#+TITLE: Cercalo Test Bench
:DRAWER:
#+STARTUP: overview

#+LANGUAGE: en
#+EMAIL: dehaeze.thomas@gmail.com
#+AUTHOR: Dehaeze Thomas

#+PROPERTY: header-args:matlab  :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :results none
#+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :eval no-export
#+PROPERTY: header-args:matlab+ :output-dir figs
#+PROPERTY: header-args:matlab+ :tangle matlab/frf_processing.m
#+PROPERTY: header-args:matlab+ :mkdirp yes
:END:


* 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

* Identification of the Plant
#+begin_src matlab
  fs = 1e4;
  Ts = 1/fs;
#+end_src

We generate white noise with the "random number" simulink block, and we filter that noise.

#+begin_src matlab
  Gi = (1)/(1+s/2/pi/100);
#+end_src

#+begin_src matlab :results output replace
  c2d(Gi, Ts, 'tustin')
#+end_src

#+RESULTS:
#+begin_example
c2d(Gi, Ts, 'tustin')

ans =

  0.030459 (z+1)
  --------------
    (z-0.9391)

Sample time: 0.0001 seconds
Discrete-time zero/pole/gain model.
#+end_example

#+begin_src matlab
  load('mat/data_001.mat', 't', 'ux')
#+end_src

#+begin_src matlab
  figure; plot(t, ux)
#+end_src

#+begin_src matlab
  [tf_est, freqs] = tfestimate(ux, yx, hanning(ceil(length(ux)/10)), [], [], fs);

  % h = idfrd(tf_est, freqs*2*pi, Ts);
#+end_src

#+begin_src matlab
figure;
ax1 = subplot(2, 1, 1);
hold on;
plot(freqs, abs(tf_est),'--')
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]');
hold off;

ax2 = subplot(2, 1, 2);
hold on;
plot(freqs, mod(180+180/pi*phase(tf_est), 360)-180,'--')
set(gca,'xscale','log');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
xlabel('Frequency [$Hz$]'); ylabel('Phase [deg]');
hold off;
#+end_src