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Acta Mechanica Sinica
Erschienen in: Acta Mechanica Sinica 3/2017

21.03.2017 | Research Paper

Optimal feedback gains of a delayed proportional-derivative (PD) control for balancing an inverted pendulum

verfasst von: Qiang Wang, Zaihua Wang

Erschienen in: Acta Mechanica Sinica | Ausgabe 3/2017

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Abstract

In the dynamics analysis and synthesis of a controlled system, it is important to know for what feedback gains can the controlled system decay to the demanded steady state as fast as possible. This article presents a systematic method for finding the optimal feedback gains by taking the stability of an inverted pendulum system with a delayed proportional-derivative controller as an example. First, the condition for the existence and uniqueness of the stable region in the gain plane is obtained by using the D-subdivision method and the method of stability switch. Then the same procedure is used repeatedly to shrink the stable region by decreasing the real part of the rightmost characteristic root. Finally, the optimal feedback gains within the stable region that minimizes the real part of the rightmost root are expressed by an explicit formula. With the optimal feedback gains, the controlled inverted pendulum decays to its trivial equilibrium at the fastest speed when the initial values around the origin are fixed. The main results are checked by numerical simulation.
Vorheriger Artikel A macroscopic multi-mechanism based constitutive model for the thermo-mechanical cyclic degeneration of shape memory effect of NiTi shape memory alloy

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Metadaten
Titel
Optimal feedback gains of a delayed proportional-derivative (PD) control for balancing an inverted pendulum
verfasst von
Qiang Wang
Zaihua Wang
Publikationsdatum
21.03.2017
Verlag
The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences
Erschienen in
Acta Mechanica Sinica / Ausgabe 3/2017
Print ISSN: 0567-7718
Elektronische ISSN: 1614-3116
DOI
https://doi.org/10.1007/s10409-017-0655-x

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