1116 lines
38 KiB
HTML
1116 lines
38 KiB
HTML
<?xml version="1.0" encoding="utf-8"?>
|
|
<?xml version="1.0" encoding="utf-8"?>
|
|
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
|
|
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
|
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
|
<head>
|
|
<!-- 2020-04-24 ven. 18:43 -->
|
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
|
<title>Design of the Nano-Hexapod and associated Control Architectures - Summary</title>
|
|
<meta name="generator" content="Org mode" />
|
|
<meta name="author" content="Thomas Dehaeze" />
|
|
<link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
|
|
<link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
|
|
<script src="./js/jquery.min.js"></script>
|
|
<script src="./js/bootstrap.min.js"></script>
|
|
<script src="./js/jquery.stickytableheaders.min.js"></script>
|
|
<script src="./js/readtheorg.js"></script>
|
|
<script>MathJax = {
|
|
tex: {
|
|
tags: 'ams',
|
|
macros: {bm: ["\\boldsymbol{#1}",1],}
|
|
}
|
|
};
|
|
</script>
|
|
<script type="text/javascript" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
|
|
</head>
|
|
<body>
|
|
<div id="org-div-home-and-up">
|
|
<a accesskey="h" href="./index.html"> UP </a>
|
|
|
|
|
<a accesskey="H" href="./index.html"> HOME </a>
|
|
</div><div id="content">
|
|
<h1 class="title">Design of the Nano-Hexapod and associated Control Architectures - Summary</h1>
|
|
<div id="table-of-contents">
|
|
<h2>Table of Contents</h2>
|
|
<div id="text-table-of-contents">
|
|
<ul>
|
|
<li><a href="#org0e81ed3">1. Introduction to Feedback Systems and Noise budgeting</a>
|
|
<ul>
|
|
<li><a href="#org5582f57">1.1. Feedback System</a>
|
|
<ul>
|
|
<li><a href="#org19a5b96">1.1.1. Simplified Feedback Control Diagram for the NASS</a></li>
|
|
<li><a href="#orgbc812f3">1.1.2. How does the feedback loop is modifying the system behavior?</a></li>
|
|
<li><a href="#orgf4e06db">1.1.3. Trade off: Disturbance Reduction / Noise Injection</a></li>
|
|
<li><a href="#org0c8edbb">1.1.4. Trade off: Robustness / Performance</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orgb62ce2a">1.2. Dynamic error budgeting</a>
|
|
<ul>
|
|
<li><a href="#org8660756">1.2.1. Power Spectral Density</a></li>
|
|
<li><a href="#orgcad1a65">1.2.2. Cumulative Power Spectrum</a></li>
|
|
<li><a href="#org9c7c3f1">1.2.3. Modification of a signal’s PSD when going through an LTI system</a></li>
|
|
<li><a href="#orga1dab10">1.2.4. PSD of combined signals</a></li>
|
|
<li><a href="#org4d605e1">1.2.5. Dynamic Noise Budgeting</a></li>
|
|
</ul>
|
|
</li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#org8ca4100">2. Identification of the Micro-Station Dynamics</a>
|
|
<ul>
|
|
<li><a href="#orgd29be87">2.1. Setup</a></li>
|
|
<li><a href="#org9742a99">2.2. Results</a></li>
|
|
<li><a href="#org56e7067">2.3. Conclusion</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orgb5c3a23">3. Identification of the Disturbances</a>
|
|
<ul>
|
|
<li><a href="#orge7fad51">3.1. Ground Motion</a></li>
|
|
<li><a href="#org5a7da27">3.2. Stage Vibration - Effect of Control systems</a></li>
|
|
<li><a href="#org03de925">3.3. Stage Vibration - Effect of Motion</a></li>
|
|
<li><a href="#org50da187">3.4. Sum of all disturbances</a></li>
|
|
<li><a href="#org161e425">3.5. Better measurement of the effect of disturbances</a></li>
|
|
<li><a href="#orgb9a9cf1">3.6. Conclusion</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#org083a8f8">4. Multi Body Model</a>
|
|
<ul>
|
|
<li><a href="#orgd9ae0b9">4.1. Validity of the model</a></li>
|
|
<li><a href="#orge11e487">4.2. Wanted position of the sample and position error</a></li>
|
|
<li><a href="#org5945af2">4.3. Simulation of Experiments</a></li>
|
|
<li><a href="#org337b7e5">4.4. Conclusion</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#org5551d84">5. Optimal Nano-Hexapod Design</a>
|
|
<ul>
|
|
<li><a href="#orgd3de157">5.1. Optimal Stiffness to reduce the effect of disturbances</a></li>
|
|
<li><a href="#org8091d40">5.2. Optimal Stiffness</a></li>
|
|
<li><a href="#org1f5706f">5.3. Sensors to be included</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orge96cfff">6. Robust Control Architecture</a>
|
|
<ul>
|
|
<li><a href="#org2a7d7b7">6.1. Simulation of Tomography Experiments</a></li>
|
|
<li><a href="#org98b634b">6.2. Conclusion</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orga69770f">7. Further notes</a></li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<p>
|
|
The overall objective is to design a nano-hexapod an the associated control architecture that allows the stabilization of samples down to \(\approx 10nm\) in presence of disturbances and system variability.
|
|
</p>
|
|
|
|
|
|
<p>
|
|
To understand the design challenges of such system, a short introduction to Feedback control is provided in Section <a href="#org15583dd">1</a>.
|
|
The mathematical tools (Power Spectral Density, Noise Budgeting, …) that will be used throughout this study are also introduced.
|
|
</p>
|
|
|
|
|
|
<p>
|
|
To be able to develop both the nano-hexapod and the control architecture in an optimal way, we need a good estimation of:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>the micro-station dynamics (Section <a href="#orge54bb61">2</a>)</li>
|
|
<li>the frequency content of the important source of disturbances in play such as vibration of stages and ground motion (Section <a href="#org5baf125">3</a>)</li>
|
|
</ul>
|
|
|
|
|
|
<p>
|
|
We then develop a model of the system that must represent all the important physical effects in play.
|
|
Such model is presented in Section <a href="#org444ed79">4</a>.
|
|
</p>
|
|
|
|
|
|
<p>
|
|
A modular model of the nano-hexapod is then included in the system.
|
|
The effects of the nano-hexapod characteristics on the dynamics are then studied.
|
|
Based on that, an optimal choice of the nano-hexapod stiffness is made (Section <a href="#org555a8dc">5</a>).
|
|
</p>
|
|
|
|
|
|
<p>
|
|
Finally, using the optimally designed nano-hexapod, a robust control architecture is developed.
|
|
Simulations are performed to show that this design gives acceptable performance and the required robustness (Section <a href="#orgb43d859">6</a>).
|
|
</p>
|
|
|
|
<div id="outline-container-org0e81ed3" class="outline-2">
|
|
<h2 id="org0e81ed3"><span class="section-number-2">1</span> Introduction to Feedback Systems and Noise budgeting</h2>
|
|
<div class="outline-text-2" id="text-1">
|
|
<p>
|
|
<a id="org15583dd"></a>
|
|
</p>
|
|
|
|
<p>
|
|
In this section, we first introduce some basics of <b>feedback systems</b> (Section <a href="#orga94e210">1.1</a>).
|
|
This should highlight the challenges in terms of combined performance and robustness.
|
|
</p>
|
|
|
|
|
|
<p>
|
|
In Section <a href="#orgfebd41c">1.2</a> is introduced the <b>dynamic error budgeting</b> which is a powerful tool that allows to derive the total error in a dynamic system from multiple disturbance sources.
|
|
This tool will be widely used throughout this study to both predict the performances and identify the effects that do limit the performances.
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org5582f57" class="outline-3">
|
|
<h3 id="org5582f57"><span class="section-number-3">1.1</span> Feedback System</h3>
|
|
<div class="outline-text-3" id="text-1-1">
|
|
<p>
|
|
<a id="orga94e210"></a>
|
|
</p>
|
|
<p>
|
|
The use of feedback control as several advantages and pitfalls that are listed below (taken from <a class='org-ref-reference' href="#schmidt14_desig_high_perfor_mechat_revis_edition">schmidt14_desig_high_perfor_mechat_revis_edition</a>):
|
|
</p>
|
|
|
|
<ul class="org-ul">
|
|
<li><b>Advantages</b>:
|
|
<ul class="org-ul">
|
|
<li><b>Reduction of the effect of disturbances</b>:
|
|
Disturbances affecting the sample vibrations are observed by the sensor signal, and therefore the feedback controller can compensate for them</li>
|
|
<li><b>Handling of uncertainties</b>:
|
|
Feedback controlled systems can also be designed for <i>robustness</i>, which means that the stability and performance requirements are guaranteed even for parameter variation of the controller mechatronics system</li>
|
|
</ul></li>
|
|
<li><b>Pitfalls</b>:
|
|
<ul class="org-ul">
|
|
<li><b>Limited reaction speed</b>:
|
|
A feedback controller reacts on the difference between the reference signal (wanted motion) and the measurement (actual motion), which means that the error has to occur first <i>before</i> the controller can correct for it.
|
|
The limited reaction speed means that the controller will be able to compensate the positioning errors only in some frequency band, called the controller <i>bandwidth</i></li>
|
|
<li><b>Feedback of noise</b>:
|
|
By closing the loop, the sensor noise is also fed back and will induce positioning errors</li>
|
|
<li><b>Can introduce instability</b>:
|
|
Feedback control can destabilize a stable plant.
|
|
Thus the <i>robustness</i> properties of the feedback system must be carefully guaranteed</li>
|
|
</ul></li>
|
|
</ul>
|
|
</div>
|
|
|
|
<div id="outline-container-org19a5b96" class="outline-4">
|
|
<h4 id="org19a5b96"><span class="section-number-4">1.1.1</span> Simplified Feedback Control Diagram for the NASS</h4>
|
|
<div class="outline-text-4" id="text-1-1-1">
|
|
<p>
|
|
Let’s consider the block diagram shown in Figure <a href="#org48f8fbd">1</a> where the signals are:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>\(y\): the relative position of the sample with respect to the granite (the quantity we wish to control)</li>
|
|
<li>\(d\): the disturbances affecting \(y\) (ground motion, vibration of stages)</li>
|
|
<li>\(n\): the noise of the sensor measuring \(y\)</li>
|
|
<li>\(r\): the reference signal, corresponding to the wanted \(y\)</li>
|
|
<li>\(\epsilon = r - y\): the position error</li>
|
|
</ul>
|
|
|
|
<p>
|
|
And the dynamical blocks are:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>\(G\): representing the dynamics from forces/torques applied by the nano-hexapod to the relative position sample/granite \(y\)</li>
|
|
<li>\(G_d\): representing how the disturbances (e.g. ground motion) are affecting the relative position sample/granite \(y\)</li>
|
|
<li>\(K\): representing the controller (to be designed)</li>
|
|
</ul>
|
|
|
|
|
|
<div id="org48f8fbd" class="figure">
|
|
<p><img src="figs/classical_feedback_small.png" alt="classical_feedback_small.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 1: </span>Block Diagram of a simple feedback system</p>
|
|
</div>
|
|
|
|
<p>
|
|
Without the use of feedback (i.e. nano-hexapod), the disturbances will induce a sample motion error equal to:
|
|
</p>
|
|
\begin{equation}
|
|
y = G_d d \label{eq:open_loop_error}
|
|
\end{equation}
|
|
<p>
|
|
which is out of the specifications (micro-meter range compare to the required \(\approx 10nm\)).
|
|
</p>
|
|
|
|
<p>
|
|
In the next section, we see how the use of the feedback system permits to lower the effect of the disturbances \(d\) on the sample motion error.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgbc812f3" class="outline-4">
|
|
<h4 id="orgbc812f3"><span class="section-number-4">1.1.2</span> How does the feedback loop is modifying the system behavior?</h4>
|
|
<div class="outline-text-4" id="text-1-1-2">
|
|
<p>
|
|
If we write down the position error signal \(\epsilon = r - y\) as a function of the reference signal \(r\), the disturbances \(d\) and the measurement noise \(n\) (using the feedback diagram in Figure <a href="#org48f8fbd">1</a>), we obtain:
|
|
\[ \epsilon = \frac{1}{1 + GK} r + \frac{GK}{1 + GK} n - \frac{G_d}{1 + GK} d \]
|
|
</p>
|
|
|
|
<p>
|
|
We usually note:
|
|
</p>
|
|
\begin{align}
|
|
S &= \frac{1}{1 + GK} \\
|
|
T &= \frac{GK}{1 + GK}
|
|
\end{align}
|
|
<p>
|
|
where \(S\) is called the sensibility transfer function and \(T\) the transmissibility transfer function.
|
|
</p>
|
|
|
|
<p>
|
|
And the position error can be rewritten as:
|
|
</p>
|
|
\begin{equation}
|
|
\epsilon = S r + T n - G_d S d \label{eq:closed_loop_error}
|
|
\end{equation}
|
|
|
|
|
|
<p>
|
|
From Eq. \eqref{eq:closed_loop_error} representing the closed-loop system behavior, we can see that:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>the effect of disturbances \(d\) on \(\epsilon\) is multiplied by a factor \(S\) compared to the open-loop case</li>
|
|
<li>the measurement noise \(n\) is injected and multiplied by a factor \(T\)</li>
|
|
</ul>
|
|
|
|
<p>
|
|
Ideally, we would like to design the controller \(K\) such that:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>\(|S|\) is small to limit the effect of disturbances</li>
|
|
<li>\(|T|\) is small to limit the injection of sensor noise</li>
|
|
</ul>
|
|
|
|
<p>
|
|
As shown in the next section, there is a trade-off between the disturbance reduction and the noise injection.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf4e06db" class="outline-4">
|
|
<h4 id="orgf4e06db"><span class="section-number-4">1.1.3</span> Trade off: Disturbance Reduction / Noise Injection</h4>
|
|
<div class="outline-text-4" id="text-1-1-3">
|
|
<p>
|
|
We have from the definition of \(S\) and \(T\) that:
|
|
</p>
|
|
\begin{equation}
|
|
S + T = \frac{1}{1 + GK} + \frac{GK}{1 + GK} = 1
|
|
\end{equation}
|
|
<p>
|
|
meaning that we cannot have \(|S|\) and \(|T|\) small at the same time.
|
|
</p>
|
|
|
|
<p>
|
|
There is therefore a <b>trade-off between the disturbance rejection and the measurement noise filtering</b>.
|
|
</p>
|
|
|
|
|
|
<p>
|
|
Typical shapes of \(|S|\) and \(|T|\) as a function of frequency are shown in Figure <a href="#orgfd11d00">2</a>.
|
|
We can observe that \(|S|\) and \(|T|\) exhibit different behaviors depending on the frequency band:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li><b>At low frequency</b> (inside the control bandwidth):
|
|
<ul class="org-ul">
|
|
<li>\(|S|\) can be made small and thus the effect of disturbances is reduced</li>
|
|
<li>\(|T| \approx 1\) and all the sensor noise is transmitted</li>
|
|
</ul></li>
|
|
<li><b>At high frequency</b> (outside the control bandwidth):
|
|
<ul class="org-ul">
|
|
<li>\(|S| \approx 1\) and the feedback system does not reduce the effect of disturbances</li>
|
|
<li>\(|T|\) is small and thus the sensor noise is filtered</li>
|
|
</ul></li>
|
|
<li><b>Near the crossover frequency</b> (between the two frequency bands):
|
|
<ul class="org-ul">
|
|
<li>The effect of disturbances is increased</li>
|
|
</ul></li>
|
|
</ul>
|
|
|
|
|
|
<div id="orgfd11d00" class="figure">
|
|
<p><img src="figs/h-infinity-2-blocs-constrains.png" alt="h-infinity-2-blocs-constrains.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 2: </span>Typical shapes and constrain of the Sensibility and Transmibility closed-loop transfer functions</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org0c8edbb" class="outline-4">
|
|
<h4 id="org0c8edbb"><span class="section-number-4">1.1.4</span> Trade off: Robustness / Performance</h4>
|
|
<div class="outline-text-4" id="text-1-1-4">
|
|
<p>
|
|
<a id="orgf4d6950"></a>
|
|
</p>
|
|
|
|
<p>
|
|
As shown in the previous section, the effect of disturbances is reduced <i>inside</i> the control bandwidth.
|
|
</p>
|
|
|
|
<p>
|
|
Moreover, the slope of \(|S(j\omega)|\) is limited for stability reasons (not explained here), and therefore a large control bandwidth is required to obtain sufficient disturbance rejection at lower frequencies (where the disturbances have large effects).
|
|
</p>
|
|
|
|
<p>
|
|
The next important question is <b>what effects do limit the attainable control bandwidth?</b>
|
|
</p>
|
|
|
|
|
|
<p>
|
|
The main issue it that for stability reasons, <b>the behavior of the mechanical system must be known with only small uncertainty in the vicinity of the crossover frequency</b>.
|
|
</p>
|
|
|
|
<p>
|
|
For mechanical systems, this generally means that control bandwidth should take place before any appearing of flexible dynamics (Right part of Figure <a href="#org3fae3bb">3</a>).
|
|
</p>
|
|
|
|
|
|
<div id="org3fae3bb" class="figure">
|
|
<p><img src="figs/oomen18_next_gen_loop_gain.png" alt="oomen18_next_gen_loop_gain.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 3: </span>Envisaged developments in motion systems. In traditional motion systems, the control bandwidth takes place in the rigid-body region. In the next generation systemes, flexible dynamics are foreseen to occur within the control bandwidth. <a class='org-ref-reference' href="#oomen18_advan_motion_contr_precis_mechat">oomen18_advan_motion_contr_precis_mechat</a></p>
|
|
</div>
|
|
|
|
<p>
|
|
This also means that <b>any possible change in the system should have a small impact on the system dynamics in the vicinity of the crossover</b>.
|
|
</p>
|
|
|
|
<p>
|
|
For the NASS, the possible changes in the system are:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>a modification of the payload mass and dynamics</li>
|
|
<li>a change of experimental condition: spindle’s rotation speed, position of each micro-station’s stage</li>
|
|
<li>a change in the micro-station dynamics (change of mechanical elements, aging effect, …)</li>
|
|
</ul>
|
|
|
|
<p>
|
|
The nano-hexapod and the control architecture have to be developed such that the feedback system remains stable and exhibit acceptable performance for all these possible changes in the system.
|
|
</p>
|
|
|
|
<p>
|
|
This problem of <b>robustness</b> represent one of the main challenge for the design of the NASS.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb62ce2a" class="outline-3">
|
|
<h3 id="orgb62ce2a"><span class="section-number-3">1.2</span> Dynamic error budgeting</h3>
|
|
<div class="outline-text-3" id="text-1-2">
|
|
<p>
|
|
<a id="orgfebd41c"></a>
|
|
</p>
|
|
<p>
|
|
The dynamic error budgeting is a powerful tool to study the effect of multiple error sources and to see how the feedback system does reduce the effect
|
|
</p>
|
|
|
|
<p>
|
|
To understand how to use and understand it, the Power Spectral Density and the Cumulative Power Spectrum are first introduced.
|
|
Then, is shown how does multiple error sources are combined and modified by dynamical systems.
|
|
</p>
|
|
|
|
<p>
|
|
Finally,
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org8660756" class="outline-4">
|
|
<h4 id="org8660756"><span class="section-number-4">1.2.1</span> Power Spectral Density</h4>
|
|
<div class="outline-text-4" id="text-1-2-1">
|
|
<p>
|
|
The <b>Power Spectral Density</b> (PSD) \(S_{xx}(f)\) of the time domain signal \(x(t)\) is defined as the Fourier transform of the autocorrelation function:
|
|
\[ S_{xx}(\omega) = \int_{-\infty}^{\infty} R_{xx}(\tau) e^{-j \omega \tau} d\tau \ \frac{[\text{unit of } x]^2}{\text{Hz}} \]
|
|
</p>
|
|
|
|
<p>
|
|
The PSD \(S_{xx}(\omega)\) represents the <b>distribution of the (average) signal power over frequency</b>.
|
|
</p>
|
|
|
|
<p>
|
|
Thus, the total power in the signal can be obtained by integrating these infinitesimal contributions, the Root Mean Square (RMS) value of the signal \(x(t)\) is then:
|
|
</p>
|
|
\begin{equation}
|
|
x_{\text{rms}} = \sqrt{\int_{0}^{\infty} S_{xx}(\omega) d\omega}
|
|
\end{equation}
|
|
|
|
<p>
|
|
One can also integrate the infinitesimal power \(S_{xx}(\omega)d\omega\) over a finite frequency band to obtain the power of the signal \(x\) in that frequency band:
|
|
</p>
|
|
\begin{equation}
|
|
P_{f_1,f_2} = \int_{f_1}^{f_2} S_{xx}(\omega) d\omega \quad [\text{unit of } x]^2
|
|
\end{equation}
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgcad1a65" class="outline-4">
|
|
<h4 id="orgcad1a65"><span class="section-number-4">1.2.2</span> Cumulative Power Spectrum</h4>
|
|
<div class="outline-text-4" id="text-1-2-2">
|
|
<p>
|
|
The <b>Cumulative Power Spectrum</b> is the cumulative integral of the Power Spectral Density starting from \(0\ \text{Hz}\) with increasing frequency:
|
|
</p>
|
|
\begin{equation}
|
|
CPS_x(f) = \int_0^f S_{xx}(\nu) d\nu \quad [\text{unit of } x]^2
|
|
\end{equation}
|
|
<p>
|
|
The Cumulative Power Spectrum taken at frequency \(f\) thus represent the power in the signal in the frequency band \(0\) to \(f\).
|
|
</p>
|
|
|
|
|
|
<p>
|
|
An alternative definition of the Cumulative Power Spectrum can be used where the PSD is integrated from \(f\) to \(\infty\):
|
|
</p>
|
|
\begin{equation}
|
|
CPS_x(f) = \int_f^\infty S_{xx}(\nu) d\nu \quad [\text{unit of } x]^2
|
|
\end{equation}
|
|
<p>
|
|
And thus \(CPS_x(f)\) represents the power in the signal \(x\) for frequencies above \(f\).
|
|
</p>
|
|
|
|
|
|
<p>
|
|
The Cumulative Power Spectrum will be used to determine in which frequency band the effect of disturbances should be reduced, and thus the approximate required control bandwidth.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org9c7c3f1" class="outline-4">
|
|
<h4 id="org9c7c3f1"><span class="section-number-4">1.2.3</span> Modification of a signal’s PSD when going through an LTI system</h4>
|
|
<div class="outline-text-4" id="text-1-2-3">
|
|
<p>
|
|
Let’s consider a signal \(u\) with a PSD \(S_{uu}\) going through a LTI system \(G(s)\) that outputs a signal \(y\) with a PSD (Figure <a href="#orgc8d8af3">4</a>).
|
|
</p>
|
|
|
|
|
|
<div id="orgc8d8af3" class="figure">
|
|
<p><img src="figs/psd_lti_system.png" alt="psd_lti_system.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 4: </span>LTI dynamical system \(G(s)\) with input signal \(u\) and output signal \(y\)</p>
|
|
</div>
|
|
|
|
<p>
|
|
The Power Spectral Density of the output signal \(y\) can be computed using:
|
|
</p>
|
|
\begin{equation}
|
|
S_{yy}(\omega) = \left|G(j\omega)\right|^2 S_{uu}(\omega)
|
|
\end{equation}
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga1dab10" class="outline-4">
|
|
<h4 id="orga1dab10"><span class="section-number-4">1.2.4</span> PSD of combined signals</h4>
|
|
<div class="outline-text-4" id="text-1-2-4">
|
|
<p>
|
|
Let’s consider a signal \(y\) that is the sum of two <b>uncorrelated</b> signals \(u\) and \(v\) (Figure <a href="#org4d671c6">5</a>).
|
|
</p>
|
|
|
|
<p>
|
|
We have that the PSD of \(y\) is equal to sum of the PSD and \(u\) and the PSD of \(v\) (can be easily shown from the definition of the PSD):
|
|
\[ S_{yy} = S_{uu} + S_{vv} \]
|
|
</p>
|
|
|
|
|
|
<div id="org4d671c6" class="figure">
|
|
<p><img src="figs/psd_sum.png" alt="psd_sum.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 5: </span>\(y\) as the sum of two signals \(u\) and \(v\)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4d605e1" class="outline-4">
|
|
<h4 id="org4d605e1"><span class="section-number-4">1.2.5</span> Dynamic Noise Budgeting</h4>
|
|
<div class="outline-text-4" id="text-1-2-5">
|
|
<p>
|
|
Let’s consider the Feedback architecture in Figure <a href="#org48f8fbd">1</a> where the position error \(\epsilon\) is equal to:
|
|
\[ \epsilon = S r + T n - G_d S d \]
|
|
</p>
|
|
|
|
<p>
|
|
If we suppose that the signals \(r\), \(n\) and \(d\) are <b>uncorrelated</b> (which is a good approximation in our case), the PSD of \(\epsilon\) is:
|
|
\[ S_{\epsilon \epsilon}(\omega) = |S(j\omega)|^2 S_{rr}(\omega) + |T(j\omega)|^2 S_{nn}(\omega) + |G_d(j\omega) S(j\omega)|^2 S_{dd}(\omega) \]
|
|
</p>
|
|
|
|
<p>
|
|
And we can compute the RMS value of the residual motion using:
|
|
</p>
|
|
\begin{align*}
|
|
\epsilon_\text{rms} &= \sqrt{ \int_0^\infty S_{\epsilon\epsilon}(\omega) d\omega} \\
|
|
&= \sqrt{ \int_0^\infty \Big( |S(j\omega)|^2 S_{rr}(\omega) + |T(j\omega)|^2 S_{nn}(\omega) + |G_d(j\omega) S(j\omega)|^2 S_{dd}(\omega) \Big) d\omega }
|
|
\end{align*}
|
|
|
|
|
|
<p>
|
|
To estimate the PSD of the position error \(\epsilon\) and thus the RMS residual motion (in closed-loop), we need to determine:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>The Power Spectral Densities of the signals affecting the system:
|
|
<ul class="org-ul">
|
|
<li>\(S_{dd}\): disturbances, this will be done in Section <a href="#org5baf125">3</a></li>
|
|
<li>\(S_{nn}\): sensor noise, this can be estimated from the sensor data-sheet</li>
|
|
<li>\(S_{rr}\):</li>
|
|
</ul></li>
|
|
<li>The dynamics of the complete system comprising the micro-station and the nano-hexapod: \(G\), \(G_d\).
|
|
To do so, we need to identify the dynamics of the micro-station (Section <a href="#orge54bb61">2</a>), include this dynamics in a model (Section <a href="#org444ed79">4</a>) and add a model of the nano-hexapod to the model (Section <a href="#org555a8dc">5</a>)</li>
|
|
<li>The controller \(K\) that will be designed in Section <a href="#orgb43d859">6</a></li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org8ca4100" class="outline-2">
|
|
<h2 id="org8ca4100"><span class="section-number-2">2</span> Identification of the Micro-Station Dynamics</h2>
|
|
<div class="outline-text-2" id="text-2">
|
|
<p>
|
|
<a id="orge54bb61"></a>
|
|
</p>
|
|
<p>
|
|
<a href="https://tdehaeze.github.io/meas-analysis/">https://tdehaeze.github.io/meas-analysis/</a>
|
|
</p>
|
|
|
|
<p>
|
|
Modal Analysis: <a href="https://tdehaeze.github.io/meas-analysis/modal-analysis/index.html">https://tdehaeze.github.io/meas-analysis/modal-analysis/index.html</a>
|
|
</p>
|
|
|
|
<p>
|
|
The obtained dynamics will allows us to compare the dynamics of the model.
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd29be87" class="outline-3">
|
|
<h3 id="orgd29be87"><span class="section-number-3">2.1</span> Setup</h3>
|
|
<div class="outline-text-3" id="text-2-1">
|
|
<p>
|
|
In order to perform to <b>Modal Analysis</b> and to obtain first a response model, the following devices were used:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>An <b>acquisition system</b> (OROS) with 24bits ADCs</li>
|
|
<li>3 tri-axis <b>Accelerometers</b></li>
|
|
<li>An <b>Instrumented Hammer</b></li>
|
|
</ul>
|
|
|
|
<p>
|
|
The measurement thus consists of:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>Exciting the structure at the same location with the Hammer (Figure <a href="#orgbd643a8">7</a>)</li>
|
|
<li>Move the accelerometers to measure all the DOF of the structure.
|
|
The position of the accelerometers are:
|
|
<ul class="org-ul">
|
|
<li>4 on the first granite</li>
|
|
<li>4 on the second granite</li>
|
|
<li>4 on top of the translation stage (figure <a href="#orgf23c45c">6</a>)</li>
|
|
<li>4 on top of the tilt stage</li>
|
|
<li>3 on top of the spindle</li>
|
|
<li>4 on top of the hexapod</li>
|
|
</ul></li>
|
|
</ul>
|
|
|
|
<p>
|
|
In total, 69 degrees of freedom are measured (23 tri axis accelerometers).
|
|
</p>
|
|
|
|
|
|
<div id="orgf23c45c" class="figure">
|
|
<p><img src="figs/accelerometers_ty_overview.jpg" alt="accelerometers_ty_overview.jpg" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 6: </span>Figure caption</p>
|
|
</div>
|
|
|
|
|
|
|
|
<div id="orgbd643a8" class="figure">
|
|
<p><img src="figs/hammer_z.gif" alt="hammer_z.gif" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 7: </span>Figure caption</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org9742a99" class="outline-3">
|
|
<h3 id="org9742a99"><span class="section-number-3">2.2</span> Results</h3>
|
|
<div class="outline-text-3" id="text-2-2">
|
|
<p>
|
|
From the measurements, we obtain
|
|
</p>
|
|
|
|
<ul class="org-ul">
|
|
<li>Reduction of the</li>
|
|
<li>solid body assumption</li>
|
|
<li>verification of the assumption => ok</li>
|
|
</ul>
|
|
|
|
|
|
<div id="org2b50593" class="figure">
|
|
<p><img src="figs/mode1.gif" alt="mode1.gif" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 8: </span>Figure caption</p>
|
|
</div>
|
|
|
|
|
|
<div id="org26c4596" class="figure">
|
|
<p><img src="figs/mode6.gif" alt="mode6.gif" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 9: </span>Figure caption</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org56e7067" class="outline-3">
|
|
<h3 id="org56e7067"><span class="section-number-3">2.3</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-2-3">
|
|
<p>
|
|
The reduction of the number of degrees of freedom from 69 (23 accelerometers with each 3DOF) to 36 (6 solid bodies with 6 DOF) seems to work well.
|
|
</p>
|
|
|
|
<p>
|
|
This confirms the fact that the stages are indeed behaving as a solid body in the frequency band of interest. This valid the fact that a multi-body model can be used to represent the dynamics of the micro-station.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb5c3a23" class="outline-2">
|
|
<h2 id="orgb5c3a23"><span class="section-number-2">3</span> Identification of the Disturbances</h2>
|
|
<div class="outline-text-2" id="text-3">
|
|
<p>
|
|
<a id="org5baf125"></a>
|
|
</p>
|
|
<p>
|
|
<a href="https://tdehaeze.github.io/meas-analysis/">https://tdehaeze.github.io/meas-analysis/</a>
|
|
</p>
|
|
|
|
<p>
|
|
Open Loop Noise budget: <a href="https://tdehaeze.github.io/nass-simscape/disturbances.html">https://tdehaeze.github.io/nass-simscape/disturbances.html</a>
|
|
</p>
|
|
|
|
|
|
<p>
|
|
Static Guiding errors:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>measured at the PEL</li>
|
|
<li>low frequency errors, will thus be compensated</li>
|
|
</ul>
|
|
|
|
<p>
|
|
The problem are on the high frequency disturbances
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orge7fad51" class="outline-3">
|
|
<h3 id="orge7fad51"><span class="section-number-3">3.1</span> Ground Motion</h3>
|
|
<div class="outline-text-3" id="text-3-1">
|
|
<p>
|
|
<a id="org4bc114c"></a>
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
|
|
<div id="outline-container-org5a7da27" class="outline-3">
|
|
<h3 id="org5a7da27"><span class="section-number-3">3.2</span> Stage Vibration - Effect of Control systems</h3>
|
|
<div class="outline-text-3" id="text-3-2">
|
|
<p>
|
|
<a id="org8950c62"></a>
|
|
</p>
|
|
|
|
<p>
|
|
Control system of each stage has been tested
|
|
<a href="https://tdehaeze.github.io/meas-analysis/disturbance-control-system/index.html">https://tdehaeze.github.io/meas-analysis/disturbance-control-system/index.html</a>
|
|
<a href="https://tdehaeze.github.io/meas-analysis/2018-10-15%20-%20Marc/index.html">https://tdehaeze.github.io/meas-analysis/2018-10-15%20-%20Marc/index.html</a>
|
|
</p>
|
|
|
|
<p>
|
|
25Hz vertical motion when the <b>Spindle</b> is turned on (even when not rotating).
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-org03de925" class="outline-3">
|
|
<h3 id="org03de925"><span class="section-number-3">3.3</span> Stage Vibration - Effect of Motion</h3>
|
|
<div class="outline-text-3" id="text-3-3">
|
|
<p>
|
|
<a id="org2389841"></a>
|
|
</p>
|
|
|
|
<p>
|
|
We consider:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>The rotation of the Spindle</li>
|
|
<li>The translation of the Translation Stage</li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org50da187" class="outline-3">
|
|
<h3 id="org50da187"><span class="section-number-3">3.4</span> Sum of all disturbances</h3>
|
|
<div class="outline-text-3" id="text-3-4">
|
|
|
|
<div id="org44769b8" class="figure">
|
|
<p><img src="figs/dist_effect_relative_motion.png" alt="dist_effect_relative_motion.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 10: </span>Amplitude Spectral Density fo the motion error due to disturbances</p>
|
|
</div>
|
|
|
|
|
|
|
|
<div id="orgd9feeea" class="figure">
|
|
<p><img src="figs/dist_effect_relative_motion_cas.png" alt="dist_effect_relative_motion_cas.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 11: </span>Cumulative Amplitude Spectrum of the motion error due to disturbances</p>
|
|
</div>
|
|
|
|
|
|
<p>
|
|
Expected required bandwidth
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org161e425" class="outline-3">
|
|
<h3 id="org161e425"><span class="section-number-3">3.5</span> Better measurement of the effect of disturbances</h3>
|
|
<div class="outline-text-3" id="text-3-5">
|
|
<p>
|
|
Here, the measurement were made with inertial sensors.
|
|
However, we are interested in the relative motion of the sample with respect to the granite and not the absolute motion.
|
|
</p>
|
|
|
|
|
|
<p>
|
|
The best measurement of the disturbances would be to have the metrology already functioning.
|
|
</p>
|
|
|
|
|
|
<p>
|
|
We could perform a measurement using the X-ray.
|
|
</p>
|
|
|
|
<p>
|
|
Detector Requirement:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>Sample frequency above \(400Hz\)</li>
|
|
<li>Resolution of \(\approx 20nm\)</li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb9a9cf1" class="outline-3">
|
|
<h3 id="orgb9a9cf1"><span class="section-number-3">3.6</span> Conclusion</h3>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org083a8f8" class="outline-2">
|
|
<h2 id="org083a8f8"><span class="section-number-2">4</span> Multi Body Model</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
<p>
|
|
<a id="org444ed79"></a>
|
|
</p>
|
|
<p>
|
|
<a href="https://tdehaeze.github.io/nass-simscape/">https://tdehaeze.github.io/nass-simscape/</a>
|
|
</p>
|
|
|
|
<p>
|
|
Multi-Body model
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd9ae0b9" class="outline-3">
|
|
<h3 id="orgd9ae0b9"><span class="section-number-3">4.1</span> Validity of the model</h3>
|
|
<div class="outline-text-3" id="text-4-1">
|
|
<p>
|
|
The mass/inertia of each stage is automatically computed from the geometry and the density of the materials.
|
|
</p>
|
|
|
|
<p>
|
|
The stiffness of each joint is first set to measured values or stiffness from data sheets.
|
|
</p>
|
|
|
|
<p>
|
|
Then, the values of the stiffness and damping of each joint is manually tuned until the obtained dynamics is sufficiently close to the measured dynamics.
|
|
</p>
|
|
|
|
|
|
<p>
|
|
We could, from the measurement, automatically extract the stiffness and damping values, we this would have required a lot of work and having a perfect match is not required here.
|
|
</p>
|
|
|
|
<p>
|
|
Comparison model - measurements : <a href="https://tdehaeze.github.io/nass-simscape/identification.html">https://tdehaeze.github.io/nass-simscape/identification.html</a>
|
|
</p>
|
|
|
|
|
|
<div id="orgcfe5cbf" class="figure">
|
|
<p><img src="figs/identification_comp_top_stages.png" alt="identification_comp_top_stages.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 12: </span>Figure caption</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge11e487" class="outline-3">
|
|
<h3 id="orge11e487"><span class="section-number-3">4.2</span> Wanted position of the sample and position error</h3>
|
|
<div class="outline-text-3" id="text-4-2">
|
|
<p>
|
|
From the reference position of each stage, we can compute the wanted pose of the sample with respect to the granite.
|
|
This is done with multiple transformation matrices.
|
|
</p>
|
|
|
|
<p>
|
|
Then, from the measurement of the metrology corresponding to the position of the sample with respect to the granite, we can compute the position error of the sample expressed in a frame fixed to the nano-hexapod.
|
|
</p>
|
|
|
|
|
|
<div id="org526364d" class="figure">
|
|
<p><img src="figs/control-schematic-nass.png" alt="control-schematic-nass.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 13: </span>Figure caption</p>
|
|
</div>
|
|
|
|
<p>
|
|
Measurement of the sample’s position - conversion of positioning error in the frame of the Nano-hexapod for control: <a href="https://tdehaeze.github.io/nass-simscape/positioning_error.html">https://tdehaeze.github.io/nass-simscape/positioning_error.html</a>
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5945af2" class="outline-3">
|
|
<h3 id="org5945af2"><span class="section-number-3">4.3</span> Simulation of Experiments</h3>
|
|
<div class="outline-text-3" id="text-4-3">
|
|
<p>
|
|
Now that the
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>dynamics of the model is tuned</li>
|
|
<li>disturbances are included in the model</li>
|
|
</ul>
|
|
|
|
<p>
|
|
We can perform simulation of experiments.
|
|
</p>
|
|
|
|
<p>
|
|
<a href="https://tdehaeze.github.io/nass-simscape/experiments.html">https://tdehaeze.github.io/nass-simscape/experiments.html</a>
|
|
</p>
|
|
|
|
<p>
|
|
<a href="#orgafb2424">14</a>
|
|
</p>
|
|
|
|
|
|
<div id="orgafb2424" class="figure">
|
|
<p><img src="figs/exp_scans_rz_dist.png" alt="exp_scans_rz_dist.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 14: </span>Position error of the Sample with respect to the granite during a Tomography Experiment with included disturbances</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org337b7e5" class="outline-3">
|
|
<h3 id="org337b7e5"><span class="section-number-3">4.4</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-4-4">
|
|
<div class="important">
|
|
<p>
|
|
Possible to study many effects.
|
|
Extraction of transfer function like \(G\) and \(G_d\).
|
|
</p>
|
|
|
|
<p>
|
|
Simulation of experiments to validate performance.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5551d84" class="outline-2">
|
|
<h2 id="org5551d84"><span class="section-number-2">5</span> Optimal Nano-Hexapod Design</h2>
|
|
<div class="outline-text-2" id="text-5">
|
|
<p>
|
|
<a id="org555a8dc"></a>
|
|
</p>
|
|
<p>
|
|
As explain before, the nano-hexapod properties (mass, stiffness, architecture, …) will influence:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>the plant dynamics \(G\)</li>
|
|
<li>the effect of disturbances \(G_d\)</li>
|
|
</ul>
|
|
|
|
<p>
|
|
We which here to choose the nano-hexapod properties such that:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>has an easy</li>
|
|
<li>minimize the</li>
|
|
<li>minimize \(|G_d|\)</li>
|
|
</ul>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd3de157" class="outline-3">
|
|
<h3 id="orgd3de157"><span class="section-number-3">5.1</span> Optimal Stiffness to reduce the effect of disturbances</h3>
|
|
</div>
|
|
|
|
<div id="outline-container-org8091d40" class="outline-3">
|
|
<h3 id="org8091d40"><span class="section-number-3">5.2</span> Optimal Stiffness</h3>
|
|
<div class="outline-text-3" id="text-5-2">
|
|
<p>
|
|
The goal is to design a system that is <b>robust</b>.
|
|
</p>
|
|
|
|
<p>
|
|
Thus, we have to identify the sources of uncertainty and try to minimize them.
|
|
</p>
|
|
|
|
<p>
|
|
Uncertainty in the system can be caused by:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>Effect of Support Compliance: <a href="https://tdehaeze.github.io/nass-simscape/uncertainty_support.html">https://tdehaeze.github.io/nass-simscape/uncertainty_support.html</a></li>
|
|
<li>Effect of Payload Dynamics: <a href="https://tdehaeze.github.io/nass-simscape/uncertainty_payload.html">https://tdehaeze.github.io/nass-simscape/uncertainty_payload.html</a></li>
|
|
<li>Effect of experimental condition (micro-station pose, spindle rotation): <a href="https://tdehaeze.github.io/nass-simscape/uncertainty_experiment.html">https://tdehaeze.github.io/nass-simscape/uncertainty_experiment.html</a></li>
|
|
</ul>
|
|
|
|
<p>
|
|
All these uncertainty will limit the maximum attainable bandwidth.
|
|
</p>
|
|
|
|
<p>
|
|
Fortunately, the nano-hexapod stiffness have an influence on the dynamical uncertainty induced by the above effects.
|
|
</p>
|
|
|
|
<p>
|
|
Determination of the optimal stiffness based on all the effects:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li><a href="https://tdehaeze.github.io/nass-simscape/uncertainty_optimal_stiffness.html">https://tdehaeze.github.io/nass-simscape/uncertainty_optimal_stiffness.html</a></li>
|
|
</ul>
|
|
|
|
<div class="conclusion">
|
|
<p>
|
|
|
|
</p>
|
|
|
|
</div>
|
|
|
|
|
|
<p>
|
|
The main performance limitation are payload variability
|
|
</p>
|
|
<div class="question">
|
|
<p>
|
|
Main problem: heavy samples with small stiffness.
|
|
The first resonance frequency of the sample will limit the performance.
|
|
</p>
|
|
|
|
</div>
|
|
|
|
|
|
<p>
|
|
The nano-hexapod stiffness will also change the sensibility to disturbances.
|
|
</p>
|
|
|
|
<p>
|
|
Effect of Nano-hexapod stiffness on the Sensibility to disturbances: <a href="https://tdehaeze.github.io/nass-simscape/optimal_stiffness_disturbances.html">https://tdehaeze.github.io/nass-simscape/optimal_stiffness_disturbances.html</a>
|
|
</p>
|
|
|
|
<div class="conclusion">
|
|
<p>
|
|
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1f5706f" class="outline-3">
|
|
<h3 id="org1f5706f"><span class="section-number-3">5.3</span> Sensors to be included</h3>
|
|
<div class="outline-text-3" id="text-5-3">
|
|
<p>
|
|
Ways to damp:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>Force Sensor</li>
|
|
<li>Relative Velocity Sensors</li>
|
|
<li>Inertial Sensor</li>
|
|
</ul>
|
|
|
|
|
|
|
|
<p>
|
|
<a href="https://tdehaeze.github.io/rotating-frame/index.html">https://tdehaeze.github.io/rotating-frame/index.html</a>
|
|
</p>
|
|
|
|
<p>
|
|
Sensors to be included:
|
|
</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-orge96cfff" class="outline-2">
|
|
<h2 id="orge96cfff"><span class="section-number-2">6</span> Robust Control Architecture</h2>
|
|
<div class="outline-text-2" id="text-6">
|
|
<p>
|
|
<a id="orgb43d859"></a>
|
|
</p>
|
|
<p>
|
|
<a href="https://tdehaeze.github.io/nass-simscape/optimal_stiffness_control.html">https://tdehaeze.github.io/nass-simscape/optimal_stiffness_control.html</a>
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org2a7d7b7" class="outline-3">
|
|
<h3 id="org2a7d7b7"><span class="section-number-3">6.1</span> Simulation of Tomography Experiments</h3>
|
|
<div class="outline-text-3" id="text-6-1">
|
|
<p>
|
|
<a id="org4321b79"></a>
|
|
</p>
|
|
|
|
<ul class="org-ul">
|
|
<li>Make several animations
|
|
<ul class="org-ul">
|
|
<li class="off"><code>[ ]</code> One of a tomography experiment where we see all the station rotating</li>
|
|
<li class="off"><code>[ ]</code> A zoom on at the nano-meter level to see how the wanted position is moving</li>
|
|
</ul></li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org98b634b" class="outline-3">
|
|
<h3 id="org98b634b"><span class="section-number-3">6.2</span> Conclusion</h3>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-orga69770f" class="outline-2">
|
|
<h2 id="orga69770f"><span class="section-number-2">7</span> Further notes</h2>
|
|
<div class="outline-text-2" id="text-7">
|
|
<p>
|
|
Soft granite
|
|
</p>
|
|
|
|
<p>
|
|
Sensible to detector motion?
|
|
</p>
|
|
|
|
<p>
|
|
Common metrology frame for the nano-focusing optics and the measurement of the sample position?
|
|
</p>
|
|
|
|
<p>
|
|
Cable forces?
|
|
</p>
|
|
|
|
<p>
|
|
Slip-Ring noise?
|
|
</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="date">Date: 04-2020</p>
|
|
<p class="author">Author: Thomas Dehaeze</p>
|
|
<p class="date">Created: 2020-04-24 ven. 18:43</p>
|
|
</div>
|
|
</body>
|
|
</html>
|