Update Content - 2022-04-19

content/book/pintelon12_system_ident.md

@@ -0,0 +1,24 @@
++++
+title = "System identification : a frequency domain approach"
+author = ["Dehaeze Thomas"]
+draft = true
++++
+
+Tags
+: [System Identification]({{< relref "system_identification.md" >}})
+
+Reference
+: (<a href="#citeproc_bib_item_1">Pintelon and Schoukens 2012</a>)
+
+Author(s)
+: Pintelon, R., &amp; Schoukens, J.
+
+Year
+: 2012
+
+
+## Bibliography {#bibliography}
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Pintelon, Rik, and Johan Schoukens. 2012. <i>System Identification : a Frequency Domain Approach</i>. Hoboken, N.J. Piscataway, NJ: Wiley IEEE Press. doi:<a href="https://doi.org/10.1002/9781118287422">10.1002/9781118287422</a>.</div>
+</div>

content/zettels/quadrant_photodiodes.md

@@ -8,8 +8,6 @@ category = "equipment"
 Tags
 : [Position Sensors]({{< relref "position_sensors.md" >}}), [Optics]({{< relref "optics.md" >}})
 
-Some bibliography (<a href="#citeproc_bib_item_3">Manojlović 2011</a>; <a href="#citeproc_bib_item_4">Wu et al. 2015</a>; <a href="#citeproc_bib_item_2">Li et al. 2019</a>).
-
 
 ## Working principle {#working-principle}
 
@@ -43,7 +41,7 @@ Basic requirements (taken from [here](https://www.aptechnologies.co.uk/home/supp
 
 Estimation of the linear region.
 
-The relation between the spot size and the quadrant photodiode sensitivity is well explained in (<a href="#citeproc_bib_item_1">Lee et al. 2010</a>).
+The relation between the spot size and the quadrant photodiode sensitivity is well explained in (<a href="#citeproc_bib_item_2">Lee et al. 2010</a>).
 
 Usually, single mode laser are used such that the beam profile can well be approximated by a Gaussian distribution.
 The irradiance distribution is then:
@@ -66,6 +64,16 @@ It is function of:
 -   the spot size
 -   the gain size
 
+Spot size of collimated bean at focal plane of a lens ([link](https://www.gentec-eo.com/blog/spot-size-of-laser-beam)).
+
+See:
+
+-   (<a href="#citeproc_bib_item_5">Ng, Tan, and Foo 2007</a>)
+-   (<a href="#citeproc_bib_item_4">Manojlović 2011</a>)
+-   (<a href="#citeproc_bib_item_6">Wu et al. 2015</a>)
+-   (<a href="#citeproc_bib_item_1">Azaryan et al. 2019</a>)
+-   (<a href="#citeproc_bib_item_3">Li et al. 2019</a>)
+
 
 ## Electrical Readout {#electrical-readout}
 
@@ -150,9 +158,13 @@ We now that the maximum translation of the beam is \\(\Delta z = 1\\,mm\\) and t
 
 ## Bibliography {#bibliography}
 
+## References
+
 <style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
-  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Lee, Eun Joong, Youngok Park, Chul Sung Kim, and Taejoon Kouh. 2010. “Detection Sensitivity of the Optical Beam Deflection Method Characterized with the Optical Spot Size on the Detector.” <i>Current Applied Physics</i> 10 (3): 834–37. doi:<a href="https://doi.org/10.1016/j.cap.2009.10.003">10.1016/j.cap.2009.10.003</a>.</div>
-  <div class="csl-entry"><a id="citeproc_bib_item_2"></a>Li, Qing, Shaoxiong Xu, Jiawei Yu, Lingjie Yan, and Yongmei Huang. 2019. “An Improved Method for the Position Detection of a Quadrant Detector for Free Space Optical Communication.” <i>Sensors</i> 19 (1): 175. doi:<a href="https://doi.org/10.3390/s19010175">10.3390/s19010175</a>.</div>
-  <div class="csl-entry"><a id="citeproc_bib_item_3"></a>Manojlović, Lazo M. 2011. “Quadrant Photodetector Sensitivity.” <i>Applied Optics</i> 50 (20). Optical Society of America: 3461–69.</div>
-  <div class="csl-entry"><a id="citeproc_bib_item_4"></a>Wu, Jiabin, Yunshan Chen, Shijie Gao, Yimang Li, and Zhiyong Wu. 2015. “Improved Measurement Accuracy of Spot Position on an Ingaas Quadrant Detector.” <i>Applied Optics</i> 54 (27). Optical Society of America: 8049–54.</div>
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Azaryan, N. S., J. A. Budagov, M. V. Lyablin, A. A. Pluzhnikov, B. Di Girolamo, J.-Ch. Gayde, and D. Mergelkuhl. 2019. “Position-Sensitive Photoreceivers: Sensitivity and Detectable Range of Displacements of a Focused Single-Mode Laser Beam.” <i>Physics of Particles and Nuclei Letters</i> 16 (4): 354–76. doi:<a href="https://doi.org/10.1134/s1547477119040058">10.1134/s1547477119040058</a>.</div>
+  <div class="csl-entry"><a id="citeproc_bib_item_2"></a>Lee, Eun Joong, Youngok Park, Chul Sung Kim, and Taejoon Kouh. 2010. “Detection Sensitivity of the Optical Beam Deflection Method Characterized with the Optical Spot Size on the Detector.” <i>Current Applied Physics</i> 10 (3): 834–37. doi:<a href="https://doi.org/10.1016/j.cap.2009.10.003">10.1016/j.cap.2009.10.003</a>.</div>
+  <div class="csl-entry"><a id="citeproc_bib_item_3"></a>Li, Qing, Shaoxiong Xu, Jiawei Yu, Lingjie Yan, and Yongmei Huang. 2019. “An Improved Method for the Position Detection of a Quadrant Detector for Free Space Optical Communication.” <i>Sensors</i> 19 (1): 175. doi:<a href="https://doi.org/10.3390/s19010175">10.3390/s19010175</a>.</div>
+  <div class="csl-entry"><a id="citeproc_bib_item_4"></a>Manojlović, Lazo M. 2011. “Quadrant Photodetector Sensitivity.” <i>Applied Optics</i> 50 (20). Optical Society of America: 3461–69.</div>
+  <div class="csl-entry"><a id="citeproc_bib_item_5"></a>Ng, T.W., H.Y. Tan, and S.L. Foo. 2007. “Small Gaussian Laser Beam Diameter Measurement Using a Quadrant Photodiode.” <i>Optics &#38;Amp; Laser Technology</i> 39 (5): 1098–1100. doi:<a href="https://doi.org/10.1016/j.optlastec.2006.06.001">10.1016/j.optlastec.2006.06.001</a>.</div>
+  <div class="csl-entry"><a id="citeproc_bib_item_6"></a>Wu, Jiabin, Yunshan Chen, Shijie Gao, Yimang Li, and Zhiyong Wu. 2015. “Improved Measurement Accuracy of Spot Position on an Ingaas Quadrant Detector.” <i>Applied Optics</i> 54 (27). Optical Society of America: 8049–54.</div>
 </div>

content/zettels/system_identification.md

@@ -8,7 +8,165 @@ Tags
 : [Modal Analysis]({{< relref "modal_analysis.md" >}})
 
 
+## SISO Identification {#siso-identification}
+
+
+### Problem Description {#problem-description}
+
+<a id="figure--fig:siso-identification-schematic"></a>
+
+{{< figure src="/ox-hugo/siso_identification_schematic.png" caption="<span class=\"figure-number\">Figure 1: </span>Block diagram of the SISO system identification" >}}
+
+<a id="figure--fig:siso-identification-schematic-simplier"></a>
+
+{{< figure src="/ox-hugo/siso_identification_schematic_simplier.png" caption="<span class=\"figure-number\">Figure 2: </span>Simpler Block diagram of the SISO system identification" >}}
+
+<div class="note">
+
+If the open-loop system is unstable, first design a simple controller that stabilizes the system and then identify the closed-loop system.
+
+</div>
+
+
+### Design of the Excitation Signal {#design-of-the-excitation-signal}
+
+
+#### Introduction {#introduction}
+
+There are several choices for excitation signals:
+
+-   Impulse, Steps
+-   Sweep Sinus
+-   Random noise, Periodic signals
+
+
+#### Random noise with specific ASD {#random-noise-with-specific-asd}
+
+The ASD of the measured output is:
+
+\begin{equation}
+\Gamma\_{y\_m}(\omega) = \Gamma\_d(\omega) + \Gamma\_u(\omega) \cdot |G(j\omega)|
+\end{equation}
+
+And we want the effect of the excitation signal to be much higher than the effect of the exogenous signals (measurement noise, input noise, disturbances).
+
+\begin{equation}
+\Gamma\_u(\omega) \gg \Gamma\_d(\omega) \cdot |G(j\omega)|^{-1}
+\end{equation}
+
+Note that \\(\Gamma\_d(\omega)\\) can be estimated by measuring the system output in the absence of any excitation signal.
+The plant magnitude \\(|G(j\omega)|\\) can be roughly estimated from a first identification with bad coherence.
+
+In order to design a random excitation signal with specific spectral characteristics, first a signal with an ASD equal to one is generated (i.e. white noise with unity ASD):
+
+```matlab
+Ts = 1e-4; % Sampling Time [s]
+t = 0:Ts:10; % Time Vector [s]
+
+%% Signal with an ASD equal to one
+u_norm = sqrt(1/2/Ts)*randn(length(t), 1);
+```
+
+Then, a transfer function whose magnitude \\(|G\_u(j\omega)|\\) has the same shape as the wanted excitation ASD \\(\Gamma\_u(\omega)\\) is designed:
+
+```matlab
+%% Transfer function representing the wanted ASD
+G_u = tf([1], [1/2/pi/100 1]);
+```
+
+Finally `lsim` is used to compute the shaped excitation signal.
+
+```matlab
+%% Shape the ASD of the excitation signal
+u = lsim(G_u, u_norm, t);
+```
+
+
+#### Choose Sampling Frequency and Duration of Excitation {#choose-sampling-frequency-and-duration-of-excitation}
+
+<div class="important">
+
+The sampling frequency \\(F\_s\\) will determine the maximum frequency \\(F\_{\text{max}}\\) that can be estimated (see Nyquist theorem):
+
+\begin{equation}
+F\_{\text{max}} = \frac{1}{2} F\_s
+\end{equation}
+
+</div>
+
+<div class="important">
+
+The duration of excitation \\(T\_{\text{exc}}\\) will determine the minimum frequency \\(F\_{\text{min}}\\) that can be estimated:
+
+\begin{equation}
+F\_{\text{min}} = \frac{1}{T\_{\text{exc}}}
+\end{equation}
+
+It will also corresponds to the frequency resolution \\(\Delta f\\):
+
+\begin{equation}
+\Delta f = \frac{1}{T\_{\text{exc}}}
+\end{equation}
+
+</div>
+
+In order to increase the estimation quality, averaging can be use with a longer excitation duration.
+A factor 10 is usually good enough, therefore the excitation time can be taken as:
+
+\begin{equation}
+T\_{\text{exc}} \approx \frac{10}{F\_{\text{min}}}
+\end{equation}
+
+<div class="exampl">
+
+Therefore, if the system has to be identified from 1Hz up to 500Hz, the sampling frequency should be:
+
+\begin{equation}
+F\_s = 2 F\_{\text{max}} = 1\\,\text{kHz}
+\end{equation}
+
+Then, the excitation duration should be (10 averaging):
+
+\begin{equation}
+T\_{\text{exc}} = \frac{10}{1} = 10\\,s
+\end{equation}
+
+</div>
+
+
+### Computation of the Frequency Response Function {#computation-of-the-frequency-response-function}
+
+
+#### Windowing Function {#windowing-function}
+
+
+#### Example {#example}
+
+`tfestimate`
+
+```matlab
+[G, f] = tfestimate(u, y, win, [], [], 1/Ts);
+```
+
+
+### Verification of the Identification Quality {#verification-of-the-identification-quality}
+
+`mscohere`
+
+```matlab
+[coh, f] = mscohere(u, y, win, [], [], 1/Ts);
+```
+
+
+## Reference Books {#reference-books}
+
+-   (<a href="#citeproc_bib_item_1">Pintelon and Schoukens 2012</a>)
+-   (<a href="#citeproc_bib_item_2">Schoukens, Pintelon, and Rolain 2012</a>)
+
+
 ## Bibliography {#bibliography}
 
 <style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Pintelon, Rik, and Johan Schoukens. 2012. <i>System Identification : a Frequency Domain Approach</i>. Hoboken, N.J. Piscataway, NJ: Wiley IEEE Press. doi:<a href="https://doi.org/10.1002/9781118287422">10.1002/9781118287422</a>.</div>
+  <div class="csl-entry"><a id="citeproc_bib_item_2"></a>Schoukens, Johan, Rik Pintelon, and Yves Rolain. 2012. <i>Mastering System Identification in 100 Exercises</i>. John Wiley &#38; Sons.</div>
 </div>

content/zettels/tuned_mass_damper.md

@@ -0,0 +1,29 @@
++++
+title = "Tuned Mass Damper"
+author = ["Dehaeze Thomas"]
+draft = false
++++
+
+Tags
+: [Passive Damping]({{< relref "passive_damping.md" >}})
+
+Review: (<a href="#citeproc_bib_item_1">Elias and Matsagar 2017</a>)
+
+
+## Working Principle {#working-principle}
+
+{{< youtube qDzGCgLu59A >}}
+
+
+## Manufacturers {#manufacturers}
+
+<https://vibratec.se/en/product/high-frequency-tuned-mass-damper/>
+
+
+## Bibliography {#bibliography}
+
+## References
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Elias, Said, and Vasant Matsagar. 2017. “Research Developments in Vibration Control of Structures Using Passive Tuned Mass Dampers.” <i>Annual Reviews in Control</i> 44 (nil): 129–56. doi:<a href="https://doi.org/10.1016/j.arcontrol.2017.09.015">10.1016/j.arcontrol.2017.09.015</a>.</div>
+</div>