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Thomas Dehaeze 2024-03-23 11:10:15 +01:00
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@ -110,9 +110,9 @@ Prefix for figures/section/tables =test_apa=
- Dynamical measurements (Section 3) - Dynamical measurements (Section 3)
- Simscape Model (Section 4) - Simscape Model (Section 4)
** TODO [#B] Add sitffness of APA shell from FEM ** TODO [#C] Add sitffness of APA shell from FEM :@philipp:
** TODO [#B] Check things about resistor in parallel with the force sensor ** TODO [#C] Check things about resistor in parallel with the force sensor
Verify that everything interesting to say about that is either done before in the thesis or in this report. Verify that everything interesting to say about that is either done before in the thesis or in this report.
@ -130,8 +130,7 @@ The first goal is to characterize the APA300ML in terms of:
- The dynamics from the generated DAC voltage (going to the voltage amplifiers and then applied on the actuator stacks) to the induced displacement, and to the measured voltage by the force sensor stack. - The dynamics from the generated DAC voltage (going to the voltage amplifiers and then applied on the actuator stacks) to the induced displacement, and to the measured voltage by the force sensor stack.
Also the "actuator constant" and "sensor constant" are identified. Also the "actuator constant" and "sensor constant" are identified.
This is done in Section ref:sec:test_apa_dynamics. This is done in Section ref:sec:test_apa_dynamics.
- Compare the measurements with the Simscape models (2DoF, Super-Element) in order to tuned/validate the models. - Compare the measurements with the two Simscape models: 2DoF (Section ref:sec:test_apa_model_2dof) Super-Element (Section ref:sec:test_apa_model_flexible)
This is explained in Section ref:sec:test_apa_simscape.
#+name: tab:test_apa_section_matlab_code #+name: tab:test_apa_section_matlab_code
#+caption: Report sections and corresponding Matlab files #+caption: Report sections and corresponding Matlab files
@ -153,10 +152,10 @@ The first goal is to characterize the APA300ML in terms of:
** Introduction :ignore: ** Introduction :ignore:
Before using the measurement bench to characterize the APA300ML, first simple measurements are performed: Before using the measurement bench to characterize the APA300ML, first simple measurements are performed:
- Section ref:sec:test_apa_geometrical_measurements: the geometric tolerances of the interface planes are checked - Section ref:ssec:test_apa_geometrical_measurements: the geometric tolerances of the interface planes are checked
- Section ref:sec:test_apa_electrical_measurements: the capacitance of the piezoelectric stacks is measured - Section ref:ssec:test_apa_electrical_measurements: the capacitance of the piezoelectric stacks is measured
- Section ref:sec:test_apa_stroke_measurements: the stroke of each APA is measured - Section ref:ssec:test_apa_stroke_measurements: the stroke of each APA is measured
- Section ref:sec:test_apa_spurious_resonances: the "spurious" resonances of the APA are investigated - Section ref:ssec:test_apa_spurious_resonances: the "spurious" resonances of the APA are investigated
** Matlab Init :noexport:ignore: ** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
@ -180,7 +179,7 @@ Before using the measurement bench to characterize the APA300ML, first simple me
#+end_src #+end_src
** Geometrical Measurements ** Geometrical Measurements
<<sec:test_apa_geometrical_measurements>> <<ssec:test_apa_geometrical_measurements>>
To measure the flatness of the two mechanical interfaces of the APA300ML, a small measurement bench is installed on top of a metrology granite with very good flatness. To measure the flatness of the two mechanical interfaces of the APA300ML, a small measurement bench is installed on top of a metrology granite with very good flatness.
@ -252,7 +251,7 @@ data2orgtable(1e6*apa_d', {'APA 1', 'APA 2', 'APA 3', 'APA 4', 'APA 5', 'APA 6',
| APA 7 | 18.7 | | APA 7 | 18.7 |
** Electrical Measurements ** Electrical Measurements
<<sec:test_apa_electrical_measurements>> <<ssec:test_apa_electrical_measurements>>
From the documentation of the APA300ML, the total capacitance of the three stacks should be between $18\,\mu F$ and $26\,\mu F$ with a nominal capacitance of $20\,\mu F$. From the documentation of the APA300ML, the total capacitance of the three stacks should be between $18\,\mu F$ and $26\,\mu F$ with a nominal capacitance of $20\,\mu F$.
@ -286,7 +285,7 @@ This may be due to the fact that the manufacturer measures the capacitance with
| APA 7 | 4.85 | 9.85 | | APA 7 | 4.85 | 9.85 |
** Stroke and Hysteresis Measurement ** Stroke and Hysteresis Measurement
<<sec:test_apa_stroke_measurements>> <<ssec:test_apa_stroke_measurements>>
The goal is here to verify that the stroke of the APA300ML is as specified in the datasheet. The goal is here to verify that the stroke of the APA300ML is as specified in the datasheet.
To do so, one side of the APA is fixed to the granite, and a displacement probe[fn:2] is located on the other side as shown in Figure ref:fig:test_apa_stroke_bench. To do so, one side of the APA is fixed to the granite, and a displacement probe[fn:2] is located on the other side as shown in Figure ref:fig:test_apa_stroke_bench.
@ -306,7 +305,7 @@ The measured stroke is approximately $250\,\mu m$ when using only two of the thr
This is even above what is specified as the nominal stroke in the data-sheet ($304\,\mu m$, therefore $\approx 200\,\mu m$ if only two stacks are used). This is even above what is specified as the nominal stroke in the data-sheet ($304\,\mu m$, therefore $\approx 200\,\mu m$ if only two stacks are used).
It is clear from Figure ref:fig:test_apa_stroke_result that "APA 3" has an issue compared to the other units. It is clear from Figure ref:fig:test_apa_stroke_result that "APA 3" has an issue compared to the other units.
This confirms the abnormal electrical measurements made in Section ref:sec:test_apa_electrical_measurements. This confirms the abnormal electrical measurements made in Section ref:ssec:test_apa_electrical_measurements.
This unit was send sent back to Cedrat and a new one was shipped back. This unit was send sent back to Cedrat and a new one was shipped back.
From now on, only the six APA that behave as expected will be used. From now on, only the six APA that behave as expected will be used.
@ -348,8 +347,7 @@ exportFig('figs/test_apa_stroke_result.pdf', 'width', 'full', 'height', 'normal'
[[file:figs/test_apa_stroke_result.png]] [[file:figs/test_apa_stroke_result.png]]
** Flexible Mode Measurement ** Flexible Mode Measurement
SCHEDULED: <2024-03-27 Wed> <<ssec:test_apa_spurious_resonances>>
<<sec:test_apa_spurious_resonances>>
In this section, the flexible modes of the APA300ML are investigated both experimentally and using a Finite Element Model. In this section, the flexible modes of the APA300ML are investigated both experimentally and using a Finite Element Model.
@ -513,10 +511,12 @@ The bench is schematically shown in Figure ref:fig:test_apa_schematic and the si
| $d_e$ | Encoder Measurement | $m$ | | $d_e$ | Encoder Measurement | $m$ |
This bench will be used to: This bench will be used to:
- measure the dynamics of the APA (from $V_a$ to $d_e$ and $d_a$ in Section ref:ssec:test_apa_meas_frf_disp, and from $V_a$ to $V_s$ in section ref:ssec:test_apa_meas_frf_force) - ref:ssec:test_apa_hysteresis
- ref:ssec:test_apa_stiffness
- measure the dynamics of the APA (section ref:ssec:test_apa_meas_dynamics)
- estimate the added damping using Integral Force Feedback (Section ref:ssec:test_apa_iff_locus) - estimate the added damping using Integral Force Feedback (Section ref:ssec:test_apa_iff_locus)
These measurements will also be used to tune the model of the APA in Section ref:sec:test_apa_simscape. These measurements will also be used to tune the developed models of the APA (in Section ref:sec:test_apa_model_2dof for the 2DoF model, and in Section ref:sec:test_apa_model_flexible for the flexible model).
** Matlab Init :noexport:ignore: ** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
@ -1182,7 +1182,7 @@ exportFig('figs/test_apa_iff_root_locus.pdf', 'width', 'wide', 'height', 'tall')
So far, all the measured FRF are showing the dynamical behavior that was expected. So far, all the measured FRF are showing the dynamical behavior that was expected.
#+end_important #+end_important
* 2 Degrees of Freedom Model * APA300ML - 2 Degrees of Freedom Model
:PROPERTIES: :PROPERTIES:
:header-args:matlab+: :tangle matlab/test_apa_3_model_2dof.m :header-args:matlab+: :tangle matlab/test_apa_3_model_2dof.m
:END: :END:
@ -1191,11 +1191,9 @@ So far, all the measured FRF are showing the dynamical behavior that was expecte
** Introduction :ignore: ** Introduction :ignore:
In this section, a simscape model (Figure ref:fig:test_apa_bench_model) of the measurement bench is used to compare the model of the APA with the measured frequency response functions. In this section, a simscape model (Figure ref:fig:test_apa_bench_model) of the measurement bench is used to compare the model of the APA with the measured frequency response functions.
After the transfer functions are extracted from the model (Section ref:sec:simscape_bench_apa_first_id), the comparison of the obtained dynamics with the measured FRF will permit to: A 2 degrees of freedom model is used to model the APA300ML.
1. Estimate the "actuator constant" and "sensor constant" (Section ref:sec:simscape_bench_apa_id_constants) This model is presented in Section ref:ssec:test_apa_2dof_model and the procedure to tuned the model is described in Section ref:ssec:test_apa_2dof_model_tuning.
- "Actuator constant": Gain from the applied voltage $V_a$ to the generated Force $F_a$ The obtained model dynamics is compared with the measurements in Section ref:ssec:test_apa_2dof_model_result.
- "Sensor constant": Gain from the sensor stack strain $\delta L$ to the generated voltage $V_s$
2. Tune the model of the APA to match the measured dynamics (Section ref:sec:simscape_bench_apa_tune_2dof_model)
#+name: fig:test_apa_bench_model #+name: fig:test_apa_bench_model
#+caption: Screenshot of the Simscape model #+caption: Screenshot of the Simscape model
@ -1620,6 +1618,7 @@ ga = d33*n*ka; % Actuator Constant [N/V]
#+end_src #+end_src
** Comparison of the obtained dynamics ** Comparison of the obtained dynamics
<<ssec:test_apa_flexible_comp_frf>>
The obtained dynamics using the /super element/ with the tuned "sensor gain" and "actuator gain" are compared with the experimentally identified frequency response functions in Figure ref:fig:test_apa_super_element_comp_frf. The obtained dynamics using the /super element/ with the tuned "sensor gain" and "actuator gain" are compared with the experimentally identified frequency response functions in Figure ref:fig:test_apa_super_element_comp_frf.

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test-bench-apa.tex
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@ -1,4 +1,4 @@
% Created 2024-03-22 Fri 19:12 % Created 2024-03-23 Sat 11:09
% 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}
@ -35,8 +35,7 @@ This is performed in Section \ref{sec:test_apa_basic_meas}.
\item The dynamics from the generated DAC voltage (going to the voltage amplifiers and then applied on the actuator stacks) to the induced displacement, and to the measured voltage by the force sensor stack. \item The dynamics from the generated DAC voltage (going to the voltage amplifiers and then applied on the actuator stacks) to the induced displacement, and to the measured voltage by the force sensor stack.
Also the ``actuator constant'' and ``sensor constant'' are identified. Also the ``actuator constant'' and ``sensor constant'' are identified.
This is done in Section \ref{sec:test_apa_dynamics}. This is done in Section \ref{sec:test_apa_dynamics}.
\item Compare the measurements with the Simscape models (2DoF, Super-Element) in order to tuned/validate the models. \item Compare the measurements with the two Simscape models: 2DoF (Section \ref{sec:test_apa_model_2dof}) Super-Element (Section \ref{sec:test_apa_model_flexible})
This is explained in Section \ref{sec:test_apa_simscape}.
\end{itemize} \end{itemize}
\begin{table}[htbp] \begin{table}[htbp]
@ -58,13 +57,13 @@ Section \ref{sec:test_apa_model_flexible} & \texttt{test\_apa\_4\_model\_flexibl
Before using the measurement bench to characterize the APA300ML, first simple measurements are performed: Before using the measurement bench to characterize the APA300ML, first simple measurements are performed:
\begin{itemize} \begin{itemize}
\item Section \ref{sec:test_apa_geometrical_measurements}: the geometric tolerances of the interface planes are checked \item Section \ref{ssec:test_apa_geometrical_measurements}: the geometric tolerances of the interface planes are checked
\item Section \ref{sec:test_apa_electrical_measurements}: the capacitance of the piezoelectric stacks is measured \item Section \ref{ssec:test_apa_electrical_measurements}: the capacitance of the piezoelectric stacks is measured
\item Section \ref{sec:test_apa_stroke_measurements}: the stroke of each APA is measured \item Section \ref{ssec:test_apa_stroke_measurements}: the stroke of each APA is measured
\item Section \ref{sec:test_apa_spurious_resonances}: the ``spurious'' resonances of the APA are investigated \item Section \ref{ssec:test_apa_spurious_resonances}: the ``spurious'' resonances of the APA are investigated
\end{itemize} \end{itemize}
\section{Geometrical Measurements} \section{Geometrical Measurements}
\label{sec:test_apa_geometrical_measurements} \label{ssec:test_apa_geometrical_measurements}
To measure the flatness of the two mechanical interfaces of the APA300ML, a small measurement bench is installed on top of a metrology granite with very good flatness. To measure the flatness of the two mechanical interfaces of the APA300ML, a small measurement bench is installed on top of a metrology granite with very good flatness.
@ -98,7 +97,7 @@ APA 7 & 18.7\\
\end{tabularx} \end{tabularx}
\end{table} \end{table}
\section{Electrical Measurements} \section{Electrical Measurements}
\label{sec:test_apa_electrical_measurements} \label{ssec:test_apa_electrical_measurements}
From the documentation of the APA300ML, the total capacitance of the three stacks should be between \(18\,\mu F\) and \(26\,\mu F\) with a nominal capacitance of \(20\,\mu F\). From the documentation of the APA300ML, the total capacitance of the three stacks should be between \(18\,\mu F\) and \(26\,\mu F\) with a nominal capacitance of \(20\,\mu F\).
@ -136,7 +135,7 @@ APA 7 & 4.85 & 9.85\\
\end{tabularx} \end{tabularx}
\end{table} \end{table}
\section{Stroke and Hysteresis Measurement} \section{Stroke and Hysteresis Measurement}
\label{sec:test_apa_stroke_measurements} \label{ssec:test_apa_stroke_measurements}
The goal is here to verify that the stroke of the APA300ML is as specified in the datasheet. The goal is here to verify that the stroke of the APA300ML is as specified in the datasheet.
To do so, one side of the APA is fixed to the granite, and a displacement probe\footnote{Millimar 1318 probe, specified linearity better than \(1\,\mu m\)} is located on the other side as shown in Figure \ref{fig:test_apa_stroke_bench}. To do so, one side of the APA is fixed to the granite, and a displacement probe\footnote{Millimar 1318 probe, specified linearity better than \(1\,\mu m\)} is located on the other side as shown in Figure \ref{fig:test_apa_stroke_bench}.
@ -157,7 +156,7 @@ The measured stroke is approximately \(250\,\mu m\) when using only two of the t
This is even above what is specified as the nominal stroke in the data-sheet (\(304\,\mu m\), therefore \(\approx 200\,\mu m\) if only two stacks are used). This is even above what is specified as the nominal stroke in the data-sheet (\(304\,\mu m\), therefore \(\approx 200\,\mu m\) if only two stacks are used).
It is clear from Figure \ref{fig:test_apa_stroke_result} that ``APA 3'' has an issue compared to the other units. It is clear from Figure \ref{fig:test_apa_stroke_result} that ``APA 3'' has an issue compared to the other units.
This confirms the abnormal electrical measurements made in Section \ref{sec:test_apa_electrical_measurements}. This confirms the abnormal electrical measurements made in Section \ref{ssec:test_apa_electrical_measurements}.
This unit was send sent back to Cedrat and a new one was shipped back. This unit was send sent back to Cedrat and a new one was shipped back.
From now on, only the six APA that behave as expected will be used. From now on, only the six APA that behave as expected will be used.
@ -167,7 +166,7 @@ From now on, only the six APA that behave as expected will be used.
\caption{\label{fig:test_apa_stroke_result}Generated voltage across the two piezoelectric stack actuators to estimate the stroke of the APA300ML (left). Measured displacement as a function of the applied voltage (right)} \caption{\label{fig:test_apa_stroke_result}Generated voltage across the two piezoelectric stack actuators to estimate the stroke of the APA300ML (left). Measured displacement as a function of the applied voltage (right)}
\end{figure} \end{figure}
\section{Flexible Mode Measurement} \section{Flexible Mode Measurement}
\label{sec:test_apa_spurious_resonances} \label{ssec:test_apa_spurious_resonances}
In this section, the flexible modes of the APA300ML are investigated both experimentally and using a Finite Element Model. In this section, the flexible modes of the APA300ML are investigated both experimentally and using a Finite Element Model.
@ -282,11 +281,13 @@ The bench is schematically shown in Figure \ref{fig:test_apa_schematic} and the
This bench will be used to: This bench will be used to:
\begin{itemize} \begin{itemize}
\item measure the dynamics of the APA (from \(V_a\) to \(d_e\) and \(d_a\) in Section \ref{ssec:test_apa_meas_frf_disp}, and from \(V_a\) to \(V_s\) in section \ref{ssec:test_apa_meas_frf_force}) \item \ref{ssec:test_apa_hysteresis}
\item \ref{ssec:test_apa_stiffness}
\item measure the dynamics of the APA (section \ref{ssec:test_apa_meas_dynamics})
\item estimate the added damping using Integral Force Feedback (Section \ref{ssec:test_apa_iff_locus}) \item estimate the added damping using Integral Force Feedback (Section \ref{ssec:test_apa_iff_locus})
\end{itemize} \end{itemize}
These measurements will also be used to tune the model of the APA in Section \ref{sec:test_apa_simscape}. These measurements will also be used to tune the developed models of the APA (in Section \ref{sec:test_apa_model_2dof} for the 2DoF model, and in Section \ref{sec:test_apa_model_flexible} for the flexible model).
\section{Hysteresis} \section{Hysteresis}
\label{ssec:test_apa_hysteresis} \label{ssec:test_apa_hysteresis}
@ -485,18 +486,14 @@ The two obtained root loci are compared in Figure \ref{fig:test_apa_iff_root_loc
\begin{important} \begin{important}
So far, all the measured FRF are showing the dynamical behavior that was expected. So far, all the measured FRF are showing the dynamical behavior that was expected.
\end{important} \end{important}
\chapter{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 compare the model of the APA with the measured frequency response functions. In this section, a simscape model (Figure \ref{fig:test_apa_bench_model}) of the measurement bench is used to compare the model of the APA with the measured frequency response functions.
After the transfer functions are extracted from the model (Section \ref{sec:simscape_bench_apa_first_id}), the comparison of the obtained dynamics with the measured FRF will permit to: A 2 degrees of freedom model is used to model the APA300ML.
\begin{enumerate} This model is presented in Section \ref{ssec:test_apa_2dof_model} and the procedure to tuned the model is described in Section \ref{ssec:test_apa_2dof_model_tuning}.
\item Estimate the ``actuator constant'' and ``sensor constant'' (Section \ref{sec:simscape_bench_apa_id_constants}) The obtained model dynamics is compared with the measurements in Section \ref{ssec:test_apa_2dof_model_result}.
\item ``Actuator constant'': Gain from the applied voltage \(V_a\) to the generated Force \(F_a\)
\item ``Sensor constant'': Gain from the sensor stack strain \(\delta L\) to the generated voltage \(V_s\)
\item Tune the model of the APA to match the measured dynamics (Section \ref{sec:simscape_bench_apa_tune_2dof_model})
\end{enumerate}
\begin{figure}[htbp] \begin{figure}[htbp]
\centering \centering
@ -667,6 +664,7 @@ From these parameters, \(g_s = 5.1\,V/\mu m\) and \(g_a = 26\,N/V\) were obtaine
\end{tabularx} \end{tabularx}
\end{table} \end{table}
\section{Comparison of the obtained dynamics} \section{Comparison of the obtained dynamics}
\label{ssec:test_apa_flexible_comp_frf}
The obtained dynamics using the \emph{super element} with the tuned ``sensor gain'' and ``actuator gain'' are compared with the experimentally identified frequency response functions in Figure \ref{fig:test_apa_super_element_comp_frf}. The obtained dynamics using the \emph{super element} with the tuned ``sensor gain'' and ``actuator gain'' are compared with the experimentally identified frequency response functions in Figure \ref{fig:test_apa_super_element_comp_frf}.