Add one figure that shows to optimal xi for kp
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After Width: | Height: | Size: 109 KiB |
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matlab/figs/mod_iff_damping_kp.pdf
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matlab/figs/mod_iff_damping_kp.pdf
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After Width: | Height: | Size: 57 KiB |
@ -491,13 +491,29 @@ The frequencies of the transmission zeros of the system are increasing with the
|
||||
Therefore, even though the parallel stiffness $k_p$ should be larger than $m \Omega^2$ for stability reasons, it should not be taken too high as this would limit the attainable bandwidth.
|
||||
|
||||
For any $k_p > m \Omega^2$, the control gain $g$ can be tuned such that the maximum simultaneous damping $\xi_\text{opt}$ is added to 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 $g_\text{opt} \approx 2 \omega_0$.
|
||||
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||||
#+name: fig:root_locus_iff_kps_opt
|
||||
#+caption: Root Locus for IFF when parallel stiffness $k_p$ is added, $\Omega = 0.1 \omega_0$
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||||
#+attr_latex: :environment subfigure :width 0.45\linewidth :align c
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||||
| file:figs/root_locus_iff_kps.pdf | file:figs/root_locus_opt_gain_iff_kp.pdf |
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||||
| <<fig:root_locus_iff_kps>> Comparison of three parallel stiffnesses $k_p$ | <<fig:root_locus_opt_gain_iff_kp>> $k_p = 5 m \Omega^2$, optimal damping $\xi_\text{opt}$ is shown |
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#+attr_latex: :options [t]{0.48\linewidth}
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#+begin_minipage
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||||
#+name: fig:root_locus_iff_kps
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#+caption: Comparison the Root Locus for three parallel stiffnessses $k_p$
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||||
#+attr_latex: :width \linewidth :float nil
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||||
[[file:figs/root_locus_iff_kps.pdf]]
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#+end_minipage
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\hfill
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#+attr_latex: :options [t]{0.48\linewidth}
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#+begin_minipage
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||||
#+name: fig:mod_iff_damping_kp
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||||
#+caption: Optimal Damping Ratio $\xi_\text{opt}$ and the corresponding optimal gain $g_\text{opt}$ as a function of $\alpha$
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||||
#+attr_latex: :width \linewidth :float nil
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||||
[[file:figs/mod_iff_damping_kp.pdf]]
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#+end_minipage
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||||
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||||
# #+name: fig:root_locus_iff_kps_opt
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||||
# #+caption: Root Locus for IFF when parallel stiffness $k_p$ is added, $\Omega = 0.1 \omega_0$
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# #+attr_latex: :environment subfigure :width 0.45\linewidth :align c
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||||
# | file:figs/root_locus_iff_kps.pdf | file:figs/mod_iff_damping_kp.pdf |
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||||
# | <<fig:root_locus_iff_kps>> Comparison of three parallel stiffnesses $k_p$ | <<fig:root_locus_opt_gain_iff_kp>> $k_p = 5 m \Omega^2$, optimal damping $\xi_\text{opt}$ is shown |
|
||||
|
||||
* Comparison and Discussion
|
||||
<<sec:comparison>>
|
||||
@ -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.
|
||||
|
||||
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Reference in New Issue
Block a user