#+TITLE: The Nano Active Stabilization System - Results on ESRF ID31 beamline - Matlab Computation
:DRAWER:
#+HTML_LINK_HOME: ../index.html
#+HTML_LINK_UP:   ../index.html

#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
#+HTML_HEAD: <script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>

#+BIND: org-latex-image-default-option "scale=1"
#+BIND: org-latex-bib-compiler "biber"
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#+LaTeX_CLASS: scrreprt
#+LaTeX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12, parskip=full]
#+LaTeX_HEADER_EXTRA: \input{preamble.tex}
#+LATEX_HEADER_EXTRA: \addbibresource{ref.bib}

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

#+begin_export html
  <hr>
  <p>This report is also available as a <a href="./index.pdf">pdf</a>.</p>
  <hr>
#+end_export

* Introduction                                                        :ignore:

# The matlab code is accessible on [[https://zenodo.org/record/3894343][Zonodo]] and [[https://github.com/tdehaeze/dehaeze20_contr_stewa_platf][Github]] cite:dehaeze20_activ_dampin_rotat_posit_platf. It can also be download as a =.zip= file [[file:matlab.zip][here]].

# To run the Matlab code, go in the =matlab= directory and run the following Matlab files corresponding to each section.

# #+caption: Paper's sections and corresponding Matlab files
# | Sections                           | Matlab File                |
# |------------------------------------+----------------------------|
# | Section [[sec:system_description]]     | =s1_system_description.m=  |
# | Section [[sec:iff_pure_int]]           | =s2_iff_pure_int.m=        |
# | Section [[sec:iff_pseudo_int]]         | =s3_iff_hpf.m=             |
# | Section [[sec:iff_parallel_stiffness]] | =s4_iff_kp.m=              |
# | Section [[sec:comparison]]             | =s5_act_damp_comparison.m= |

* System Description and Analysis
:PROPERTIES:
:header-args:matlab+: :tangle matlab/s1_system_description.m
:END:
<<sec:system_description>>

** 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
  addpath('./matlab/');
  addpath('./src/');
#+end_src

* Notations
<<sec:notations>>

# |                                   | Mathematical Notation        | Matlab        | Unit    |
# |-----------------------------------+------------------------------+---------------+---------|
# | Actuator Stiffness                | $k$                          | =k=           | N/m     |
# | Actuator Damping                  | $c$                          | =c=           | N/(m/s) |
# | Payload Mass                      | $m$                          | =m=           | kg      |
# | Damping Ratio                     | $\xi = \frac{c}{2\sqrt{km}}$ | =xi=          |         |
# | Actuator Force                    | $\bm{F}, F_u, F_v$           | =F= =Fu= =Fv= | N       |
# | Force Sensor signal               | $\bm{f}, f_u, f_v$           | =f= =fu= =fv= | N       |
# | Relative Displacement             | $\bm{d}, d_u, d_v$           | =d= =du= =dv= | m       |
# | Resonance freq. when $\Omega = 0$ | $\omega_0$                   | =w0=          | rad/s   |
# | Rotation Speed                    | $\Omega = \dot{\theta}$      | =W=           | rad/s   |
# | Low Pass Filter corner frequency  | $\omega_i$                   | =wi=          | rad/s   |

# |                  | Mathematical Notation | Matlab | Unit    |
# |------------------+-----------------------+--------+---------|
# | Laplace variable | $s$                   | =s=    |         |
# | Complex number   | $j$                   | =j=    |         |
# | Frequency        | $\omega$              | =w=    | [rad/s] |

* Bibliography                                                        :ignore:
# #+latex: \printbibliography
# bibliography:ref.bib