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

Michalski Jacek, Mrotek Mikołaj, Kozierski Piotr

Pomiary Automatyka Robotyka

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2024

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R. 28, nr 1

31--39

PL

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.

EN

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.

2

Boundary controllability of nonlinear stochastic fractional systems in Hilbert spaces

Mabel Lizzy R., Balachandran K.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 1

123--133

EN

Sufficient conditions for the controllability of nonlinear stochastic fractional boundary control systems are established. The equivalent integral equations are derived for both linear and nonlinear systems, and the control function is given in terms of the pseudoinverse operator. The Banach contraction mapping theorem is used to obtain the result. A controllability result for nonlinear stochastic fractional integrodifferential systems is also attained. Examples are included to illustrate the theory.

3

On infinite horizon active fault diagnosis for a class of non-linear non-Gaussian systems

Punčochář I., Šimandl M.

International Journal of Applied Mathematics and Computer Science

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2014

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Vol. 24, no. 4

795--807

EN

The paper considers the problem of active fault diagnosis for discrete-time stochastic systems over an infinite time horizon. It is assumed that the switching between a fault-free and finitely many faulty conditions can be modelled by a finite-state Markov chain and the continuous dynamics of the observed system can be described for the fault-free and each faulty condition by non-linear non-Gaussian models with a fully observed continuous state. The design of an optimal active fault detector that generates decisions and inputs improving the quality of detection is formulated as a dynamic optimization problem. As the optimal solution obtained by dynamic programming requires solving the Bellman functional equation, approximate techniques are employed to obtain a suboptimal active fault detector.

4

Asynchronous distributed state estimation for continuous-time stochastic processes

Kowalczuk Z., Domżalski M.

International Journal of Applied Mathematics and Computer Science

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2013

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Vol. 23, no. 2

327--339

EN

The problem of state estimation of a continuous-time stochastic process using an Asynchronous Distributed multi-sensor Estimation (ADE) system is considered. The state of a process of interest is estimated by a group of local estimators constituting the proposed ADE system. Each estimator is based, e.g., on a Kalman filter and performs single sensor filtration and fusion of its local results with the results from other/remote processors to compute possibly the best state estimates. In performing data fusion, however, two important issues need to be addressed namely, the problem of asynchronism of local processors and the issue of unknown correlation between asynchronous data in local processors. Both the problems, along with their solutions, are investigated in this paper. Possible applications and effectiveness of the proposed ADE approach are illustrated by simulated experiments, including a non-complete connection graph of such a distributed estimation system.

5

Minimax LQG control

Petersen I. R.

International Journal of Applied Mathematics and Computer Science

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2006

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Vol. 16, no. 3

309-323

EN

This paper presents an overview of some recent results concerning the emerging theory of minimax LQG control for uncertain systems with a relative entropy constraint uncertainty description. This is an important new robust control system design methodology providing minimax optimal performance in terms of a quadratic cost functional. The paper first considers some standard uncertainty descriptions to motivate the relative entropy constraint uncertainty description. The minimax LQG problem under consideration is further motivated by analysing the basic properties of relative entropy. The paper then presents a solution to a worst case control system performance problem which can be generalized to the minimax LQG problem. The solution to this minimax LQG control problem is found to be closely connected to the problem of risk-sensitive optimal control.

6

Equivalent linearization with criteria in probability density function space for stochastic systems under parametric excitations

Socha L.

Zeszyty Naukowe. Budownictwo / Politechnika Śląska

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1999

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z. 86

197-207

EN

The concept of equivalent linearization in probability density space for dynamic systems under parametric Gaussian excitations is considered in this paper. New criteria of linearization and two approximate approaches are proposed.

PL

W artykule przedstawiono koncepcję równoważnej linearyzacji z kryteriami w przestrzeni funkcji gęstości prawdopodobieństw dla stochastycznych układów dynamicznych z wymuszeniami parametrycznymi. Zaproponowano nowe kryteria linearyzacji i dwie techniki linearyzacji.