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1

Robust H[infinity] output feedback control for constrained discretetime piecewise affine systems with time-parametric uncertainties

Wang J.

Przegląd Elektrotechniczny

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2012

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R. 88, nr 3b

84-87

EN

In this study, a novel robust H[infinity] output feedback control scheme is presented for discrete-time piecewise affine (PWA) systems in the presence of time-varying uncertainties, external disturbance and time-domain constraints. The suggested control method is formulated as linear matrix inequalities (LMIs). The basic idea of them is to construct piecewise quadratic Lyapunov function and introduce a dissipation inequality to guarantee the system energy dissipation. The designed controllers not only guarantee the stability of the closed-loop systems, but also obtain the disturbance attenuation ability.

PL

Zaprezentowano nowy odporny układ sterowania ze sprzężeniem typu H[nieskończoność] do systemów PWA. Uwzględniono obecność zmiennych w czasie niepewności, zewnętrznych zakłóceń i czasowo zależnych wymuszeń.

2

Two steps piecewise affine identification of nonlinear systems

Stevek J., Szucs A., Kvasnica M., Fikar M., Kozak S.

Archives of Control Sciences

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2012

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Vol. 22, no. 4

371-388

EN

Given a set of input-output measurements, the paper proposes a method for approximation of a nonlinear system by a piecewise affine model (PWA). First step of the two-stage procedure is identification from input-output data, in order to obtain an appropriate nonlinear function in analytic form. The analytic expression of the model can be represented either by a static nonlinear function or by a dynamic system and can be obtained using a basis function expansion modeling approach. Subsequently we employ nonlinear programming to derive optimal PWA approximation of the identified model such that the approximation error is minimized. Moreover, we show that approximation of multivariate systems can be transformed into a series of one-dimensional approximations, which can be solved efficiently using standard optimization techniques.

3

Stability Analysis of a Patched LQR Control System for Constrained Multi-Mass Electrical Drives

Vašak M., Petrić N.

Przegląd Elektrotechniczny

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2009

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R. 85, nr 7

109-114

EN

In this paper we analyze a recently introduced protective predictive controller patch for motor drives with elastic transmission that are subject to physical and safety constraints on their variables. The protective patch is obtained using invariant sets methodology and is used in combination with the classical LQR controller. The easy implementation of the patch on-line allows the correction of the LQR control signal in order to suppress the violation of constraints in the future and thus avoid possibly dangerous and/or drive-harmful situations during the transients. Since LQR controller itself in the absence of constraints guarantees stability of the control system, we show how the stability of the constrained control system with a controller composed of the combination of LQR and the protective patch may be confirmed.

PL

W artykule autorzy analizują nową koncepcję regulatora predykcyjnego dla napędu elektrycznego z połączeniem sprężystym. Opisywane rozwiązanie bazuje na połączeniu metody teorii zbiórow przyciągania z klasycznym regulatorem LQR. Umożliwia ono ograniczenie wartości chwilowych zmiennych stanu i sterowania. Rozwiązanie to, łatwe w implementacji, zapewnia stabilną pracę napędu w stanach przejściowych, a tym samym, zabezpiecza przed mechanicznym, trwałym uszkodzeniem połączenia silnika z obciążeniem. Autorzy szczegółowo opisali nowe rozwiązanie w formie analitycznej, porównując pracę układów z regulatorem klasycznym i zmodyfikowanym.