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Add control kinematics block diagram

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Thomas Dehaeze 2025-02-12 15:40:46 +01:00
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commit c81cd4fbb6
14 changed files with 2372 additions and 80 deletions
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matlab/nass_model.slx
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matlab/src/initializeSimplifiedNanoHexapod.m
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@ -1,6 +1,7 @@
function [nano_hexapod] = initializeSimplifiedNanoHexapod(args)
arguments
args.type char {mustBeMember(args.type,{'none', 'stewart'})} = 'stewart'
%% initializeFramesPositions
args.H (1,1) double {mustBeNumeric, mustBePositive} = 95e-3 % Height of the nano-hexapod [m]
args.MO_B (1,1) double {mustBeNumeric} = 150e-3 % Height of {B} w.r.t. {M} [m]
@ -61,6 +62,13 @@ function [nano_hexapod] = initializeSimplifiedNanoHexapod(args)
stewart = initializeStewartPlatform();
switch args.type
case 'none'
stewart.type = 0;
case 'stewart'
stewart.type = 1;
end
stewart = initializeFramesPositions(stewart, ...
'H', args.H, ...
'MO_B', args.MO_B);

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matlab/subsystems/micro_hexapod_bot_plate.slx
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matlab/subsystems/micro_hexapod_strut.slx
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matlab/subsystems/micro_hexapod_top_plate.slx
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187
simscape-nass.org
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@ -219,8 +219,8 @@ CLOSED: [2025-02-12 Wed 12:10] SCHEDULED: <2025-02-12 Wed>
- [X] Remove nano-hexapod model and add simplified model
- [ ] Add "cylindrical" payloads (configurable in mass)
** TODO [#B] Add payload configurable subsystem
SCHEDULED: <2025-02-12 Wed>
** DONE [#B] Add payload configurable subsystem
CLOSED: [2025-02-12 Wed 14:17] SCHEDULED: <2025-02-12 Wed>
** TODO [#B] Discuss the necessity of estimated Rz?
@ -231,6 +231,16 @@ Here it can be reminded when doing the control in the cartesian frame.
** TODO [#B] Check if things are compatible to results of uniaxial model
** TODO [#C] Check if it would be interesting to show soft/stiff nano-hexapod plants
- [ ] Would we see u-station dynamics with very stiff nano-hexapod?
- [ ] Would rotation be difficult to handle with soft nano-hexapod?
** DONE [#A] Add possibility to configure the nano-hexapod to be fully rigid
CLOSED: [2025-02-12 Wed 14:46]
- Use to compare TF without the NASS
** CANC [#C] What performance metric can we use? :@christophe:
CLOSED: [2024-11-12 Tue 09:22]
- State "CANC" from "QUES" [2024-11-12 Tue 09:22]
@ -264,16 +274,21 @@ In this section:
<<sec:nass_kinematics>>
** Introduction :ignore:
- Explain how the position error can be expressed in the frame of the nano-hexapod
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/positioning_error.org][positioning_error]]: Explain how the NASS control is made (computation of the wanted position, measurement of the sample position, computation of the errors)
- Control architecture, block diagram
- Explained during the last section: HAC-IFF
Decentralized IFF
Centralized HAC, control in the frame of the struts
- To compute the positioning errors in the frame of the struts
- Compute the wanted pose of the sample with respect to the granite using the micro-station kinematics (Section ref:ssec:nass_ustation_kinematics)
- Measure the sample pose with respect to the granite using the external metrology and internal metrology for Rz (Section ref:ssec:nass_sample_pose_error)
- Compute the sample pose error and map these errors in the frame of the struts (Section ref:ssec:nass_error_struts)
- The complete control architecture is shown in Section ref:ssec:nass_control_architecture
- Schematic with micro-station + nass + metrology + control system
- Zoom in the control system with blocs
- Then explain all the blocs
- 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
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/positioning_error.org][positioning_error]]: Explain how the NASS control is made (computation of the wanted position, measurement of the sample position, computation of the errors)
- [ ] Schematic with micro-station + nass + metrology + control system => explain what is inside the control system
#+name: fig:nass_concept_schematic
#+caption: Figure caption
[[file:figs/nass_concept_schematic.png]]
** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
@ -301,17 +316,112 @@ In this section:
#+end_src
** Micro Station Kinematics
<<ssec:nass_ustation_kinematics>>
- from ref:ssec:ustation_kinematics, computation of the wanted sample pose from the setpoint of each stage.
wanted pose = Tdy * Try * Trz * Tu
** Computation of the sample's pose error
<<ssec:nass_sample_pose_error>>
From metrology (here supposed to be perfect 6-DoF), compute the sample's pose error.
Has to invert the homogeneous transformation.
** Position error in the frame of the nano-hexapod
In reality, 5DoF metrology => have to estimate the Rz using spindle encoder + nano-hexapod internal metrology (micro-hexapod does not perform Rz rotation).
Explain how to compute the errors in the frame of the struts (rotating)
** Position error in the frame of the struts
<<ssec:nass_error_struts>>
Explain how to compute the errors in the frame of the struts (rotating):
- Errors in the granite frame
- Errors in the frame of the nano-hexapod
- Errors in the frame of the struts => used for control
** Control Architecture
<<ssec:nass_control_architecture>>
- 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
#+begin_src latex :file nass_control_architecture.pdf
\begin{tikzpicture}
% Blocs
\node[block={2.0cm}{1.0cm}, fill=colorblue!20!white] (metrology) {Metrology};
\node[block={2.0cm}{2.0cm}, below=0.1 of metrology, align=center, fill=colorblue!20!white] (nhexa) {Nano\\Hexapod};
\node[block={3.0cm}{1.5cm}, below=0.1 of nhexa, align=center, fill=colorblue!20!white] (ustation) {Micro\\Station};
\coordinate[] (inputf) at ($(nhexa.south west)!0.5!(nhexa.north west)$);
\coordinate[] (outputfn) at ($(nhexa.south east)!0.3!(nhexa.north east)$);
\coordinate[] (outputde) at ($(nhexa.south east)!0.7!(nhexa.north east)$);
\coordinate[] (outputDy) at ($(ustation.south east)!0.1!(ustation.north east)$);
\coordinate[] (outputRy) at ($(ustation.south east)!0.5!(ustation.north east)$);
\coordinate[] (outputRz) at ($(ustation.south east)!0.9!(ustation.north east)$);
\node[block={1.0cm}{1.0cm}, right=0.5 of outputde, fill=colorred!20!white] (Rz_kinematics) {$\bm{J}_{R_z}^{-1}$};
\node[block={2.0cm}{2.0cm}, right=2.2 of ustation, align=center, fill=colorred!20!white] (ustation_kinematics) {Compute\\Reference\\Position};
\node[block={2.0cm}{2.0cm}, right=0.8 of ustation_kinematics, align=center, fill=colorred!20!white] (compute_error) {Compute\\Error\\Position};
\node[block={2.0cm}{2.0cm}, above=0.8 of compute_error, align=center, fill=colorred!20!white] (compute_pos) {Compute\\Sample\\Position};
\node[block={1.0cm}{1.0cm}, right=0.8 of compute_error, fill=colorred!20!white] (hexa_jacobian) {$\bm{J}$};
\coordinate[] (inputMetrology) at ($(compute_error.north east)!0.3!(compute_error.north west)$);
\coordinate[] (inputRz) at ($(compute_error.north east)!0.7!(compute_error.north west)$);
\node[addb={+}{}{}{}{}, right=0.4 of Rz_kinematics, fill=colorred!20!white] (addRz) {};
\draw[->] (Rz_kinematics.east) -- (addRz.west);
\draw[->] (outputRz-|addRz)node[branch]{} -- (addRz.south);
\draw[->] (outputDy) node[above right]{$r_{D_y}$} -- (outputDy-|ustation_kinematics.west);
\draw[->] (outputRy) node[above right]{$r_{R_y}$} -- (outputRy-|ustation_kinematics.west);
\draw[->] (outputRz) node[above right]{$r_{R_z}$} -- (outputRz-|ustation_kinematics.west);
\draw[->] (metrology.east)node[above right]{$[D_x,\,D_y,\,D_z,\,R_x,\,R_y]$} -- (compute_pos.west|-metrology);
\draw[->] (addRz.east)node[above right]{$R_z$} -- (compute_pos.west|-addRz);
\draw[->] (compute_pos.south)node -- (compute_error.north)node[above right]{$\bm{y}_{\mathcal{X}}$};
\draw[->] (outputde) -- (Rz_kinematics.west) node[above left]{$\bm{\mathcal{L}}$};
\draw[->] (ustation_kinematics.east) -- (compute_error.west) node[above left]{$\bm{r}_{\mathcal{X}}$};
\draw[->] (compute_error.east) -- (hexa_jacobian.west) node[above left]{$\bm{\epsilon\mathcal{X}}$};
\draw[->] (hexa_jacobian.east) -- ++(1.8, 0) node[above left]{$\bm{\epsilon\mathcal{L}}$};
\draw[->] (outputfn) -- ($(outputfn-|hexa_jacobian.east) + (1.0, 0)$)coordinate(fn) node[above left]{$\bm{f}_n$};
\begin{scope}[on background layer]
\node[fit={(metrology.north-|ustation.west) (hexa_jacobian.east|-compute_error.south)}, fill=black!10!white, draw, dashed, inner sep=4pt] (plant) {};
\node[anchor={north east}] at (plant.north east){$\text{Plant}$};
\end{scope}
\node[block, above=0.2 of plant, fill=coloryellow!20!white] (Kiff) {$\bm{K}_{\text{IFF}}$};
\draw[->] ($(fn)-(0.6,0)$)node[branch]{} |- (Kiff.east);
\node[addb={+}{}{}{}{}, left=0.8 of inputf] (addf) {};
\draw[->] (Kiff.west) -| (addf.north);
\begin{scope}[on background layer]
\node[fit={(plant.south-|fn) (addf.west|-Kiff.north)}, fill=black!20!white, draw, dashed, inner sep=4pt] (damped_plant) {};
\node[anchor={north east}] at (damped_plant.north east){$\text{Damped Plant}$};
\end{scope}
\begin{scope}[on background layer]
\node[fit={(metrology.north-|ustation.west) (hexa_jacobian.east|-compute_error.south)}, fill=black!10!white, draw, dashed, inner sep=4pt] (plant) {};
\node[anchor={north east}] at (plant.north east){$\text{Plant}$};
\end{scope}
\node[block, left=0.8 of addf, fill=colorgreen!20!white] (Khac) {$\bm{K}_{\text{HAC}}$};
\draw[->] ($(hexa_jacobian.east)+(1.4,0)$)node[branch]{} |- ($(Khac.west)+(-0.4, -3.4)$) |- (Khac.west);
\draw[->] (Khac.east) -- node[midway, above]{$\bm{f}^{\prime}$} (addf.west);
\draw[->] (addf.east) -- (inputf) node[above left]{$\bm{f}$};
\end{tikzpicture}
#+end_src
#+name: fig:nass_control_architecture
#+caption: 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.
#+attr_latex: :width \linewidth
#+RESULTS:
[[file:figs/nass_control_architecture.png]]
* Decentralized Active Damping
:PROPERTIES:
@ -320,11 +430,15 @@ Explain how to compute the errors in the frame of the struts (rotating)
<<sec:nass_active_damping>>
** Introduction :ignore:
- How to apply/optimize IFF on an hexapod? ()
- How to apply/optimize IFF on an hexapod?
- Robustness to payload mass
- Root Locus
- Damping optimization
Explain which samples are tested:
- 1kg, 25kg, 50kg
- cylindrical, 200mm height?
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/control_active_damping.org][control_active_damping]]
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/control-active-damping.org][active damping for stewart platforms]]
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/bibliography.org::*Vibration Control and Active Damping][Vibration Control and Active Damping]]
@ -356,6 +470,10 @@ Explain how to compute the errors in the frame of the struts (rotating)
** IFF Plant
- [ ] Show how it changes with the payload mass (1, 25, 50)
- [ ] Effect of rotation (no rotation - 60rpm)
- [ ] Added parallel stiffness
#+begin_src matlab
%% Identify the plant dynamics using the Simscape model
@ -388,23 +506,25 @@ initializeReferences();
% 'eL1', 'eL2', 'eL3', 'eL4', 'eL5', 'eL6'};
#+end_src
- Show how it changes with the payload mass (1, 25, 50)
- Effect of rotation (1rpm, 60rpm)
** Controller Design
- Apply IFF
- Show Root Locus
- Use Integral controller (with parallel stiffness)
- Show Root Locus (show that without parallel stiffness => unstable?)
- Choose optimal gain.
Here in MIMO, cannot have optimal damping for all modes. (there is a paper that tries to optimize that)
- Show robustness to change of payload (loci?)
- Show robustness to change of payload (loci?) / Change of rotating velocity ?
- Reference to paper showing stability in MIMO for decentralized IFF
** Sensitivity to disturbances
- Compute transfer functions from spindle vertical error to sample vertical error with IFF (and compare without the NASS)
- Same for horizontal
- Maybe noise budgeting, but may be complex in MIMO...
Disturbances:
- floor motion
- Spindle X and Z
- Direct forces?
- Compute sensitivity to disturbances with and without IFF (and compare without the NASS)
- Maybe noise budgeting, but may be complex in MIMO... ?
* Centralized Active Vibration Control
:PROPERTIES:
@ -451,22 +571,21 @@ From control kinematics:
** HAC Plant
- Compute transfer function from u to dL (with IFF applied)
** Effect of Payload mass
- Show effect of payload mass + rotation
- [ ] Compute transfer function from $\bm{f}$ to $\bm{\epsilon\mathcal{L}}$ (with IFF applied) for all masses
- [ ] Show effect of rotation
- [ ] Show effect of payload mass
- [ ] Compare with undamped plants
** Controller design
- Show robustness with Loci
- [ ] Show design HAC with formulas and parameters
- [ ] Show robustness with Loci for all masses
** Sensitivity to disturbances
- Compute transfer functions from spindle vertical error to sample vertical error with HAC-IFF
Compare without the NASS, and with just IFF
- Same for horizontal
- Maybe noise budgeting, but may be complex in MIMO...
** Tomography experiment
@ -1802,6 +1921,7 @@ end
function [nano_hexapod] = initializeSimplifiedNanoHexapod(args)
arguments
args.type char {mustBeMember(args.type,{'none', 'stewart'})} = 'stewart'
%% initializeFramesPositions
args.H (1,1) double {mustBeNumeric, mustBePositive} = 95e-3 % Height of the nano-hexapod [m]
args.MO_B (1,1) double {mustBeNumeric} = 150e-3 % Height of {B} w.r.t. {M} [m]
@ -1862,6 +1982,13 @@ function [nano_hexapod] = initializeSimplifiedNanoHexapod(args)
stewart = initializeStewartPlatform();
switch args.type
case 'none'
stewart.type = 0;
case 'stewart'
stewart.type = 1;
end
stewart = initializeFramesPositions(stewart, ...
'H', args.H, ...
'MO_B', args.MO_B);

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simscape-nass.tex
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@ -1,4 +1,4 @@
% Created 2025-02-12 Wed 11:34
% Created 2025-02-12 Wed 15:35
% Intended LaTeX compiler: pdflatex
\documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt}
@ -39,84 +39,121 @@ In this section:
\item Simulation of experiments
\end{itemize}
\begin{table}[htbp]
\centering
\begin{tabularx}{0.6\linewidth}{lX}
\toprule
\textbf{Sections} & \textbf{Matlab File}\\
\midrule
Section \ref{sec:nass_1_a} & \texttt{nass\_1\_.m}\\
\bottomrule
\end{tabularx}
\caption{\label{tab:nass_section_matlab_code}Report sections and corresponding Matlab files}
\end{table}
\chapter{Control Kinematics}
\label{sec:nass_kinematics}
\begin{itemize}
\item Explain how the position error can be expressed in the frame of the nano-hexapod
\item[{$\square$}] \href{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/positioning\_error.org}{positioning\_error}: Explain how the NASS control is made (computation of the wanted position, measurement of the sample position, computation of the errors)
\item Control architecture, block diagram
\item Schematic with micro-station + nass + metrology + control system
\item Zoom in the control system with blocs
\item Then explain all the blocs
\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 Explained during the last section: HAC-IFF
Decentralized IFF
Centralized HAC, control in the frame of the struts
\item To compute the positioning errors in the frame of the struts
\begin{itemize}
\item Compute the wanted pose of the sample with respect to the granite using the micro-station kinematics (Section \ref{ssec:nass_ustation_kinematics})
\item Measure the sample pose with respect to the granite using the external metrology and internal metrology for Rz (Section \ref{ssec:nass_sample_pose_error})
\item Compute the sample pose error and map these errors in the frame of the struts (Section \ref{ssec:nass_error_struts})
\end{itemize}
\item The complete control architecture is shown in Section \ref{ssec:nass_control_architecture}
\item[{$\square$}] \href{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/positioning\_error.org}{positioning\_error}: Explain how the NASS control is made (computation of the wanted position, measurement of the sample position, computation of the errors)
\item[{$\square$}] Schematic with micro-station + nass + metrology + control system => explain what is inside the control system
\end{itemize}
\begin{figure}[htbp]
\centering
\includegraphics[scale=1]{figs/nass_concept_schematic.png}
\caption{\label{fig:nass_concept_schematic}Figure caption}
\end{figure}
\section{Micro Station Kinematics}
\label{ssec:nass_ustation_kinematics}
\begin{itemize}
\item from \ref{ssec:ustation_kinematics}, computation of the wanted sample pose from the setpoint of each stage.
\end{itemize}
wanted pose = Tdy * Try * Trz * Tu
\section{Computation of the sample's pose error}
\label{ssec:nass_sample_pose_error}
From metrology (here supposed to be perfect 6-DoF), compute the sample's pose error.
Has to invert the homogeneous transformation.
\section{Position error in the frame of the nano-hexapod}
In reality, 5DoF metrology => have to estimate the Rz using spindle encoder + nano-hexapod internal metrology (micro-hexapod does not perform Rz rotation).
Explain how to compute the errors in the frame of the struts (rotating)
\section{Position error in the frame of the struts}
\label{ssec:nass_error_struts}
Explain how to compute the errors in the frame of the struts (rotating):
\begin{itemize}
\item Errors in the granite frame
\item Errors in the frame of the nano-hexapod
\item Errors in the frame of the struts => used for control
\end{itemize}
\section{Control Architecture}
\label{ssec:nass_control_architecture}
\begin{itemize}
\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}
\end{figure}
\chapter{Decentralized Active Damping}
\label{sec:nass_active_damping}
\begin{itemize}
\item How to apply/optimize IFF on an hexapod? ()
\item How to apply/optimize IFF on an hexapod?
\item Robustness to payload mass
\item Root Locus
\item Damping optimization
\end{itemize}
\item\relax [ ]\href{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/control\_active\_damping.org}{control\_active\_damping}
\item\relax [ ]\href{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/control-active-damping.org}{active damping for stewart platforms}
\item\relax [ ]\href{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/bibliography.org}{Vibration Control and Active Damping}
Explain which samples are tested:
\begin{itemize}
\item 1kg, 25kg, 50kg
\item cylindrical, 200mm height?
\item[{$\square$}] \href{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/control\_active\_damping.org}{control\_active\_damping}
\item[{$\square$}] \href{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/control-active-damping.org}{active damping for stewart platforms}
\item[{$\square$}] \href{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/bibliography.org}{Vibration Control and Active Damping}
\end{itemize}
\section{IFF Plant}
\begin{itemize}
\item Show how it changes with the payload mass (1, 25, 50)
\item Effect of rotation (1rpm, 60rpm)
\item[{$\square$}] Show how it changes with the payload mass (1, 25, 50)
\item[{$\square$}] Effect of rotation (no rotation - 60rpm)
\item[{$\square$}] Added parallel stiffness
\end{itemize}
\section{Controller Design}
\begin{itemize}
\item Apply IFF
\item Show Root Locus
\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?)
\item 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:
\begin{itemize}
\item Compute transfer functions from spindle vertical error to sample vertical error with IFF (and compare without the NASS)
\item Same for horizontal
\item Maybe noise budgeting, but may be complex in MIMO\ldots{}
\item floor motion
\item Spindle X and Z
\item Direct forces?
\item Compute sensitivity to disturbances with and without IFF (and compare without the NASS)
\item Maybe noise budgeting, but may be complex in MIMO\ldots{} ?
\end{itemize}
\chapter{Centralized Active Vibration Control}
@ -138,19 +175,17 @@ From control kinematics:
\section{HAC Plant}
\begin{itemize}
\item Compute transfer function from u to dL (with IFF applied)
\end{itemize}
\section{Effect of Payload mass}
\begin{itemize}
\item Show effect of payload mass + rotation
\item[{$\square$}] Compute transfer function from \(\bm{f}\) to \(\bm{\epsilon\mathcal{L}}\) (with IFF applied) for all masses
\item[{$\square$}] Show effect of rotation
\item[{$\square$}] Show effect of payload mass
\item[{$\square$}] Compare with undamped plants
\end{itemize}
\section{Controller design}
\begin{itemize}
\item Show robustness with Loci
\item[{$\square$}] Show design HAC with formulas and parameters
\item[{$\square$}] Show robustness with Loci for all masses
\end{itemize}
\section{Sensitivity to disturbances}
@ -159,7 +194,6 @@ From control kinematics:
\item Compute transfer functions from spindle vertical error to sample vertical error with HAC-IFF
Compare without the NASS, and with just IFF
\item Same for horizontal
\item Maybe noise budgeting, but may be complex in MIMO\ldots{}
\end{itemize}
\section{Tomography experiment}