The Application of an Adaptive Controller Combined with the LQR Controller for the Inverted Pendulum

eng Artykuł w języku angielskim DOI: 10.14313/PAR_234/47

wyślij Jakub Żegleń-Włodarczyk AGH Akademia Górniczo-Hutnicza, Wydział Elektrotechniki, Automatyki, Informatyki i Inżynierii Biomedycznej

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Abstract

The inverted pendulum is an unstable system with nonlinear dynamics. The task of controlling the inverted pendulum is complex. Therefore, the inverted pendulum over the years has become one of the most important systems on which every controller is tested. Here the objective is to control the system in such a way that the inverted pendulum stabilizes in the upright position. This analysis proposes a non-linear Lyapunov-based controller. The controller at hand, only provides the pendulum’s stabilization, therefore an additional module is needed – in this case the LQR controller. Both modules are combined with each other by using a two-loop parallel design. The newly designed controller has been experimentally tested and compared to the single LQR controller.

Keywords

adaptive controller, inverted pendulum, LQR control

Zastosowanie regulatora adaptacyjnego w połączeniu z regulatorem LQR dla wahadła odwróconego

Streszczenie

Odwrócone wahadło jest niestabilnym systemem o nieliniowej dynamice. Zadanie sterowania wahadłem odwróconym jest trudne, dlatego też układ ten przez lata stał się jednym z najważniejszych systemów, na których testowane są wszelkiego rodzaju regulatory. Celem sterowania systemem jest ustabilizowanie wahadła odwróconego w pozycji pionowo skierowanej ku górze. W artykule zaproponowano nowy algorytm adaptacyjny dla wahadła, będący kombinacją regulatora LQR oraz regulatora nieliniowego bazującego na twierdzeniu Lapunova. Oba moduły są połączone za pomocą dwupętlowej konstrukcji równoległej. Nowo zaprojektowany regulator został przetestowany eksperymentalnie i porównany z niezależnym modułem LQR.

Słowa kluczowe

LQR control, regulator adaptacyjny, wahadło odwrócone

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