#+TITLE:     Control in a rotating frame
#+AUTHOR:    Dehaeze Thomas
#+EMAIL:     dehaeze.thomas@gmail.com
#+DATE:      {{{time(%Y-%m-%d)}}}
#+DESCRIPTION: Course about Optimal and Robust Control
#+KEYWORDS:  control optimal robust lqr lqg hinfinity
#+LANGUAGE:  en
#+STARTUP: beamer
#+LaTeX_CLASS: clean-beamer
#+LaTeX_CLASS_OPTIONS: [t]
#+OPTIONS:   H:2
#+OPTIONS:   num:t toc:t ::t |:t ^:{} -:t f:t *:t <:t
#+SELECT_TAGS: export
#+EXCLUDE_TAGS: noexport
#+COLUMNS: %20ITEM %13BEAMER_env(Env) %6BEAMER_envargs(Args) %4BEAMER_col(Col) %7BEAMER_extra(Extra)
#+latex_header: \AtBeginSection[]{\begin{frame}<beamer>\frametitle{Topic}\tableofcontents[currentsection]\end{frame}}

* Simscape Model
#+name: fig:simscape
#+caption: Screen of simscape multibody model
#+attr_latex: :float t :width 0.7\linewidth
[[./Figures/simscape.png]]

* Simscape Model
#+name: fig:simulink_ctrl
#+caption: Simulink Blocks
#+attr_latex: :float t :width 0.9\linewidth
[[./Figures/simulink_ctrl.png]]

* Identification in the rotating frame
The rotation speed increase the coupling between the rotating actuators and sensors (figure ref:fig:G_u_v).

#+name: fig:G_u_v
#+caption: Transfer function from forces to displacement in the rotating frame
#+attr_latex: :float t
[[./Figures/G_u_v.pdf]]

* Identification in the cartesian frame
#+name: fig:G_x_y
#+caption: Plant from force to displacement in the cartesian frame
#+attr_latex: :float t :width 0.8\linewidth
[[./Figures/G_x_y.pdf]]

* Identification in the cartesian frame
#+name: fig:G_x_y_e
#+caption: Plant from force to displacement in the cartesian frame with small angle estimation error
#+attr_latex: :float t :width 0.8\linewidth
[[./Figures/G_x_y_e.pdf]]

* Control result
#+name: fig:D_x_y
#+caption: Control result with a simple PID
#+attr_latex: :float t :width 0.8\linewidth
[[./Figures/D_x_y.pdf]]