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Thomas Dehaeze 2024-04-02 19:18:03 +02:00
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nass-uniaxial-model.org
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@ -1702,6 +1702,9 @@ exportFig('figs/uniaxial_cas_d_disturbances_payload_masses.pdf', 'width', 'wide'
[[file:figs/uniaxial_cas_d_disturbances_payload_masses.png]] [[file:figs/uniaxial_cas_d_disturbances_payload_masses.png]]
** Conclusion ** Conclusion
:PROPERTIES:
:UNNUMBERED: t
:END:
#+begin_important #+begin_important
In order to have a closed-loop residual vibration $d \approx 20\,nm\text{ rms}$, if a simple feedback controller is used, the required closed-loop bandwidth would be: In order to have a closed-loop residual vibration $d \approx 20\,nm\text{ rms}$, if a simple feedback controller is used, the required closed-loop bandwidth would be:
@ -3424,6 +3427,9 @@ exportFig('figs/uniaxial_active_damping_robustness_mass_root_locus.pdf', 'width'
[[file:figs/uniaxial_active_damping_robustness_mass_root_locus.png]] [[file:figs/uniaxial_active_damping_robustness_mass_root_locus.png]]
** Conclusion ** Conclusion
:PROPERTIES:
:UNNUMBERED: t
:END:
#+begin_important #+begin_important
Conclusions for Active Damping: Conclusions for Active Damping:
@ -4276,6 +4282,10 @@ exportFig('figs/uniaxial_cas_hac_lac.pdf', 'width', 'full', 'height', 'normal');
[[file:figs/uniaxial_cas_hac_lac.png]] [[file:figs/uniaxial_cas_hac_lac.png]]
** Conclusion ** Conclusion
:PROPERTIES:
:UNNUMBERED: t
:END:
#+begin_important #+begin_important
Based on the open-loop noise budgeting made in Section ref:sec:uniaxial_noise_budgeting, the closed-loop bandwidth required to obtain acceptable vibration levels was estimated. Based on the open-loop noise budgeting made in Section ref:sec:uniaxial_noise_budgeting, the closed-loop bandwidth required to obtain acceptable vibration levels was estimated.
In order to obtain such bandwidth, the HAC-LAC strategy was followed which consists of applying an active damping controller and then a high authority position feedback controller. In order to obtain such bandwidth, the HAC-LAC strategy was followed which consists of applying an active damping controller and then a high authority position feedback controller.
@ -4711,6 +4721,10 @@ exportFig('figs/uniaxial_effect_support_compliance_dynamics_d.pdf', 'width', 'fu
[[file:figs/uniaxial_effect_support_compliance_dynamics_d.png]] [[file:figs/uniaxial_effect_support_compliance_dynamics_d.png]]
** Conclusion ** Conclusion
:PROPERTIES:
:UNNUMBERED: t
:END:
#+begin_important #+begin_important
In order to study the impact of the support compliance on the plant dynamics, simple models shown in Figure ref:fig:uniaxial_support_compliance_models were used. In order to study the impact of the support compliance on the plant dynamics, simple models shown in Figure ref:fig:uniaxial_support_compliance_models were used.
@ -5577,6 +5591,10 @@ exportFig('figs/uniaxial_sample_flexibility_noise_budget_y.pdf', 'width', 'full'
#+end_figure #+end_figure
** Conclusion ** Conclusion
:PROPERTIES:
:UNNUMBERED: t
:END:
#+begin_important #+begin_important
Payload dynamics is usually a major concern when designing a positioning system. Payload dynamics is usually a major concern when designing a positioning system.
For the NASS, the sample may present internal dynamics and limited fixation stiffness to the nano-hexapod platform. For the NASS, the sample may present internal dynamics and limited fixation stiffness to the nano-hexapod platform.

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nass-uniaxial-model.tex
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@ -1,4 +1,4 @@
% Created 2024-03-27 Wed 14:33 % Created 2024-04-02 Tue 19:16
% 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}
@ -315,8 +315,7 @@ The conclusion is that the sample's mass has little effect on the cumulative amp
\includegraphics[scale=1]{figs/uniaxial_cas_d_disturbances_payload_masses.png} \includegraphics[scale=1]{figs/uniaxial_cas_d_disturbances_payload_masses.png}
\caption{\label{fig:uniaxial_cas_d_disturbances_payload_masses}Cumulative Amplitude Spectrum of the relative motion d due to all disturbances, for two sample masses} \caption{\label{fig:uniaxial_cas_d_disturbances_payload_masses}Cumulative Amplitude Spectrum of the relative motion d due to all disturbances, for two sample masses}
\end{figure} \end{figure}
\section{Conclusion} \section*{Conclusion}
\begin{important} \begin{important}
In order to have a closed-loop residual vibration \(d \approx 20\,nm\text{ rms}\), if a simple feedback controller is used, the required closed-loop bandwidth would be: In order to have a closed-loop residual vibration \(d \approx 20\,nm\text{ rms}\), if a simple feedback controller is used, the required closed-loop bandwidth would be:
\begin{itemize} \begin{itemize}
@ -498,8 +497,7 @@ We can see that having heavier samples yields larger damping for IFF and smaller
\includegraphics[scale=1]{figs/uniaxial_active_damping_robustness_mass_root_locus.png} \includegraphics[scale=1]{figs/uniaxial_active_damping_robustness_mass_root_locus.png}
\caption{\label{fig:uniaxial_active_damping_robustness_mass_root_locus}Active Damping Robustness to change of sample's mass - Root Locus for all three damping techniques with 3 different sample's masses} \caption{\label{fig:uniaxial_active_damping_robustness_mass_root_locus}Active Damping Robustness to change of sample's mass - Root Locus for all three damping techniques with 3 different sample's masses}
\end{figure} \end{figure}
\section{Conclusion} \section*{Conclusion}
\begin{important} \begin{important}
Conclusions for Active Damping: Conclusions for Active Damping:
\begin{itemize} \begin{itemize}
@ -677,7 +675,7 @@ Obtained root mean square values of the distance \(d\) are better for the soft n
\includegraphics[scale=1]{figs/uniaxial_cas_hac_lac.png} \includegraphics[scale=1]{figs/uniaxial_cas_hac_lac.png}
\caption{\label{fig:uniaxial_cas_hac_lac}Cumulative Amplitude Spectrum for all three nano-hexapod stiffnesses - Comparison of OL, IFF and HAC-LAC cases} \caption{\label{fig:uniaxial_cas_hac_lac}Cumulative Amplitude Spectrum for all three nano-hexapod stiffnesses - Comparison of OL, IFF and HAC-LAC cases}
\end{figure} \end{figure}
\section{Conclusion} \section*{Conclusion}
\begin{important} \begin{important}
Based on the open-loop noise budgeting made in Section \ref{sec:uniaxial_noise_budgeting}, the closed-loop bandwidth required to obtain acceptable vibration levels was estimated. Based on the open-loop noise budgeting made in Section \ref{sec:uniaxial_noise_budgeting}, the closed-loop bandwidth required to obtain acceptable vibration levels was estimated.
In order to obtain such bandwidth, the HAC-LAC strategy was followed which consists of applying an active damping controller and then a high authority position feedback controller. In order to obtain such bandwidth, the HAC-LAC strategy was followed which consists of applying an active damping controller and then a high authority position feedback controller.
@ -740,7 +738,6 @@ When the relative displacement of the nano-hexapod \(L\) is to be controlled (dy
This is why it is very common to have stiff piezoelectric stages fixed at the very top of positioning stages. This is why it is very common to have stiff piezoelectric stages fixed at the very top of positioning stages.
In such case, the control of the piezoelectric stage using its integrated metrology (typically capacitive sensors) is quite simple as the plant is not much affected by the dynamics of the support on which is it fixed. In such case, the control of the piezoelectric stage using its integrated metrology (typically capacitive sensors) is quite simple as the plant is not much affected by the dynamics of the support on which is it fixed.
If a soft nano-hexapod is used, the support dynamics appears in the dynamics between \(F\) and \(L\) (see Figure \ref{fig:uniaxial_effect_support_compliance_dynamics}, left) which will impact the control robustness and performance. If a soft nano-hexapod is used, the support dynamics appears in the dynamics between \(F\) and \(L\) (see Figure \ref{fig:uniaxial_effect_support_compliance_dynamics}, left) which will impact the control robustness and performance.
\begin{figure}[htbp] \begin{figure}[htbp]
@ -759,7 +756,7 @@ On the contrary, if a ``stiff'' nano-hexapod is used, the support dynamics appea
\includegraphics[scale=1]{figs/uniaxial_effect_support_compliance_dynamics_d.png} \includegraphics[scale=1]{figs/uniaxial_effect_support_compliance_dynamics_d.png}
\caption{\label{fig:uniaxial_effect_support_compliance_dynamics_d}Effect of the support compliance on the transfer functions from \(F\) to \(d\)} \caption{\label{fig:uniaxial_effect_support_compliance_dynamics_d}Effect of the support compliance on the transfer functions from \(F\) to \(d\)}
\end{figure} \end{figure}
\section{Conclusion} \section*{Conclusion}
\begin{important} \begin{important}
In order to study the impact of the support compliance on the plant dynamics, simple models shown in Figure \ref{fig:uniaxial_support_compliance_models} were used. In order to study the impact of the support compliance on the plant dynamics, simple models shown in Figure \ref{fig:uniaxial_support_compliance_models} were used.
@ -891,7 +888,7 @@ What happens is that above \(\omega_s\), even though the motion \(d\) can be con
\end{subfigure} \end{subfigure}
\caption{\label{fig:uniaxial_sample_flexibility_noise_budget}Cumulative Amplitude Spectrum of the distances \(d\) and \(y\). The effect of the sample's flexibility does not affects much \(d\) but is detrimental to the stability of \(y\). A sample mass \(m_s = 1\,\text{kg}\) is used for the simulations.} \caption{\label{fig:uniaxial_sample_flexibility_noise_budget}Cumulative Amplitude Spectrum of the distances \(d\) and \(y\). The effect of the sample's flexibility does not affects much \(d\) but is detrimental to the stability of \(y\). A sample mass \(m_s = 1\,\text{kg}\) is used for the simulations.}
\end{figure} \end{figure}
\section{Conclusion} \section*{Conclusion}
\begin{important} \begin{important}
Payload dynamics is usually a major concern when designing a positioning system. Payload dynamics is usually a major concern when designing a positioning system.
For the NASS, the sample may present internal dynamics and limited fixation stiffness to the nano-hexapod platform. For the NASS, the sample may present internal dynamics and limited fixation stiffness to the nano-hexapod platform.