Simulation of tomography experiments

matlab/src/initializeSimplifiedNanoHexapod.m

@@ -15,7 +15,7 @@ function [nano_hexapod] = initializeSimplifiedNanoHexapod(args)
         %% Actuators
         args.actuator_type char {mustBeMember(args.actuator_type,{'1dof', '2dof', 'flexible'})} = '1dof'
         args.actuator_k   (1,1) double {mustBeNumeric, mustBePositive} = 1e6
-        args.actuator_kp  (1,1) double {mustBeNumeric, mustBeNonnegative} = 1e4
+        args.actuator_kp  (1,1) double {mustBeNumeric, mustBeNonnegative} = 5e4
         args.actuator_ke  (1,1) double {mustBeNumeric, mustBePositive} = 4952605
         args.actuator_ka  (1,1) double {mustBeNumeric, mustBePositive} = 2476302
         args.actuator_c   (1,1) double {mustBeNumeric, mustBePositive} = 50

simscape-nass.tex

@@ -1,4 +1,4 @@
-% Created 2025-02-12 Wed 15:35
+% Created 2025-02-12 Wed 17:40
 % Intended LaTeX compiler: pdflatex
 \documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt}
 
@@ -97,13 +97,12 @@ Explain how to compute the errors in the frame of the struts (rotating):
 \item Say that there are many control strategies.
 It will be the topic of chapter 2.3.
 Here, we start with something simple: control in the frame of the struts
-\item[{$\square$}] block diagram of the complete control architecture
 \end{itemize}
 
 \begin{figure}[htbp]
 \centering
 \includegraphics[scale=1,width=\linewidth]{figs/nass_control_architecture.png}
-\caption{\label{fig:nass_control_architecture}Figure caption}
+\caption{\label{fig:nass_control_architecture}The physical systems are shown in blue, the control kinematics in red, the decentralized Integral Force Feedback in yellow and the centralized High Authority Controller in green.}
 \end{figure}
 
 \chapter{Decentralized Active Damping}
@@ -113,6 +112,7 @@ Here, we start with something simple: control in the frame of the struts
 \item Robustness to payload mass
 \item Root Locus
 \item Damping optimization
+\item \textbf{Parallel stiffness?}
 \end{itemize}
 
 Explain which samples are tested:
@@ -132,17 +132,37 @@ Explain which samples are tested:
 \item[{$\square$}] Added parallel stiffness
 \end{itemize}
 
+Coupling
+
+Effect of rotation
+
+Effect of payload mass
+
 \section{Controller Design}
 
+Low pass filter needs to be added (because now: DC gain)
+
+\begin{equation}\label{eq:nass_kiff}
+    \bm{K}_{\text{IFF}}(s) = g \cdot \begin{bmatrix}
+        K_{\text{IFF}}(s) & & 0 \\
+        & \ddots & \\
+        0 & & K_{\text{IFF}}(s)
+    \end{bmatrix}, \quad K_{\text{IFF}}(s) = \frac{1}{s}
+\end{equation}
+
+Loop Gain:
+Root Locus => Stability
+
 \begin{itemize}
 \item Use Integral controller (with parallel stiffness)
 \item Show Root Locus (show that without parallel stiffness => unstable?)
 \item Choose optimal gain.
 Here in MIMO, cannot have optimal damping for all modes. (there is a paper that tries to optimize that)
-\item Show robustness to change of payload (loci?) / Change of rotating velocity ?
+\item[{$\square$}] Show robustness to change of payload (loci?) / Change of rotating velocity ?
 \item Reference to paper showing stability in MIMO for decentralized IFF
 \end{itemize}
 
+
 \section{Sensitivity to disturbances}
 
 Disturbances:
@@ -181,6 +201,13 @@ From control kinematics:
 \item[{$\square$}] Compare with undamped plants
 \end{itemize}
 
+Effect of rotation:
+
+Effect of IFF:
+
+Effect of payload mass
+
+Advantage of using IFF:
 \section{Controller design}
 
 \begin{itemize}
@@ -188,6 +215,12 @@ From control kinematics:
 \item[{$\square$}] Show robustness with Loci for all masses
 \end{itemize}
 
+\begin{equation}\label{eq:nass_robust_hac}
+K_{\text{HAC}}(s) = g_0 \cdot \underbrace{\frac{\omega_c}{s}}_{\text{int}} \cdot \underbrace{\frac{1}{\sqrt{\alpha}}\frac{1 + \frac{s}{\omega_c/\sqrt{\alpha}}}{1 + \frac{s}{\omega_c\sqrt{\alpha}}}}_{\text{lead}} \cdot \underbrace{\frac{1}{1 + \frac{s}{\omega_0}}}_{\text{LPF}}, \quad \left( \omega_c = 2\pi5\,\text{rad/s},\ \alpha = 2,\ \omega_0 = 2\pi30\,\text{rad/s} \right)
+\end{equation}
+
+``Decentralized'' Loop Gain:
+Characteristic Loci for three masses:
 \section{Sensitivity to disturbances}
 
 \begin{itemize}
@@ -206,6 +239,28 @@ Compare without the NASS, and with just IFF
 \item Validation of concept
 \end{itemize}
 
+\begin{figure}[htbp]
+\begin{subfigure}{0.33\textwidth}
+\begin{center}
+\includegraphics[scale=1,scale=1]{figs/nass_tomography_hac_iff_m1.png}
+\end{center}
+\subcaption{\label{fig:nass_tomography_hac_iff_m1} $m = 1\,kg$}
+\end{subfigure}
+\begin{subfigure}{0.33\textwidth}
+\begin{center}
+\includegraphics[scale=1,scale=1]{figs/nass_tomography_hac_iff_m25.png}
+\end{center}
+\subcaption{\label{fig:nass_tomography_hac_iff_m25} $m = 25\,kg$}
+\end{subfigure}
+\begin{subfigure}{0.33\textwidth}
+\begin{center}
+\includegraphics[scale=1,scale=1]{figs/nass_tomography_hac_iff_m50.png}
+\end{center}
+\subcaption{\label{fig:nass_tomography_hac_iff_m50} $m = 50\,kg$}
+\end{subfigure}
+\caption{\label{fig:nass_tomography_hac_iff}Simulation of tomography experiments}
+\end{figure}
+
 \chapter{Conclusion}
 \label{sec:nass_conclusion}