
end
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
|
title(sprintf('$k = %.0e$ [N/m]', Ks(i)))
|
|
|
|
ax2 = subplot(2, 2, 3);
|
|
hold on;
|
|
for j = 1:length(Fs)
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf_err{i,j}('Ez', 'Fz'), freqs, 'Hz'))), '-', ...
|
|
'DisplayName', sprintf('$\\omega_0 = %.0f$ [Hz]', Fs(j)));
|
|
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]);
|
|
legend('location', 'northeast');
|
|
|
|
linkaxes([ax1,ax2],'x');
|
|
xlim([freqs(1), freqs(end)]);
|
|
|
|
i = 7;
|
|
|
|
ax1 = subplot(2, 2, 2);
|
|
hold on;
|
|
for j = 1:length(Fs)
|
|
plot(freqs, abs(squeeze(freqresp(Gf_err{i,j}('Ez', 'Fz'), freqs, 'Hz'))), '-');
|
|
end
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
|
title(sprintf('$k = %.0e$ [N/m]', Ks(i)))
|
|
|
|
ax2 = subplot(2, 2, 4);
|
|
hold on;
|
|
for j = 1:length(Fs)
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf_err{i,j}('Ez', 'Fz'), freqs, 'Hz'))), '-', ...
|
|
'DisplayName', sprintf('$\\omega_0 = %.0f$ [Hz]', Fs(j)));
|
|
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]);
|
|
legend('location', 'northeast');
|
|
|
|
linkaxes([ax1,ax2],'x');
|
|
xlim([freqs(1), freqs(end)]);
|
|
#+end_src
|
|
|
|
*** Mass variation
|
|
All mixed, X direction
|
|
#+begin_src matlab :exports none
|
|
freqs = logspace(-1, 3, 1000);
|
|
|
|
figure;
|
|
|
|
ax1 = subplot(2, 1, 1);
|
|
hold on;
|
|
for i = 1:length(Ks)
|
|
for j = 1:length(Ms)
|
|
set(gca,'ColorOrderIndex',i);
|
|
plot(freqs, abs(squeeze(freqresp(Gm_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), '-');
|
|
end
|
|
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:length(Ks)
|
|
for j = 1:length(Ms)
|
|
set(gca,'ColorOrderIndex',i);
|
|
if j == 1
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), '-', ...
|
|
'DisplayName', sprintf('$K = %.0e$ [N/m]', Ks(i)));
|
|
else
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), '-', ...
|
|
'HandleVisibility', 'off');
|
|
end
|
|
end
|
|
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]);
|
|
legend('location', 'northeast');
|
|
|
|
linkaxes([ax1,ax2],'x');
|
|
xlim([freqs(1), freqs(end)]);
|
|
#+end_src
|
|
|
|
All mixed, Z direction
|
|
#+begin_src matlab :exports none
|
|
freqs = logspace(-1, 3, 1000);
|
|
|
|
figure;
|
|
|
|
ax1 = subplot(2, 1, 1);
|
|
hold on;
|
|
for i = 1:length(Ks)
|
|
for j = 1:length(Ms)
|
|
set(gca,'ColorOrderIndex',i);
|
|
plot(freqs, abs(squeeze(freqresp(Gm_err{i,j}('Ez', 'Fz'), freqs, 'Hz'))), '-');
|
|
end
|
|
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:length(Ks)
|
|
for j = 1:length(Ms)
|
|
set(gca,'ColorOrderIndex',i);
|
|
if j == 1
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_err{i,j}('Ez', 'Fz'), freqs, 'Hz'))), '-', ...
|
|
'DisplayName', sprintf('$K = %.0e$ [N/m]', Ks(i)));
|
|
else
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_err{i,j}('Ez', 'Fz'), freqs, 'Hz'))), '-', ...
|
|
'HandleVisibility', 'off');
|
|
end
|
|
end
|
|
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]);
|
|
legend('location', 'northeast');
|
|
|
|
linkaxes([ax1,ax2],'x');
|
|
xlim([freqs(1), freqs(end)]);
|
|
#+end_src
|
|
|
|
Z direction
|
|
#+begin_src matlab :exports none
|
|
freqs = logspace(-1, 3, 1000);
|
|
|
|
figure;
|
|
|
|
i = 1;
|
|
|
|
ax1 = subplot(2, 2, 1);
|
|
hold on;
|
|
for j = 1:length(Ms)
|
|
plot(freqs, abs(squeeze(freqresp(Gm_err{i,j}('Ez', 'Fz'), freqs, 'Hz'))), '-');
|
|
end
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
|
title(sprintf('$k = %.0e$ [N/m]', Ks(i)))
|
|
|
|
ax2 = subplot(2, 2, 3);
|
|
hold on;
|
|
for j = 1:length(Ms)
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_err{i,j}('Ez', 'Fz'), 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');
|
|
xlim([freqs(1), freqs(end)]);
|
|
|
|
i = 7;
|
|
|
|
ax1 = subplot(2, 2, 2);
|
|
hold on;
|
|
for j = 1:length(Ms)
|
|
plot(freqs, abs(squeeze(freqresp(Gm_err{i,j}('Ez', 'Fz'), freqs, 'Hz'))), '-');
|
|
end
|
|
hold off;
|
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
|
title(sprintf('$k = %.0e$ [N/m]', Ks(i)))
|
|
|
|
ax2 = subplot(2, 2, 4);
|
|
hold on;
|
|
for j = 1:length(Ms)
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_err{i,j}('Ez', 'Fz'), freqs, 'Hz'))), '-', ...
|
|
'DisplayName', sprintf('$m_p = %.0f$ [kg]', Ms(j)));
|
|
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]);
|
|
legend('location', 'northeast');
|
|
|
|
linkaxes([ax1,ax2],'x');
|
|
xlim([freqs(1), freqs(end)]);
|
|
#+end_src
|
|
|
|
*** Total variation
|
|
Total change of dynamics due to change of the payload:
|
|
- mass from 1kg to 50kg
|
|
- main resonance from 50Hz to 500Hz
|
|
|
|
For a soft nano-hexapod
|
|
#+begin_src matlab :exports none
|
|
i = 1;
|
|
|
|
freqs = logspace(-1, 3, 1000);
|
|
|
|
figure;
|
|
|
|
ax1 = subplot(2, 1, 1);
|
|
hold on;
|
|
for j = 1:length(Fs)
|
|
plot(freqs, abs(squeeze(freqresp(Gf_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), 'k-');
|
|
end
|
|
for j = 1:length(Ms)
|
|
plot(freqs, abs(squeeze(freqresp(Gm_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), 'k-');
|
|
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 j = 1:length(Fs)
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), 'k-');
|
|
for j = 1:length(Ms)
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), 'k-');
|
|
end
|
|
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');
|
|
xlim([freqs(1), freqs(end)]);
|
|
#+end_src
|
|
|
|
For a stiff nano-hexapod
|
|
#+begin_src matlab :exports none
|
|
i = 7;
|
|
|
|
freqs = logspace(-1, 3, 1000);
|
|
|
|
figure;
|
|
|
|
ax1 = subplot(2, 1, 1);
|
|
hold on;
|
|
for j = 1:length(Fs)
|
|
plot(freqs, abs(squeeze(freqresp(Gf_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), 'k-');
|
|
end
|
|
for j = 1:length(Ms)
|
|
plot(freqs, abs(squeeze(freqresp(Gm_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), 'k-');
|
|
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 j = 1:length(Fs)
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gf_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), 'k-');
|
|
for j = 1:length(Ms)
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_err{i,j}('Ex', 'Fx'), freqs, 'Hz'))), 'k-');
|
|
end
|
|
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');
|
|
xlim([freqs(1), freqs(end)]);
|
|
#+end_src
|
|
|
|
|
|
** Conclusion :ignore:
|
|
|