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1

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

Robust simultaneous stabilization of uncertain discrete-time systems

Pakshin P., Soloviev S.

Systems Science

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2008

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Vol. 34, no 1

39-48

EN

The paper considers a set of linear discrete-time systems with uncertain parameters. A method of synthesis of robust control which simultaneously stabilizes all the systems from this set is proposed. This method consists of two steps. First, a set of stochastic comparison systems with multiplicative noises is constructed such that if the stochastic system from this set is mean square stable then the corresponding system with uncertain parameters from the original set is robustly stable. Second, the simultaneous stabilization problem for the comparison system is solved. To find a gain matrix of the simultaneously stabilizing controller in the case of state feedback an LMI based algorithm is given and in the case of static output feedback a new method and convergent iteration algorithm are obtained.

3

Hierarchical control in a large scale stochastic system with nonclassical information structure

Duda Z., Brandys W.

Archives of Control Sciences

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2003

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Vol. 13, no. 4

493-504

EN

In the paper a synthesis of a control law for a large scale stochastic system is presented. The system composed of coupled linear subsystems and quadratic performance index which should be minimized, is considered. The problem is solved in a two-level hierarchical control structure wtih a coordinator on an upper level and local controllers on a lower level. An algorithm, in which it is possible to partially decompose calculations and to realize decentralized control, is proposed. a simple example is presented.

4

Errors of elementary floating-point operations in control algorithms

Świder Z.

Archives of Control Sciences

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2003

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Vol. 13, no. 4

505-526

EN

The paper presents analytical development of erroe variances for elementary floatinf-point operations, i.e. quantization, multiplication, and additin, based on expressions for probability density distributions. Guassian inputs are assumed and steps executed by the processor taken into account, particularly normalization of the mantissa to interval [1/2, 1). Uniform estimate (...) of the variance for the three elementary operations is obtained, where b denotes the number of mantissa bits. Error of Euler rectangular integrator (...), commonly used in digital controllers, is evaluated as well. For small sampling step the error depends primarily on precision of the addition executed by the integrator. Increase of the precision used in some small controllers is also considered. The results are verified for first-order transfer function subject to white noise, sinusoidal and constant-plus-noise inputs.

5

The asymptotic stochastic stabilityin large of finite interconnected systems

Dronka J., Rybarska-Rusinek L.

Demonstratio Mathematica

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2002

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Vol. 35, nr 4

915-925

EN

The sufficient conditions of asymptotic string stability in large of some finite composite stochastic systems are established. Nonlinear systems are considered with random noise which obeys the law of large numbers. The objective is to analyze composite systems in their lower order subsystems and in term of their interconnecting structure.

6

A comparison of statistical and equivalent linearization for stochastic dynamic systems

Socha L.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

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2001

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z. 15

323-328

EN

The objective of this paper is to show differences between statistical and equivalent linearization on an example of a nonlinear oscillator under Gaussian white noise external excitations and to establish assumptions under what conditions the both linearization techniques are the same. Two types of equivalency criteria are considered, namely mean-square criterion with Gaussian closure and square metric in probability density functions space.

PL

Celem niniejszego artykułu jest pokazanie różnic między statystyczną i równoważną linearyzacją na przykładzie oscylatora nieliniowego oraz ustalenie założeń, przy których obie metody są identyczne. Rozpatrywane będą dwa typy kryteriów: kryterium średnio-kwadratowe z Gaussowską techniką zamykania oraz kryterium kwadratowe w przestrzeni funkcji gęstości prawdopodobieństw.