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Thomas Dehaeze 2024-11-06 15:27:19 +01:00
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simscape-micro-station.org
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@ -308,6 +308,7 @@ Be able to pass custom =.mat= files (one mat file per disturbance)?
- Maybe say that we remove the excentricity (by circle fit: show it in the figure) - Maybe say that we remove the excentricity (by circle fit: show it in the figure)
- Then the rest is modelled by stochastic disturbance - Then the rest is modelled by stochastic disturbance
** TODO [#C] Add picture of measured ground motion
** TODO [#C] Add screenshot of Simscape model ** TODO [#C] Add screenshot of Simscape model
** WAIT [#B] I have no measurement of horizontal ground motion :@marc: ** WAIT [#B] I have no measurement of horizontal ground motion :@marc:
@ -1328,11 +1329,11 @@ In this section, the Simscape model of the micro-station is briefly presented.
It consists of several rigid bodies connected by springs and dampers. It consists of several rigid bodies connected by springs and dampers.
The inertia of the solid bodies as well as the stiffness properties of the guiding mechanisms are first estimated based on the CAD model and part data-sheets (Section ref:ssec:ustation_model_simscape). The inertia of the solid bodies as well as the stiffness properties of the guiding mechanisms are first estimated based on the CAD model and part data-sheets (Section ref:ssec:ustation_model_simscape).
The obtained dynamics is then compared with the modal analysis performed on the micro-station (Section ref:ssec:ustation_meas_compliance). The obtained dynamics is then compared with the modal analysis performed on the micro-station (Section ref:ssec:ustation_model_comp_dynamics).
# TODO - Add reference to uniaxial model # TODO - Add reference to uniaxial model
As the dynamics of the nano-hexapod is impacted by the micro-station compliance, the most important dynamical characteristic that should be well modeled is the overall compliance of the micro-station. As the dynamics of the nano-hexapod is impacted by the micro-station compliance, the most important dynamical characteristic that should be well modeled is the overall compliance of the micro-station.
To do so, the 6-DoF compliance of the micro-station is measured (Section ref:ssec:ustation_meas_compliance) and then compared with the 6-DoF compliance extracted from the Simscape model (Section ref:ssec:ustation_model_compliance). To do so, the 6-DoF compliance of the micro-station is measured and then compared with the 6-DoF compliance extracted from the Simscape model (Section ref:ssec:ustation_model_compliance).
** Matlab Init :noexport:ignore: ** Matlab Init :noexport:ignore:
#+begin_src matlab #+begin_src matlab
@ -1405,7 +1406,8 @@ The spring values are summarized in Table ref:tab:ustation_6dof_stiffness_values
| Spindle | $700\,N/\mu m$ | $700\,N/\mu m$ | $2\,kN/\mu m$ | $10\,Nm/\mu\text{rad}$ | $10\,Nm/\mu\text{rad}$ | - | | Spindle | $700\,N/\mu m$ | $700\,N/\mu m$ | $2\,kN/\mu m$ | $10\,Nm/\mu\text{rad}$ | $10\,Nm/\mu\text{rad}$ | - |
| Hexapod | $10\,N/\mu m$ | $10\,N/\mu m$ | $100\,N/\mu m$ | $1.5\,Nm/rad$ | $1.5\,Nm/rad$ | $0.27\,Nm/rad$ | | Hexapod | $10\,N/\mu m$ | $10\,N/\mu m$ | $100\,N/\mu m$ | $1.5\,Nm/rad$ | $1.5\,Nm/rad$ | $0.27\,Nm/rad$ |
** With comparison with the measurements ** Comparison with the measured dynamics
<<ssec:ustation_model_comp_dynamics>>
The dynamics of the micro-station was measured by placing accelerometers on each stage and by impacting the translation stage with an instrumented hammer in three directions. The dynamics of the micro-station was measured by placing accelerometers on each stage and by impacting the translation stage with an instrumented hammer in three directions.
The obtained FRF were then projected at the CoM of each stage. The obtained FRF were then projected at the CoM of each stage.
@ -1556,8 +1558,8 @@ exportFig('figs/ustation_comp_com_response_ry_z.pdf', 'width', 'third', 'height'
#+end_subfigure #+end_subfigure
#+end_figure #+end_figure
** Micro-station compliance - Measurement ** Micro-station compliance
<<ssec:ustation_meas_compliance>> <<ssec:ustation_model_compliance>>
As was shown in the previous section, the dynamics of the micro-station is complex and tuning the multi-body model parameters to obtain a perfect match is hard. As was shown in the previous section, the dynamics of the micro-station is complex and tuning the multi-body model parameters to obtain a perfect match is hard.
@ -1622,7 +1624,7 @@ F_{\mathcal{X}} = \mathbf{J}_F^t \cdot F_{\mathcal{L}}
\end{equation} \end{equation}
Using the two Jacobian matrices, the FRF from the 10 hammer impacts to the 12 accelerometer outputs can be converted to the FRF from 6 forces/torques applied at the origin of frame $\{\mathcal{X}\}$ to the 6 linear/angular accelerations of the top platform expressed with respect to $\{\mathcal{X}\}$. Using the two Jacobian matrices, the FRF from the 10 hammer impacts to the 12 accelerometer outputs can be converted to the FRF from 6 forces/torques applied at the origin of frame $\{\mathcal{X}\}$ to the 6 linear/angular accelerations of the top platform expressed with respect to $\{\mathcal{X}\}$.
The obtained FRF from forces to linear motion are shown in Figure ref:fig:ustation_frf_compliance_xyz while the FRF from torques to angular motion are shown in Figure ref:fig:ustation_frf_compliance_Rxyz. These FRF will be used for comparison with the Simscape model.
#+begin_src matlab #+begin_src matlab
% Positions and orientation of accelerometers % Positions and orientation of accelerometers
@ -1768,68 +1770,7 @@ end
FRF_cartesian = pagemtimes(Ja_inv, pagemtimes(G_raw, Jf_inv)); FRF_cartesian = pagemtimes(Ja_inv, pagemtimes(G_raw, Jf_inv));
#+end_src #+end_src
#+begin_src matlab :exports none :results none The compliance of the micro-station multi-body model is extracted by computing the transfer function from forces/torques applied to the positioning hexapod's top platform to the "absolute" motion of the top platform.
%% Measured FRF of the compliance of the micro-station in the Cartesian frame - Translations/Forces
figure;
hold on;
plot(f, abs(squeeze(FRF_cartesian(1,1,:))), '-', 'color', colors(1,:), 'DisplayName', '$D_x/F_x$')
plot(f, abs(squeeze(FRF_cartesian(2,2,:))), '-', 'color', colors(2,:), 'DisplayName', '$D_y/F_y$')
plot(f, abs(squeeze(FRF_cartesian(3,3,:))), '-', 'color', colors(3,:), 'DisplayName', '$D_z/F_z$')
hold off;
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
leg.ItemTokenSize(1) = 15;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('Magnitude [m/N]');
xlim([20, 500]); ylim([1e-9, 2e-6]);
xticks([20, 50, 100, 200, 500])
#+end_src
#+begin_src matlab :tangle no :exports results :results file none
exportFig('figs/ustation_frf_compliance_xyz.pdf', 'width', 'half', 'height', 'normal');
#+end_src
#+begin_src matlab :exports none :results none
%% Measured FRF of the compliance of the micro-station in the Cartesian frame - Rotations/Torques
figure;
hold on;
plot(f, abs(squeeze(FRF_cartesian(4,4,:))), '-', 'color', colors(1,:), 'DisplayName', '$R_x/M_x$')
plot(f, abs(squeeze(FRF_cartesian(5,5,:))), '-', 'color', colors(2,:), 'DisplayName', '$R_y/M_y$')
plot(f, abs(squeeze(FRF_cartesian(6,6,:))), '-', 'color', colors(3,:), 'DisplayName', '$R_z/M_z$')
hold off;
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
leg.ItemTokenSize(1) = 15;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('Magnitude [rad/Nm]');
xlim([20, 500]); ylim([2e-7, 1e-4]);
xticks([20, 50, 100, 200, 500])
#+end_src
#+begin_src matlab :tangle no :exports results :results file none
exportFig('figs/ustation_frf_compliance_Rxyz.pdf', 'width', 'half', 'height', 'normal');
#+end_src
#+name: fig:ustation_frf_compliance
#+caption: Measured FRF of the compliance of the micro-station expressed in frame $\{\mathcal{X}\}$. Both translation terms (\subref{fig:ustation_frf_compliance_xyz}) and rotational terms (\subref{fig:ustation_frf_compliance_Rxyz}) are displayed.
#+attr_latex: :options [htbp]
#+begin_figure
#+attr_latex: :caption \subcaption{\label{fig:ustation_frf_compliance_xyz}Compliance in translation}
#+attr_latex: :options {0.49\textwidth}
#+begin_subfigure
#+attr_latex: :width 0.95\linewidth
[[file:figs/ustation_frf_compliance_xyz.png]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:ustation_frf_compliance_Rxyz}Compliance in rotation}
#+attr_latex: :options {0.49\textwidth}
#+begin_subfigure
#+attr_latex: :width 0.95\linewidth
[[file:figs/ustation_frf_compliance_Rxyz.png]]
#+end_subfigure
#+end_figure
** Compare with the Model
<<ssec:ustation_model_compliance>>
The compliance of the micro-station is extracted from the Simscape model by computing the transfer function from forces/torques applied to the positioning hexapod's top platform to the "absolute" motion of the top platform.
These are compared with the measurements in Figure ref:fig:ustation_frf_compliance_model. These are compared with the measurements in Figure ref:fig:ustation_frf_compliance_model.
Considering how complex the micro-station compliance dynamics is, the model compliance is matching sufficiently well the measurements for the current application. Considering how complex the micro-station compliance dynamics is, the model compliance is matching sufficiently well the measurements for the current application.
@ -1906,7 +1847,7 @@ exportFig('figs/ustation_frf_compliance_Rxyz_model.pdf', 'width', 'half', 'heigh
#+end_src #+end_src
#+name: fig:ustation_frf_compliance_model #+name: fig:ustation_frf_compliance_model
#+caption: Measured FRF of the compliance of the micro-station expressed in frame $\{\mathcal{X}\}$. Both translation terms (\subref{fig:ustation_frf_compliance_xyz_model}) and rotational terms (\subref{fig:ustation_frf_compliance_Rxyz_model}) are displayed. #+caption: Compliance of the micro-station expressed in frame $\{\mathcal{X}\}$. Measured FRF are display by solid lines, while FRF extracted from the multi-body models are shown by dashed lines. Both translation terms (\subref{fig:ustation_frf_compliance_xyz_model}) and rotational terms (\subref{fig:ustation_frf_compliance_Rxyz_model}) are displayed.
#+attr_latex: :options [htbp] #+attr_latex: :options [htbp]
#+begin_figure #+begin_figure
#+attr_latex: :caption \subcaption{\label{fig:ustation_frf_compliance_xyz_model}Compliance in translation} #+attr_latex: :caption \subcaption{\label{fig:ustation_frf_compliance_xyz_model}Compliance in translation}
@ -1923,7 +1864,7 @@ exportFig('figs/ustation_frf_compliance_Rxyz_model.pdf', 'width', 'half', 'heigh
#+end_subfigure #+end_subfigure
#+end_figure #+end_figure
* Estimation of disturbances * Estimation of Disturbances
:PROPERTIES: :PROPERTIES:
:HEADER-ARGS:matlab+: :tangle matlab/ustation_3_disturbances.m :HEADER-ARGS:matlab+: :tangle matlab/ustation_3_disturbances.m
:END: :END:
@ -1970,7 +1911,7 @@ Finally, the obtained disturbance sources are compared in Section ref:ssec:ustat
<<m-init-other>> <<m-init-other>>
#+end_src #+end_src
** Measurements of disturbances ** Disturbance measurements
<<ssec:ustation_disturbances_meas>> <<ssec:ustation_disturbances_meas>>
**** Introduction :ignore: **** Introduction :ignore:
In this section, the ground motion disturbances is directly measured using geophones. In this section, the ground motion disturbances is directly measured using geophones.
@ -2033,7 +1974,7 @@ ylabel('Vertical motion [$\mu$m]')
#+end_src #+end_src
#+begin_src matlab :tangle no :exports results :results file replace #+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/ustation_ground_disturbance.pdf', 'width', 'wide', 'height', 'normal'); exportFig('figs/ustation_ground_disturbance.pdf', 'width', 'normal', 'height', 'short');
#+end_src #+end_src
#+name: fig:ustation_ground_disturbance #+name: fig:ustation_ground_disturbance

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simscape-micro-station.tex
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@ -1,4 +1,4 @@
% Created 2024-11-06 Wed 15:14 % Created 2024-11-06 Wed 15:24
% 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}
@ -359,10 +359,10 @@ In this section, the Simscape model of the micro-station is briefly presented.
It consists of several rigid bodies connected by springs and dampers. It consists of several rigid bodies connected by springs and dampers.
The inertia of the solid bodies as well as the stiffness properties of the guiding mechanisms are first estimated based on the CAD model and part data-sheets (Section \ref{ssec:ustation_model_simscape}). The inertia of the solid bodies as well as the stiffness properties of the guiding mechanisms are first estimated based on the CAD model and part data-sheets (Section \ref{ssec:ustation_model_simscape}).
The obtained dynamics is then compared with the modal analysis performed on the micro-station (Section \ref{ssec:ustation_meas_compliance}). The obtained dynamics is then compared with the modal analysis performed on the micro-station (Section \ref{ssec:ustation_model_comp_dynamics}).
As the dynamics of the nano-hexapod is impacted by the micro-station compliance, the most important dynamical characteristic that should be well modeled is the overall compliance of the micro-station. As the dynamics of the nano-hexapod is impacted by the micro-station compliance, the most important dynamical characteristic that should be well modeled is the overall compliance of the micro-station.
To do so, the 6-DoF compliance of the micro-station is measured (Section \ref{ssec:ustation_meas_compliance}) and then compared with the 6-DoF compliance extracted from the Simscape model (Section \ref{ssec:ustation_model_compliance}). To do so, the 6-DoF compliance of the micro-station is measured and then compared with the 6-DoF compliance extracted from the Simscape model (Section \ref{ssec:ustation_model_compliance}).
\section{Multi-Body Model} \section{Multi-Body Model}
\label{ssec:ustation_model_simscape} \label{ssec:ustation_model_simscape}
@ -412,7 +412,8 @@ Hexapod & \(10\,N/\mu m\) & \(10\,N/\mu m\) & \(100\,N/\mu m\) & \(1.5\,Nm/rad\)
\end{table} \end{table}
\section{With comparison with the measurements} \section{Comparison with the measured dynamics}
\label{ssec:ustation_model_comp_dynamics}
The dynamics of the micro-station was measured by placing accelerometers on each stage and by impacting the translation stage with an instrumented hammer in three directions. The dynamics of the micro-station was measured by placing accelerometers on each stage and by impacting the translation stage with an instrumented hammer in three directions.
The obtained FRF were then projected at the CoM of each stage. The obtained FRF were then projected at the CoM of each stage.
@ -444,8 +445,8 @@ Tuning the numerous model parameters to better match the measurements is an high
\caption{\label{fig:ustation_comp_com_response}FRF between the hammer impacts on the translation stage and measured stage acceleration expressed at its CoM. Comparison of the measured FRF and the ones extracted from the Simscape model. Different directions are computed and for different stages.} \caption{\label{fig:ustation_comp_com_response}FRF between the hammer impacts on the translation stage and measured stage acceleration expressed at its CoM. Comparison of the measured FRF and the ones extracted from the Simscape model. Different directions are computed and for different stages.}
\end{figure} \end{figure}
\section{Micro-station compliance - Measurement} \section{Micro-station compliance}
\label{ssec:ustation_meas_compliance} \label{ssec:ustation_model_compliance}
As was shown in the previous section, the dynamics of the micro-station is complex and tuning the multi-body model parameters to obtain a perfect match is hard. As was shown in the previous section, the dynamics of the micro-station is complex and tuning the multi-body model parameters to obtain a perfect match is hard.
@ -512,28 +513,9 @@ F_{\mathcal{X}} = \mathbf{J}_F^t \cdot F_{\mathcal{L}}
\end{equation} \end{equation}
Using the two Jacobian matrices, the FRF from the 10 hammer impacts to the 12 accelerometer outputs can be converted to the FRF from 6 forces/torques applied at the origin of frame \(\{\mathcal{X}\}\) to the 6 linear/angular accelerations of the top platform expressed with respect to \(\{\mathcal{X}\}\). Using the two Jacobian matrices, the FRF from the 10 hammer impacts to the 12 accelerometer outputs can be converted to the FRF from 6 forces/torques applied at the origin of frame \(\{\mathcal{X}\}\) to the 6 linear/angular accelerations of the top platform expressed with respect to \(\{\mathcal{X}\}\).
The obtained FRF from forces to linear motion are shown in Figure \ref{fig:ustation_frf_compliance_xyz} while the FRF from torques to angular motion are shown in Figure \ref{fig:ustation_frf_compliance_Rxyz}. These FRF will be used for comparison with the Simscape model.
\begin{figure}[htbp] The compliance of the micro-station multi-body model is extracted by computing the transfer function from forces/torques applied to the positioning hexapod's top platform to the ``absolute'' motion of the top platform.
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/ustation_frf_compliance_xyz.png}
\end{center}
\subcaption{\label{fig:ustation_frf_compliance_xyz}sub caption a}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/ustation_frf_compliance_Rxyz.png}
\end{center}
\subcaption{\label{fig:ustation_frf_compliance_Rxyz}sub caption b}
\end{subfigure}
\caption{\label{fig:ustation_frf_compliance}Measured FRF of the compliance of the micro-station expressed in frame \(\{\mathcal{X}\}\). Both translation terms (\subref{fig:ustation_frf_compliance_xyz}) and rotational terms (\subref{fig:ustation_frf_compliance_Rxyz}) are displayed.}
\end{figure}
\section{Compare with the Model}
\label{ssec:ustation_model_compliance}
The compliance of the micro-station is extracted from the Simscape model by computing the transfer function from forces/torques applied to the positioning hexapod's top platform to the ``absolute'' motion of the top platform.
These are compared with the measurements in Figure \ref{fig:ustation_frf_compliance_model}. These are compared with the measurements in Figure \ref{fig:ustation_frf_compliance_model}.
Considering how complex the micro-station compliance dynamics is, the model compliance is matching sufficiently well the measurements for the current application. Considering how complex the micro-station compliance dynamics is, the model compliance is matching sufficiently well the measurements for the current application.
@ -542,15 +524,15 @@ Considering how complex the micro-station compliance dynamics is, the model comp
\begin{center} \begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/ustation_frf_compliance_xyz_model.png} \includegraphics[scale=1,width=0.95\linewidth]{figs/ustation_frf_compliance_xyz_model.png}
\end{center} \end{center}
\subcaption{\label{fig:ustation_frf_compliance_xyz_model}sub caption a} \subcaption{\label{fig:ustation_frf_compliance_xyz_model}Compliance in translation}
\end{subfigure} \end{subfigure}
\begin{subfigure}{0.49\textwidth} \begin{subfigure}{0.49\textwidth}
\begin{center} \begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/ustation_frf_compliance_Rxyz_model.png} \includegraphics[scale=1,width=0.95\linewidth]{figs/ustation_frf_compliance_Rxyz_model.png}
\end{center} \end{center}
\subcaption{\label{fig:ustation_frf_compliance_Rxyz_model}sub caption b} \subcaption{\label{fig:ustation_frf_compliance_Rxyz_model}Compliance in rotation}
\end{subfigure} \end{subfigure}
\caption{\label{fig:ustation_frf_compliance_model}Measured FRF of the compliance of the micro-station expressed in frame \(\{\mathcal{X}\}\). Both translation terms (\subref{fig:ustation_frf_compliance_xyz_model}) and rotational terms (\subref{fig:ustation_frf_compliance_Rxyz_model}) are displayed.} \caption{\label{fig:ustation_frf_compliance_model}Compliance of the micro-station expressed in frame \(\{\mathcal{X}\}\). Measured FRF are display by solid lines, while FRF extracted from the multi-body models are shown by dashed lines. Both translation terms (\subref{fig:ustation_frf_compliance_xyz_model}) and rotational terms (\subref{fig:ustation_frf_compliance_Rxyz_model}) are displayed.}
\end{figure} \end{figure}
\chapter{Estimation of disturbances} \chapter{Estimation of disturbances}