Filtr Kalmana jako alternatywa dla rozszerzonego obserwatora stanu w algorytmie regulacji ADRC

pol Article in Polish DOI: 10.14313/PAR_251/31

send Jacek Michalski , Mikołaj Mrotek , Piotr Kozierski Politechnika Poznańska, Wydział Automatyki, Robotyki i Elektrotechniki, Instytut Robotyki i Inteligencji Maszynowej, ul. Piotrowo 3a, 60-965 Poznań

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Streszczenie

W artykule przedstawiono zmodyfikowany algorytm odpornej regulacji z aktywną kompensacją zaburzeń ADRC z wykorzystaniem filtru Kalmana KF do estymacji rozszerzonego wektora stanu. Filtrem Kalmana zastąpiono używany w podstawowej formie rozszerzony obserwator stanu ESO. Modyfikacja ta pozwoliła na poprawę odporności układu w warunkach działania pomiarowych zakłóceń stochastycznych. Przedstawiono sposób syntezy układu regulacji i doboru nastaw filtru Kalmana zapewniający skuteczność sterowania, a także pokazano ich wpływ na działanie układu. Eksperymenty zostały przeprowadzone na układzie laboratoryjnym z balansującą na stole kulą BBT. Jakość regulacji została oceniona na podstawie przebiegów czasowych oraz całkowych wskaźników jakości, dla różnych konfiguracji nastaw oraz poziomów zaszumienia. W wyniku badań wykazana została przewaga zastosowania filtru Kalmana nad obserwatorem pod kątem wrażliwości na szumy pomiarowe. Zastosowanie filtru Kalmana jako estymatora dla rozszerzonego stanu wykazało pozytywny wpływ na jakość regulacji i zdolność do odrzucania zakłóceń wewnętrznych również w układzie deterministycznym.

Słowa kluczowe

ADRC, filtr Kalmana, obiekty nieliniowe, rozszerzony obserwator stanu, stół z balansującą kulą, układ stochastyczny

Kalman Filter as an Alternative to Extended State Observer in ADRC Control Algorithm

Abstract

The article presents a modified Active Disturbance Rejection Control (ADRC) algorithm that uses the Kalman Filter (KF) for the estimation of extended state vector. The Kalman filter replaced the Extended State Observer (ESO) used in its basic form. The purpose of this modification was to improve the system robustness under conditions of stochastic measurement disturbances. The method of the control system synthesis and the Kalman filter gains selection, ensuring control efficiency, as well as their impact on the system operation, were presented. The experiments were carried out on a laboratory setup – the Ball Balancing Table (BBT). Control quality was assessed based on time plots of signals and integral performance indices for various algorithm gains configurations and different noise levels. As a result of the conducted research, the advantage of using the Kalman filter over the ESO in terms of sensitivity to measurement noises was demonstrated. Implementation of the Kalman filter as the ESO determined a positive impact on control quality and the ability to reject internal disturbance also in a deterministic system.

Keywords

ADRC, ball balancing table, extended state observer, Kalman filter, nonlinear systems, stochastic system

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