Update Content - 2021-02-13

content/article/chesne16_enhan_dampin_flexib_struc_using_force_feedb.md

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+title = "Enhanced damping of flexible structures using force feedback"
+author = ["Thomas Dehaeze"]
+draft = false
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+
+Tags
+: [Active Damping]({{< relref "active_damping" >}}), [Integral Force Feedback]({{< relref "integral_force_feedback" >}})
+
+Reference
+: ([Chesné, Milhomem, and Collette 2016](#org2953ca1))
+
+Author(s)
+: Simon Chesné, Milhomem, A., & Collette, C.
+
+Year
+: 2016
+
+One problem of Integral Force Feedback (IFF) is that the achievable damping decreases at high frequency.
+A modification of the IFF is proposed in order to significantly increase the damping of **a** selected mode.
+
+The test system is shown in Figure [1](#org9c0dbe3).
+
+Classical IFF corresponds to:
+
+\begin{equation}
+H(s) = \frac{g}{s}
+\end{equation}
+
+<a id="org9c0dbe3"></a>
+
+{{< figure src="/ox-hugo/chesne16_2dof_system.png" caption="Figure 1: Two DoF system representing a flexible structuer controlled by an active mount" >}}
+
+The proposed controller, called **alpha controller** is:
+
+\begin{equation}
+H(s) = g \frac{s + \alpha}{s^2}
+\end{equation}
+
+where \\(\alpha\\) is a parameter.
+
+A new pair of pole/zero has been introduced.
+The new pole is located at \\(s = 0\\) and the zeros at \\(s = -\alpha\\).
+
+For \\(\omega > \alpha\\) the controller is essentially an integrator.
+For \\(\omega < \alpha\\) the controller is a double integrator.
+
+Depending on the chosen \\(\alpha\\) we obtain different root locus as shown in Figure [2](#org08e7f67).
+There is an optimal gain \\(\alpha^\star\\) at which the attainable damping of the flexible mode is maximized.
+
+<a id="org08e7f67"></a>
+
+{{< figure src="/ox-hugo/chesne16_root_locus_alpha.png" caption="Figure 2: Root locus with the alpha controller for different values of \\(\alpha\\)" >}}
+
+The obtained transmissibility is shown without controller, for classical IFF and for \\(\alpha\\) controller in Figure [3](#org2c2d3d7).
+
+Using the \\(\alpha\\) controller, the compliance is however degraded a lot.
+
+<a id="org2c2d3d7"></a>
+
+{{< figure src="/ox-hugo/chesne16_transmissibility.png" caption="Figure 3: Transmissibility \\(x\_1/x\_0\\)" >}}
+
+In order to recover the compliance at low frequency, high pass filters can be added to the controller.
+
+\begin{equation}
+H(s) = g \frac{s + \alpha}{(s + \beta)^2}
+\end{equation}
+
+The condition for stability found here is:
+
+\begin{equation}
+\alpha \ge \beta/2
+\end{equation}
+
+<div class="sum">
+  <div></div>
+
+The active damping of flexible structures with collocated force sensor/actuator pairs have been reviewed in this Note.
+In the first part of the Note, two limitations of the integral force feedback (IFF) have been discussed, which are the limited damping of flexible modes and the loss of compliance.
+By slightly modifying the controller, it has been shown that the active damping of a target mode can be significantly increased.
+Analytical formulas of the optimal parameters have been derived.
+In the second part, the loss of compliance inherent to IFF has been addressed.
+It has been shown that, when a high-pass filter is inserted into the IFF controller, the compliance at low frequency can be recovered but the unconditional stability is lost.
+On the other side, with the new proposed control law, the stability is always guaranteed even when using a high-pass filter.
+
+</div>
+
+
+## Bibliography {#bibliography}
+
+<a id="org2953ca1"></a>Chesné, Simon, Ariston Milhomem, and Christophe Collette. 2016. “Enhanced Damping of Flexible Structures Using Force Feedback.” _Journal of Guidance, Control, and Dynamics_ 39 (7):1654–58. <https://doi.org/10.2514/1.g001620>.

content/article/thurner15_fiber_based_distan_sensin_inter.md

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+title = "Fiber-Based Distance Sensing Interferometry"
+author = ["Thomas Dehaeze"]
+draft = false
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+
+Tags
+: [Interferometers]({{< relref "interferometers" >}})
+
+Reference
+: ([Thurner et al. 2015](#org6f5a8f6))
+
+Author(s)
+: Thurner, K., Quacquarelli, F. P., Braun, Pierre-Francois, Dal Savio, C., & Karrai, K.
+
+Year
+: 2015
+
+
+## Bibliography {#bibliography}
+
+<a id="org6f5a8f6"></a>Thurner, Klaus, Francesca Paola Quacquarelli, Pierre-François Braun, Claudio Dal Savio, and Khaled Karrai. 2015. “Fiber-Based Distance Sensing Interferometry.” _Applied Optics_ 54 (10). Optical Society of America:3051–63.

content/techreport/merlet87_paral_manip.md

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+title = "Parallel manipulators. part i: theory design, kinematics, dynamics and control"
+author = ["Thomas Dehaeze"]
+draft = false
++++
+
+Tags
+: [Stewart Platforms]({{< relref "stewart_platforms" >}})
+
+Reference
+: ([Merlet 1987](#org07bdf3f))
+
+Author(s)
+: Merlet, J.
+
+Year
+: 1987
+
+
+## Bibliography {#bibliography}
+
+<a id="org07bdf3f"></a>Merlet, Jean-Pierre. 1987. “Parallel Manipulators. Part I: Theory Design, Kinematics, Dynamics and Control.” INRIA.