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Simscape => multi-body model

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Thomas Dehaeze 2024-11-18 11:46:34 +01:00
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@ -163,7 +163,7 @@ Two different models of the APA300ML are presented.
First, in Section ref:sec:test_apa_model_2dof, a two degrees-of-freedom model is presented, tuned, and compared with the measured dynamics.
This model is proven to accurately represent the APA300ML's axial dynamics while having low complexity.
Then, in Section ref:sec:test_apa_model_flexible, a /super element/ of the APA300ML is extracted using a finite element model and imported into Simscape.
Then, in Section ref:sec:test_apa_model_flexible, a /super element/ of the APA300ML is extracted using a finite element model and imported into the multi-body model.
This more complex model also captures well capture the axial dynamics of the APA300ML.
#+name: fig:test_apa_received
@ -1325,13 +1325,13 @@ exportFig('figs/test_apa_iff_root_locus.pdf', 'width', 'half', 'height', 'tall')
<<sec:test_apa_model_2dof>>
**** Introduction :ignore:
In this section, a Simscape model (Figure ref:fig:test_apa_bench_model) of the measurement bench is used to tune the two degrees-of-freedom model of the APA using the measured frequency response functions.
In this section, a multi-body model (Figure ref:fig:test_apa_bench_model) of the measurement bench is used to tune the two degrees-of-freedom model of the APA using the measured frequency response functions.
This two degrees-of-freedom model is developed to accurately represent the APA300ML dynamics while having low complexity and a low number of associated states.
After the model is presented, the procedure for tuning the model is described, and the obtained model dynamics is compared with the measurements.
#+name: fig:test_apa_bench_model
#+caption: Screenshot of the Simscape model
#+caption: Screenshot of the multi-body model
#+attr_latex: :width 0.8\linewidth
[[file:figs/test_apa_bench_model.png]]
@ -1502,7 +1502,7 @@ The obtained parameters of the model shown in Figure ref:fig:test_apa_2dof_model
**** Obtained Dynamics :ignore:
The dynamics of the two degrees-of-freedom model of the APA300ML are extracted using optimized parameters (listed in Table ref:tab:test_apa_2dof_parameters) from the Simscape model.
The dynamics of the two degrees-of-freedom model of the APA300ML are extracted using optimized parameters (listed in Table ref:tab:test_apa_2dof_parameters) from the multi-body model.
This is compared with the experimental data in Figure ref:fig:test_apa_2dof_comp_frf.
A good match can be observed between the model and the experimental data, both for the encoder (Figure ref:fig:test_apa_2dof_comp_frf_enc) and for the force sensor (Figure ref:fig:test_apa_2dof_comp_frf_force).
This indicates that this model represents well the axial dynamics of the APA300ML.
@ -1632,14 +1632,14 @@ exportFig('figs/test_apa_2dof_comp_frf_force.pdf', 'width', 'half', 'height', 't
**** Introduction :ignore:
In this section, a /super element/ of the APA300ML is computed using a finite element software[fn:11].
It is then imported into Simscape (in the form of a stiffness matrix and a mass matrix) and included in the same model that was used in ref:sec:test_apa_model_2dof.
It is then imported into multi-body (in the form of a stiffness matrix and a mass matrix) and included in the same model that was used in ref:sec:test_apa_model_2dof.
This procedure is illustrated in Figure ref:fig:test_apa_super_element_simscape.
Several /remote points/ are defined in the finite element model (here illustrated by colorful planes and numbers from =1= to =5=) and are then made accessible in the Simscape model as shown at the right by the "frames" =F1= to =F5=.
Several /remote points/ are defined in the finite element model (here illustrated by colorful planes and numbers from =1= to =5=) and are then made accessible in Simscape as shown at the right by the "frames" =F1= to =F5=.
For the APA300ML /super element/, 5 /remote points/ are defined.
Two /remote points/ (=1= and =2=) are fixed to the top and bottom mechanical interfaces of the APA300ML and will be used to connect the APA300ML with other mechanical elements.
Two /remote points/ (=3= and =4=) are located across two piezoelectric stacks and are used to apply internal forces representing the actuator stacks.
Finally, two /remote points/ (=4= and =4=) are located across the third piezoelectric stack, and will be used to measured the strain of the sensor stack.
Finally, two /remote points/ (=4= and =5=) are located across the third piezoelectric stack, and will be used to measured the strain of the sensor stack.
#+name: fig:test_apa_super_element_simscape
#+attr_latex: :width 1.0\linewidth
@ -1688,7 +1688,7 @@ freqs = 5*logspace(0, 3, 1000);
**** Identification of the Actuator and Sensor constants
Once the APA300ML /super element/ is included in the Simscape model, the transfer function from $F_a$ to $d_L$ and $d_e$ can be extracted.
Once the APA300ML /super element/ is included in the multi-body model, the transfer function from $F_a$ to $d_L$ and $d_e$ can be extracted.
The gains $g_a$ and $g_s$ are then tuned such that the gains of the transfer functions match the identified ones.
By doing so, $g_s = 4.9\,V/\mu m$ and $g_a = 23.2\,N/V$ are obtained.

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test-bench-apa.tex
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@ -1,4 +1,4 @@
% Created 2024-10-29 Tue 12:36
% Created 2024-11-18 Mon 11:46
% Intended LaTeX compiler: pdflatex
\documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt}
@ -56,7 +56,7 @@ Two different models of the APA300ML are presented.
First, in Section \ref{sec:test_apa_model_2dof}, a two degrees-of-freedom model is presented, tuned, and compared with the measured dynamics.
This model is proven to accurately represent the APA300ML's axial dynamics while having low complexity.
Then, in Section \ref{sec:test_apa_model_flexible}, a \emph{super element} of the APA300ML is extracted using a finite element model and imported into Simscape.
Then, in Section \ref{sec:test_apa_model_flexible}, a \emph{super element} of the APA300ML is extracted using a finite element model and imported into the multi-body model.
This more complex model also captures well capture the axial dynamics of the APA300ML.
\begin{figure}[htbp]
@ -517,7 +517,7 @@ The two obtained root loci are compared in Figure \ref{fig:test_apa_iff_root_loc
\chapter{APA300ML - 2 degrees-of-freedom Model}
\label{sec:test_apa_model_2dof}
In this section, a Simscape model (Figure \ref{fig:test_apa_bench_model}) of the measurement bench is used to tune the two degrees-of-freedom model of the APA using the measured frequency response functions.
In this section, a multi-body model (Figure \ref{fig:test_apa_bench_model}) of the measurement bench is used to tune the two degrees-of-freedom model of the APA using the measured frequency response functions.
This two degrees-of-freedom model is developed to accurately represent the APA300ML dynamics while having low complexity and a low number of associated states.
After the model is presented, the procedure for tuning the model is described, and the obtained model dynamics is compared with the measurements.
@ -525,7 +525,7 @@ After the model is presented, the procedure for tuning the model is described, a
\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=0.8\linewidth]{figs/test_apa_bench_model.png}
\caption{\label{fig:test_apa_bench_model}Screenshot of the Simscape model}
\caption{\label{fig:test_apa_bench_model}Screenshot of the multi-body model}
\end{figure}
\paragraph{Two degrees-of-freedom APA Model}
@ -610,7 +610,7 @@ The obtained parameters of the model shown in Figure \ref{fig:test_apa_2dof_mode
\end{table}
The dynamics of the two degrees-of-freedom model of the APA300ML are extracted using optimized parameters (listed in Table \ref{tab:test_apa_2dof_parameters}) from the Simscape model.
The dynamics of the two degrees-of-freedom model of the APA300ML are extracted using optimized parameters (listed in Table \ref{tab:test_apa_2dof_parameters}) from the multi-body model.
This is compared with the experimental data in Figure \ref{fig:test_apa_2dof_comp_frf}.
A good match can be observed between the model and the experimental data, both for the encoder (Figure \ref{fig:test_apa_2dof_comp_frf_enc}) and for the force sensor (Figure \ref{fig:test_apa_2dof_comp_frf_force}).
This indicates that this model represents well the axial dynamics of the APA300ML.
@ -634,14 +634,14 @@ This indicates that this model represents well the axial dynamics of the APA300M
\chapter{APA300ML - Super Element}
\label{sec:test_apa_model_flexible}
In this section, a \emph{super element} of the APA300ML is computed using a finite element software\footnote{Ansys\textsuperscript{\textregistered} was used}.
It is then imported into Simscape (in the form of a stiffness matrix and a mass matrix) and included in the same model that was used in \ref{sec:test_apa_model_2dof}.
It is then imported into multi-body (in the form of a stiffness matrix and a mass matrix) and included in the same model that was used in \ref{sec:test_apa_model_2dof}.
This procedure is illustrated in Figure \ref{fig:test_apa_super_element_simscape}.
Several \emph{remote points} are defined in the finite element model (here illustrated by colorful planes and numbers from \texttt{1} to \texttt{5}) and are then made accessible in the Simscape model as shown at the right by the ``frames'' \texttt{F1} to \texttt{F5}.
Several \emph{remote points} are defined in the finite element model (here illustrated by colorful planes and numbers from \texttt{1} to \texttt{5}) and are then made accessible in Simscape as shown at the right by the ``frames'' \texttt{F1} to \texttt{F5}.
For the APA300ML \emph{super element}, 5 \emph{remote points} are defined.
Two \emph{remote points} (\texttt{1} and \texttt{2}) are fixed to the top and bottom mechanical interfaces of the APA300ML and will be used to connect the APA300ML with other mechanical elements.
Two \emph{remote points} (\texttt{3} and \texttt{4}) are located across two piezoelectric stacks and are used to apply internal forces representing the actuator stacks.
Finally, two \emph{remote points} (\texttt{4} and \texttt{4}) are located across the third piezoelectric stack, and will be used to measured the strain of the sensor stack.
Finally, two \emph{remote points} (\texttt{4} and \texttt{5}) are located across the third piezoelectric stack, and will be used to measured the strain of the sensor stack.
\begin{figure}[htbp]
\centering
@ -651,7 +651,7 @@ Finally, two \emph{remote points} (\texttt{4} and \texttt{4}) are located across
\paragraph{Identification of the Actuator and Sensor constants}
Once the APA300ML \emph{super element} is included in the Simscape model, the transfer function from \(F_a\) to \(d_L\) and \(d_e\) can be extracted.
Once the APA300ML \emph{super element} is included in the multi-body model, the transfer function from \(F_a\) to \(d_L\) and \(d_e\) can be extracted.
The gains \(g_a\) and \(g_s\) are then tuned such that the gains of the transfer functions match the identified ones.
By doing so, \(g_s = 4.9\,V/\mu m\) and \(g_a = 23.2\,N/V\) are obtained.