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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. 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. 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. This more complex model also captures well capture the axial dynamics of the APA300ML.
#+name: fig:test_apa_received #+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>> <<sec:test_apa_model_2dof>>
**** Introduction :ignore: **** 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. 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. 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 #+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 #+attr_latex: :width 0.8\linewidth
[[file:figs/test_apa_bench_model.png]] [[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: **** 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. 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). 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. 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: **** Introduction :ignore:
In this section, a /super element/ of the APA300ML is computed using a finite element software[fn:11]. 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. 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. 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/ (=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. 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 #+name: fig:test_apa_super_element_simscape
#+attr_latex: :width 1.0\linewidth #+attr_latex: :width 1.0\linewidth
@ -1688,7 +1688,7 @@ freqs = 5*logspace(0, 3, 1000);
**** Identification of the Actuator and Sensor constants **** 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. 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. 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 % Intended LaTeX compiler: pdflatex
\documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt} \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. 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. 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. This more complex model also captures well capture the axial dynamics of the APA300ML.
\begin{figure}[htbp] \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} \chapter{APA300ML - 2 degrees-of-freedom Model}
\label{sec:test_apa_model_2dof} \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. 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. 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] \begin{figure}[htbp]
\centering \centering
\includegraphics[scale=1,width=0.8\linewidth]{figs/test_apa_bench_model.png} \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} \end{figure}
\paragraph{Two degrees-of-freedom APA Model} \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} \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}. 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}). 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. 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} \chapter{APA300ML - Super Element}
\label{sec:test_apa_model_flexible} \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}. 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}. 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. 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{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. 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] \begin{figure}[htbp]
\centering \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} \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. 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. By doing so, \(g_s = 4.9\,V/\mu m\) and \(g_a = 23.2\,N/V\) are obtained.