add sample model: try to build optimal controller for 1/s^2

MXfastStageDoc/MXfastStage.tex

@@ -199,7 +199,7 @@ $\rightarrow$ at frequencies above 200 Hz, the current increses up to 2 amps, an
 $\rightarrow$ The closed loop response becomes bad above 20Hz (motor 1 ca. -10\%, motor 2 +5\% )\\
 
 \FloatBarrier
-\subsubsection{Friction}
+\subsubsection{Friction} \label{sec:friction}
 
 To measure the friction, the stage is moved at slow speed from
 +lim to -lim. The current is proportional to the force.
@@ -763,10 +763,6 @@ scp userservo_util userphase_util usrServoSample/usralgo.ko root@SAR-CPPM-EXPMX1
 \end{verbatim}
 \end{tcolorbox}
 
-\begin{tcolorbox}[colback=red!5!white,colframe=red!75!black,colbacktitle=red!50,coltitle=black,title=TODO]
-Here is still work to do...
-\end{tcolorbox}
-
 \begin{tcolorbox}[width=15cm,colback=yellow!5!white,colframe=yellow!75!black,colbacktitle=yellow!50,coltitle=black,title=DeltaTau Shell]
 \begin{verbatim}
 root@:/opt/ppmac#
@@ -782,6 +778,11 @@ Motor[1].Ctrl =UserAlgo.ServoCtrlAddr[1]
 \end{tcolorbox}
 
 
+\FloatBarrier
+\subsection{The reality of the state space controller}
+
+The state space controller assumes that the system is observable and controlable. The bode plot shows a flat amplitude at low frequencies, which makes the feeling, that the system is observable and controlable. But in fact the reason of that flat amplitude is friction (section \ref{sec:friction}). The viscode damping is also negligable.\\
+This results to the fact that $F=m \cdot \ddot{x}$ consists of really 2 integrators. But an integrator $\frac{1}{s}$ is neighter observable and controlable. Therefore we have to check, how to implement an optimal controller for such a system.