From 520b0e0072052fbe5f559dc25e416480491602bc Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Sat, 13 Feb 2021 16:00:10 +0100 Subject: [PATCH] Update Content - 2021-02-13 --- ...n_dampin_flexib_struc_using_force_feedb.md | 91 ++++++++++++++++++ ...urner15_fiber_based_distan_sensin_inter.md | 22 +++++ content/techreport/merlet87_paral_manip.md | 22 +++++ static/ox-hugo/chesne16_2dof_system.png | Bin 0 -> 14374 bytes static/ox-hugo/chesne16_root_locus_alpha.png | Bin 0 -> 146920 bytes static/ox-hugo/chesne16_transmissibility.png | Bin 0 -> 32130 bytes 6 files changed, 135 insertions(+) create mode 100644 content/article/chesne16_enhan_dampin_flexib_struc_using_force_feedb.md create mode 100644 content/article/thurner15_fiber_based_distan_sensin_inter.md create mode 100644 content/techreport/merlet87_paral_manip.md create mode 100644 static/ox-hugo/chesne16_2dof_system.png create mode 100644 static/ox-hugo/chesne16_root_locus_alpha.png create mode 100644 static/ox-hugo/chesne16_transmissibility.png diff --git a/content/article/chesne16_enhan_dampin_flexib_struc_using_force_feedb.md b/content/article/chesne16_enhan_dampin_flexib_struc_using_force_feedb.md new file mode 100644 index 0000000..a6f8c78 --- /dev/null +++ b/content/article/chesne16_enhan_dampin_flexib_struc_using_force_feedb.md @@ -0,0 +1,91 @@ ++++ +title = "Enhanced damping of flexible structures using force feedback" +author = ["Thomas Dehaeze"] +draft = false ++++ + +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} + + + +{{< 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. + + + +{{< 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. + + + +{{< 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} + +
+
+ +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. + +
+ + +## Bibliography {#bibliography} + +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. . diff --git a/content/article/thurner15_fiber_based_distan_sensin_inter.md b/content/article/thurner15_fiber_based_distan_sensin_inter.md new file mode 100644 index 0000000..e5d9b37 --- /dev/null +++ b/content/article/thurner15_fiber_based_distan_sensin_inter.md @@ -0,0 +1,22 @@ ++++ +title = "Fiber-Based Distance Sensing Interferometry" +author = ["Thomas Dehaeze"] +draft = false ++++ + +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} + +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. diff --git a/content/techreport/merlet87_paral_manip.md b/content/techreport/merlet87_paral_manip.md new file mode 100644 index 0000000..664c36a --- /dev/null +++ b/content/techreport/merlet87_paral_manip.md @@ -0,0 +1,22 @@ ++++ +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} + +Merlet, Jean-Pierre. 1987. “Parallel Manipulators. 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