From 61850dad9903cf90e22d532329de2435752e4d58 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Mon, 18 Nov 2024 11:46:34 +0100 Subject: [PATCH] Simscape => multi-body model --- test-bench-apa.org | 16 ++++++++-------- test-bench-apa.pdf | Bin 8391525 -> 8392264 bytes test-bench-apa.tex | 18 +++++++++--------- 3 files changed, 17 insertions(+), 17 deletions(-) diff --git a/test-bench-apa.org b/test-bench-apa.org index ae2d286..b16d81e 100644 --- a/test-bench-apa.org +++ b/test-bench-apa.org @@ -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') <> **** 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. 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\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.