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Simscape => multi-body model

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Thomas Dehaeze 2024-11-18 13:06:19 +01:00
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@ -87,7 +87,7 @@
#+END_SRC #+END_SRC
* Notes :noexport: * Notes :noexport:
** Notes
Prefix for figures/section/tables =test_struts= Prefix for figures/section/tables =test_struts=
To integrate: To integrate:
@ -1112,6 +1112,7 @@ The same comparison is made for the transfer function from $u$ to $d_e$ (encoder
In this study, large dynamics differences were observed between the 5 struts. In this study, large dynamics differences were observed between the 5 struts.
Although the same resonance frequencies were seen for all of the struts (95Hz, 200Hz, 300Hz and 400Hz), the amplitude of the peaks were not the same. Although the same resonance frequencies were seen for all of the struts (95Hz, 200Hz, 300Hz and 400Hz), the amplitude of the peaks were not the same.
In addition, the location or even presence of complex conjugate zeros changes from one strut to another. In addition, the location or even presence of complex conjugate zeros changes from one strut to another.
The reason for this variability will be studied in the next section thanks to the strut model.
#+begin_src matlab :tangle no :exports none #+begin_src matlab :tangle no :exports none
%% Save the estimated FRF for further analysis %% Save the estimated FRF for further analysis
@ -1123,15 +1124,6 @@ save('./matlab/mat/meas_struts_frf.mat', 'f', 'enc_frf', 'int_frf', 'iff_frf', '
save('./mat/meas_struts_frf.mat', 'f', 'enc_frf', 'int_frf', 'iff_frf', 'strut_nums'); save('./mat/meas_struts_frf.mat', 'f', 'enc_frf', 'int_frf', 'iff_frf', 'strut_nums');
#+end_src #+end_src
** Conclusion
:PROPERTIES:
:UNNUMBERED: t
:END:
All the struts exhibit very consistent behavior from the excitation voltage $u$ to the force sensor generated voltage $V_s$ and to the interferometer measured displacement $d_a$.
However, the dynamics from $u$ to the encoder measurement $d_e$ is much more complex and vary from one strut to the another.
The reason for this variability will be studied in the next section thanks to the strut model.
* Strut Model * Strut Model
:PROPERTIES: :PROPERTIES:
:header-args:matlab+: :tangle matlab/test_struts_3_simscape_model.m :header-args:matlab+: :tangle matlab/test_struts_3_simscape_model.m
@ -1139,7 +1131,7 @@ The reason for this variability will be studied in the next section thanks to th
<<sec:test_struts_simscape>> <<sec:test_struts_simscape>>
** Introduction :ignore: ** Introduction :ignore:
The Simscape model of the strut was included in the Simscape model of the test bench (see Figure ref:fig:test_struts_simscape_model). The multi-body model of the strut was included in the multi-body model of the test bench (see Figure ref:fig:test_struts_simscape_model).
The obtained model was first used to compare the measured FRF with the existing model (Section ref:ssec:test_struts_comp_model). The obtained model was first used to compare the measured FRF with the existing model (Section ref:ssec:test_struts_comp_model).
Using a flexible APA model (extracted from a acrshort:fem), the effect of a misalignment of the APA with respect to flexible joints is studied (Section ref:ssec:test_struts_effect_misalignment). Using a flexible APA model (extracted from a acrshort:fem), the effect of a misalignment of the APA with respect to flexible joints is studied (Section ref:ssec:test_struts_effect_misalignment).
@ -1148,7 +1140,7 @@ This misalignment is estimated and measured in Section ref:ssec:test_struts_meas
The struts were then disassembled and reassemble a second time to optimize alignment (Section ref:sec:test_struts_meas_all_aligned_struts). The struts were then disassembled and reassemble a second time to optimize alignment (Section ref:sec:test_struts_meas_all_aligned_struts).
#+name: fig:test_struts_simscape_model #+name: fig:test_struts_simscape_model
#+caption: Screenshot of the Simscape model of the strut fixed to the bench #+caption: Screenshot of the multi-body model of the strut fixed to the bench
#+attr_latex: :width 0.65\linewidth #+attr_latex: :width 0.65\linewidth
[[file:figs/test_struts_simscape_model.png]] [[file:figs/test_struts_simscape_model.png]]
@ -1383,7 +1375,7 @@ exportFig('figs/test_struts_comp_frf_flexible_model_iff.pdf', 'width', 400, 'hei
#+end_src #+end_src
#+name: fig:test_struts_comp_frf_flexible_model #+name: fig:test_struts_comp_frf_flexible_model
#+caption: Comparison of the measured frequency response functions, the Simscape model using the 2 DoF APA model, and using the "flexible" APA300ML model (Super-Element extracted from a Finite Element Model). #+caption: Comparison of the measured frequency response functions, the multi-body model using the 2 DoF APA model, and using the "flexible" APA300ML model (Super-Element extracted from a Finite Element Model).
#+attr_latex: :options [htbp] #+attr_latex: :options [htbp]
#+begin_figure #+begin_figure
#+attr_latex: :caption \subcaption{\label{fig:test_struts_comp_frf_flexible_model_int}$u$ to $d_a$} #+attr_latex: :caption \subcaption{\label{fig:test_struts_comp_frf_flexible_model_int}$u$ to $d_a$}
@ -1419,7 +1411,7 @@ In this case, the "x-bending" mode at 200Hz (see Figure ref:fig:test_struts_meas
#+attr_latex: :width 0.8\linewidth #+attr_latex: :width 0.8\linewidth
[[file:figs/test_struts_misalign_schematic.png]] [[file:figs/test_struts_misalign_schematic.png]]
To verify this assumption, the dynamics from the output DAC voltage $u$ to the measured displacement by the encoder $d_e$ is computed using the flexible APA Simscape model for several misalignments in the $y$ direction. To verify this assumption, the dynamics from the output DAC voltage $u$ to the measured displacement by the encoder $d_e$ is computed using the flexible APA model for several misalignments in the $y$ direction.
The obtained dynamics are shown in Figure ref:fig:test_struts_effect_misalignment_y. The obtained dynamics are shown in Figure ref:fig:test_struts_effect_misalignment_y.
The alignment of the APA with the flexible joints has a large influence on the dynamics from actuator voltage to the measured displacement by the encoder. The alignment of the APA with the flexible joints has a large influence on the dynamics from actuator voltage to the measured displacement by the encoder.
The misalignment in the $y$ direction mostly influences: The misalignment in the $y$ direction mostly influences:
@ -1629,7 +1621,7 @@ data2orgtable([dy_bot, dy_top] , {'1', '2', '3', '4', '5'}, {'*Strut*', '*Bot*',
| 4 | -0.01 | 0.54 | | 4 | -0.01 | 0.54 |
| 5 | 0.15 | 0.02 | | 5 | 0.15 | 0.02 |
By using the measured $y$ misalignment in the Simscape model with the flexible APA model, the model dynamics from $u$ to $d_e$ is closer to the measured dynamics, as shown in Figure ref:fig:test_struts_comp_dy_tuned_model_frf_enc. By using the measured $y$ misalignment in the model with the flexible APA model, the model dynamics from $u$ to $d_e$ is closer to the measured dynamics, as shown in Figure ref:fig:test_struts_comp_dy_tuned_model_frf_enc.
A better match in the dynamics can be obtained by fine-tuning both the $x$ and $y$ misalignments (yellow curves in Figure ref:fig:test_struts_comp_dy_tuned_model_frf_enc). A better match in the dynamics can be obtained by fine-tuning both the $x$ and $y$ misalignments (yellow curves in Figure ref:fig:test_struts_comp_dy_tuned_model_frf_enc).
This confirms that misalignment between the APA and the strut axis (determined by the two flexible joints) is critical and inducing large variations in the dynamics from DAC voltage $u$ to encoder measured displacement $d_e$. This confirms that misalignment between the APA and the strut axis (determined by the two flexible joints) is critical and inducing large variations in the dynamics from DAC voltage $u$ to encoder measured displacement $d_e$.

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test-bench-struts.tex
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@ -1,4 +1,4 @@
% Created 2024-11-18 Mon 10:26 % Created 2024-11-18 Mon 13:05
% Intended LaTeX compiler: pdflatex % Intended LaTeX compiler: pdflatex
\documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt} \documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt}
@ -254,7 +254,6 @@ In addition, the computed resonance frequencies from the \acrshort{fem} are very
This validates the quality of the \acrshort{fem}. This validates the quality of the \acrshort{fem}.
\begin{table}[htbp] \begin{table}[htbp]
\caption{\label{tab:test_struts_spur_mode_freqs}Measured frequency of the flexible modes of the strut}
\centering \centering
\begin{tabularx}{0.9\linewidth}{Xccc} \begin{tabularx}{0.9\linewidth}{Xccc}
\toprule \toprule
@ -265,6 +264,8 @@ Y-Bending & 285Hz & 293Hz & 337Hz\\
Z-Torsion & 400Hz & 381Hz & 398Hz\\ Z-Torsion & 400Hz & 381Hz & 398Hz\\
\bottomrule \bottomrule
\end{tabularx} \end{tabularx}
\caption{\label{tab:test_struts_spur_mode_freqs}Measured frequency of the flexible modes of the strut}
\end{table} \end{table}
\chapter{Dynamical measurements} \chapter{Dynamical measurements}
@ -387,15 +388,11 @@ The same comparison is made for the transfer function from \(u\) to \(d_e\) (enc
In this study, large dynamics differences were observed between the 5 struts. In this study, large dynamics differences were observed between the 5 struts.
Although the same resonance frequencies were seen for all of the struts (95Hz, 200Hz, 300Hz and 400Hz), the amplitude of the peaks were not the same. Although the same resonance frequencies were seen for all of the struts (95Hz, 200Hz, 300Hz and 400Hz), the amplitude of the peaks were not the same.
In addition, the location or even presence of complex conjugate zeros changes from one strut to another. In addition, the location or even presence of complex conjugate zeros changes from one strut to another.
\section*{Conclusion}
All the struts exhibit very consistent behavior from the excitation voltage \(u\) to the force sensor generated voltage \(V_s\) and to the interferometer measured displacement \(d_a\).
However, the dynamics from \(u\) to the encoder measurement \(d_e\) is much more complex and vary from one strut to the another.
The reason for this variability will be studied in the next section thanks to the strut model. The reason for this variability will be studied in the next section thanks to the strut model.
\chapter{Strut Model} \chapter{Strut Model}
\label{sec:test_struts_simscape} \label{sec:test_struts_simscape}
The Simscape model of the strut was included in the Simscape model of the test bench (see Figure \ref{fig:test_struts_simscape_model}). The multi-body model of the strut was included in the multi-body model of the test bench (see Figure \ref{fig:test_struts_simscape_model}).
The obtained model was first used to compare the measured FRF with the existing model (Section \ref{ssec:test_struts_comp_model}). The obtained model was first used to compare the measured FRF with the existing model (Section \ref{ssec:test_struts_comp_model}).
Using a flexible APA model (extracted from a \acrshort{fem}), the effect of a misalignment of the APA with respect to flexible joints is studied (Section \ref{ssec:test_struts_effect_misalignment}). Using a flexible APA model (extracted from a \acrshort{fem}), the effect of a misalignment of the APA with respect to flexible joints is studied (Section \ref{ssec:test_struts_effect_misalignment}).
@ -406,7 +403,7 @@ The struts were then disassembled and reassemble a second time to optimize align
\begin{figure}[htbp] \begin{figure}[htbp]
\centering \centering
\includegraphics[scale=1,width=0.65\linewidth]{figs/test_struts_simscape_model.png} \includegraphics[scale=1,width=0.65\linewidth]{figs/test_struts_simscape_model.png}
\caption{\label{fig:test_struts_simscape_model}Screenshot of the Simscape model of the strut fixed to the bench} \caption{\label{fig:test_struts_simscape_model}Screenshot of the multi-body model of the strut fixed to the bench}
\end{figure} \end{figure}
\section{Model dynamics} \section{Model dynamics}
\label{ssec:test_struts_comp_model} \label{ssec:test_struts_comp_model}
@ -441,7 +438,7 @@ For the flexible model, it will be shown in the next section that by adding some
\end{center} \end{center}
\subcaption{\label{fig:test_struts_comp_frf_flexible_model_iff}$u$ to $V_s$} \subcaption{\label{fig:test_struts_comp_frf_flexible_model_iff}$u$ to $V_s$}
\end{subfigure} \end{subfigure}
\caption{\label{fig:test_struts_comp_frf_flexible_model}Comparison of the measured frequency response functions, the Simscape model using the 2 DoF APA model, and using the ``flexible'' APA300ML model (Super-Element extracted from a Finite Element Model).} \caption{\label{fig:test_struts_comp_frf_flexible_model}Comparison of the measured frequency response functions, the multi-body model using the 2 DoF APA model, and using the ``flexible'' APA300ML model (Super-Element extracted from a Finite Element Model).}
\end{figure} \end{figure}
\section{Effect of strut misalignment} \section{Effect of strut misalignment}
@ -458,7 +455,7 @@ In this case, the ``x-bending'' mode at 200Hz (see Figure \ref{fig:test_struts_m
\caption{\label{fig:test_struts_misalign_schematic}Mis-alignement between the joints and the APA} \caption{\label{fig:test_struts_misalign_schematic}Mis-alignement between the joints and the APA}
\end{figure} \end{figure}
To verify this assumption, the dynamics from the output DAC voltage \(u\) to the measured displacement by the encoder \(d_e\) is computed using the flexible APA Simscape model for several misalignments in the \(y\) direction. To verify this assumption, the dynamics from the output DAC voltage \(u\) to the measured displacement by the encoder \(d_e\) is computed using the flexible APA model for several misalignments in the \(y\) direction.
The obtained dynamics are shown in Figure \ref{fig:test_struts_effect_misalignment_y}. The obtained dynamics are shown in Figure \ref{fig:test_struts_effect_misalignment_y}.
The alignment of the APA with the flexible joints has a large influence on the dynamics from actuator voltage to the measured displacement by the encoder. The alignment of the APA with the flexible joints has a large influence on the dynamics from actuator voltage to the measured displacement by the encoder.
The misalignment in the \(y\) direction mostly influences: The misalignment in the \(y\) direction mostly influences:
@ -513,7 +510,6 @@ To check the validity of the measurement, it can be verified that the sum of the
Thickness differences for all the struts were found to be between \(0.94\,mm\) and \(1.00\,mm\) which indicate low errors compared to the misalignments found in Table \ref{tab:test_struts_meas_y_misalignment}. Thickness differences for all the struts were found to be between \(0.94\,mm\) and \(1.00\,mm\) which indicate low errors compared to the misalignments found in Table \ref{tab:test_struts_meas_y_misalignment}.
\begin{table}[htbp] \begin{table}[htbp]
\caption{\label{tab:test_struts_meas_y_misalignment}Measured \(y\) misalignment at the top and bottom of the APA. Measurements are in \(mm\)}
\centering \centering
\begin{tabularx}{0.25\linewidth}{ccc} \begin{tabularx}{0.25\linewidth}{ccc}
\toprule \toprule
@ -526,9 +522,11 @@ Thickness differences for all the struts were found to be between \(0.94\,mm\) a
5 & 0.15 & 0.02\\ 5 & 0.15 & 0.02\\
\bottomrule \bottomrule
\end{tabularx} \end{tabularx}
\caption{\label{tab:test_struts_meas_y_misalignment}Measured \(y\) misalignment at the top and bottom of the APA. Measurements are in \(mm\)}
\end{table} \end{table}
By using the measured \(y\) misalignment in the Simscape model with the flexible APA model, the model dynamics from \(u\) to \(d_e\) is closer to the measured dynamics, as shown in Figure \ref{fig:test_struts_comp_dy_tuned_model_frf_enc}. By using the measured \(y\) misalignment in the model with the flexible APA model, the model dynamics from \(u\) to \(d_e\) is closer to the measured dynamics, as shown in Figure \ref{fig:test_struts_comp_dy_tuned_model_frf_enc}.
A better match in the dynamics can be obtained by fine-tuning both the \(x\) and \(y\) misalignments (yellow curves in Figure \ref{fig:test_struts_comp_dy_tuned_model_frf_enc}). A better match in the dynamics can be obtained by fine-tuning both the \(x\) and \(y\) misalignments (yellow curves in Figure \ref{fig:test_struts_comp_dy_tuned_model_frf_enc}).
This confirms that misalignment between the APA and the strut axis (determined by the two flexible joints) is critical and inducing large variations in the dynamics from DAC voltage \(u\) to encoder measured displacement \(d_e\). This confirms that misalignment between the APA and the strut axis (determined by the two flexible joints) is critical and inducing large variations in the dynamics from DAC voltage \(u\) to encoder measured displacement \(d_e\).
@ -553,7 +551,6 @@ The alignment is then estimated using a length gauge, as described in the previo
Measured \(y\) alignments are summarized in Table \ref{tab:test_struts_meas_y_misalignment_with_pin} and are found to be bellow \(55\mu m\) for all the struts, which is much better than before (see Table \ref{tab:test_struts_meas_y_misalignment}). Measured \(y\) alignments are summarized in Table \ref{tab:test_struts_meas_y_misalignment_with_pin} and are found to be bellow \(55\mu m\) for all the struts, which is much better than before (see Table \ref{tab:test_struts_meas_y_misalignment}).
\begin{table}[htbp] \begin{table}[htbp]
\caption{\label{tab:test_struts_meas_y_misalignment_with_pin}Measured \(y\) misalignment at the top and bottom of the APA after realigning the struts using a positioning pin. Measurements are in \(mm\).}
\centering \centering
\begin{tabularx}{0.25\linewidth}{ccc} \begin{tabularx}{0.25\linewidth}{ccc}
\toprule \toprule
@ -567,6 +564,8 @@ Measured \(y\) alignments are summarized in Table \ref{tab:test_struts_meas_y_mi
6 & -0.005 & 0.055\\ 6 & -0.005 & 0.055\\
\bottomrule \bottomrule
\end{tabularx} \end{tabularx}
\caption{\label{tab:test_struts_meas_y_misalignment_with_pin}Measured \(y\) misalignment at the top and bottom of the APA after realigning the struts using a positioning pin. Measurements are in \(mm\).}
\end{table} \end{table}
The dynamics of the re-aligned struts were then measured on the same test bench (Figure \ref{fig:test_struts_bench_leg}). The dynamics of the re-aligned struts were then measured on the same test bench (Figure \ref{fig:test_struts_bench_leg}).