From f5ba579f4f4d46adc9478b5ccc22eb992b7ebe14 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Tue, 7 Jul 2020 18:48:37 +0200 Subject: [PATCH] Add one figure that shows to optimal xi for kp --- inkscape/mod_iff_damping_kp.pdf | Bin 0 -> 38747 bytes inkscape/mod_iff_damping_kp.svg | Bin 0 -> 112014 bytes matlab/figs/mod_iff_damping_kp.pdf | Bin 0 -> 24420 bytes matlab/figs/mod_iff_damping_kp.png | Bin 0 -> 58464 bytes paper/paper.org | 30 ++++++++++++++++++++++------- 5 files changed, 23 insertions(+), 7 deletions(-) create mode 100644 inkscape/mod_iff_damping_kp.pdf create mode 100644 inkscape/mod_iff_damping_kp.svg create mode 100644 matlab/figs/mod_iff_damping_kp.pdf create mode 100644 matlab/figs/mod_iff_damping_kp.png diff --git a/inkscape/mod_iff_damping_kp.pdf b/inkscape/mod_iff_damping_kp.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f7f856e89099e785aaf80f1af949e84cf0d3bf4d GIT binary patch literal 38747 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the resonances of the system. -An example is shown in Figure ref:fig:root_locus_opt_gain_iff_kp for $k_p = 5 m \Omega^2$ where the damping $\xi_{\text{opt}} \approx 0.83$ is obtained for a control gain $g_\text{opt} \approx 2 \omega_0$. +# An example is shown in Figure ref:fig:root_locus_opt_gain_iff_kp for $k_p = 5 m \Omega^2$ where the damping $\xi_{\text{opt}} \approx 0.83$ is obtained for a control gain $g_\text{opt} \approx 2 \omega_0$. -#+name: fig:root_locus_iff_kps_opt -#+caption: Root Locus for IFF when parallel stiffness $k_p$ is added, $\Omega = 0.1 \omega_0$ -#+attr_latex: :environment subfigure :width 0.45\linewidth :align c -| file:figs/root_locus_iff_kps.pdf | file:figs/root_locus_opt_gain_iff_kp.pdf | -| <> Comparison of three parallel stiffnesses $k_p$ | <> $k_p = 5 m \Omega^2$, optimal damping $\xi_\text{opt}$ is shown | +#+attr_latex: :options [t]{0.48\linewidth} +#+begin_minipage +#+name: fig:root_locus_iff_kps +#+caption: Comparison the Root Locus for three parallel stiffnessses $k_p$ +#+attr_latex: :width \linewidth :float nil +[[file:figs/root_locus_iff_kps.pdf]] +#+end_minipage +\hfill +#+attr_latex: :options [t]{0.48\linewidth} +#+begin_minipage +#+name: fig:mod_iff_damping_kp +#+caption: Optimal Damping Ratio $\xi_\text{opt}$ and the corresponding optimal gain $g_\text{opt}$ as a function of $\alpha$ +#+attr_latex: :width \linewidth :float nil +[[file:figs/mod_iff_damping_kp.pdf]] +#+end_minipage + +# #+name: fig:root_locus_iff_kps_opt +# #+caption: Root Locus for IFF when parallel stiffness $k_p$ is added, $\Omega = 0.1 \omega_0$ +# #+attr_latex: :environment subfigure :width 0.45\linewidth :align c +# | file:figs/root_locus_iff_kps.pdf | file:figs/mod_iff_damping_kp.pdf | +# | <> Comparison of three parallel stiffnesses $k_p$ | <> $k_p = 5 m \Omega^2$, optimal damping $\xi_\text{opt}$ is shown | * Comparison and Discussion <> @@ -533,7 +549,7 @@ It is interesting to note that the maximum added damping is very similar for bot The two proposed techniques are now compared in terms of closed-loop compliance and transmissibility. The compliance is defined as the transfer function from external forces applied to the payload to the displacement of the payload in an inertial frame. -The transmissibility describes the dynamic behaviour between the displacement of the rotating stage and the displacement of the payload. +The transmissibility describes the dynamic behavior between the displacement of the rotating stage and the displacement of the payload. It is used to characterize how much vibration of the rotating stage is transmitted to the payload. The two techniques are also compared with passive damping (Figure ref:fig:system) where $c = c_\text{crit}$ is tuned to critically damp the resonance when the rotating speed is null.