#+TITLE:Effect of the rotation of the Slip-Ring
:DRAWER:
#+STARTUP: overview

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#+PROPERTY: header-args:matlab  :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :results output
#+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :eval no-export
#+PROPERTY: header-args:matlab+ :output-dir figs
:END:

* Measurement Description
Random Signal is generated by one DAC of the SpeedGoat.

The signal going out of the DAC is split into two:
- one BNC cable is directly connected to one ADC of the SpeedGoat
- one BNC cable goes two times in the Slip-Ring (from bottom to top and then from top to bottom) and then is connected to one ADC of the SpeedGoat

Two measurements are done.
| Data File          | Description           |
|--------------------+-----------------------|
| =mat/data_001.mat= | Slip-ring not turning |
| =mat/data_002.mat= | Slip-ring turning     |

For each measurement, the measured signals are:
| Data File | Description                        |
|-----------+------------------------------------|
| =t=       | Time vector                        |
| =x1=      | Direct signal                      |
| =x2=      | Signal going through the Slip-Ring |

The goal is to determine is the signal is altered when the spindle is rotating.

Here, the rotation speed of the Slip-Ring is set to 1rpm.

* Matlab Init                                               :noexport:ignore:
#+begin_src matlab :exports none :results silent :noweb yes
  <<matlab-init>>
#+end_src

* Load data
We load the data of the z axis of two geophones.
#+begin_src matlab :results none
  sr_off = load('mat/data_001.mat', 't', 'x1', 'x2');
  sr_on  = load('mat/data_002.mat', 't', 'x1', 'x2');
#+end_src

* Analysis
Let's first look at the signal produced by the DAC (figure [[fig:random_signal]]).

#+begin_src matlab :results none
  figure;
  hold on;
  plot(sr_on.t,  sr_on.x1);
  hold off;
  xlabel('Time [s]'); ylabel('Voltage [V]');
  xlim([0 10]);
#+end_src

#+NAME: fig:random_signal
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/random_signal.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:random_signal
#+CAPTION: Random signal produced by the DAC
#+RESULTS: fig:random_signal
[[file:figs/random_signal.png]]

We now look at the difference between the signal directly measured by the ADC and the signal that goes through the slip-ring (figure [[fig:slipring_comp_signals]]).

#+begin_src matlab :results none
  figure;
  hold on;
  plot(sr_on.t,  sr_on.x1  -  sr_on.x2,  'DisplayName', 'Slip-Ring - $\omega = 1rpm$');
  plot(sr_off.t, sr_off.x1 - sr_off.x2,'DisplayName', 'Slip-Ring off');
  hold off;
  xlabel('Time [s]'); ylabel('Voltage [V]');
  xlim([0 10]);
  legend('Location', 'northeast');
#+end_src

#+NAME: fig:slipring_comp_signals
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/slipring_comp_signals.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:slipring_comp_signals
#+CAPTION: Alteration of the signal when the slip-ring is turning
#+RESULTS: fig:slipring_comp_signals
[[file:figs/slipring_comp_signals.png]]

#+begin_src matlab :results none
  dt = sr_on.t(2) - sr_on.t(1);
  Fs = 1/dt; % [Hz]

  win = hanning(ceil(1*Fs));
#+end_src

#+begin_src matlab :results none
  [pxx_on,  f] = pwelch(sr_on.x1  - sr_on.x2,  win, [], [], Fs);
  [pxx_off, ~] = pwelch(sr_off.x1 - sr_off.x2, win, [], [], Fs);
#+end_src

#+begin_src matlab :results none :exports none
  figure;
  hold on;
  plot(f, sqrt(pxx_on), 'DisplayName', 'Slip-Ring - $\omega = 1rpm$');
  plot(f, sqrt(pxx_off),'DisplayName', 'Slip-Ring off');
  hold off;
  set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
  xlabel('Frequency [Hz]'); ylabel('PSD $\left[\frac{V}{\sqrt{Hz}}\right]$');
  legend('Location', 'northeast');
  xlim([1, 500]);
#+end_src

#+NAME: fig:psd_noise
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/psd_noise.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:psd_noise
#+CAPTION: ASD of the measured noise
#+RESULTS: fig:psd_noise
[[file:figs/psd_noise.png]]

* Conclusion
#+begin_note
*Remaining questions*:
- Should the measurement be redone using voltage amplifiers?
- Use higher rotation speed and measure for longer periods (to have multiple revolutions) ?
#+end_note