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Methods of controller synthesis using linear matrix inequalities and model predictive control

Miller A., Rybczak M.

Zeszyty Naukowe Akademii Morskiej w Szczecinie

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2015

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nr 43 (115)

22--28

EN

Controllers based on linear matrix inequalities (LMI) and model predictive control (MPC) both use optimization methods; there are however significant differences between them. In case of LMI controllers, optimization is carried out during controller synthesis, because LMI’s are an optimization tool that requires a linear programming problem being solved. With MPC controllers, however, optimization methods are not used as much in controller synthesis as in controller algorithm operation, to determine optimal control signal values based on the found minimum of the criteria function. A square function is used with boundaries from above and below, which requires a square programming problem, with boundaries for decision variables, being solved. In this paper controller synthesis methods using LMI and MPC are shown, with a focus on the steps that need to be performed, and a comparison of both methods.

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On the Controller Synthesis for Finite-State Markov Decision Processes

Kučera A., Strazovský O.

Fundamenta Informaticae

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2008

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Vol. 82, nr 1-2

141-153

EN

We study the problem of effective controller synthesis for finite-state Markov decision processes (MDPs) and the class of properties definable in the logic PCTL extended with long-run average propositions. We show that the existence of such a controller is decidable, and we give an algorithm which computes the controller if it exists. We also address the issue of "controller robustness", i.e., the problem whether there is a controller which still guarantees the satisfaction of a given property when the probabilities in the considered MDP slightly deviate from their original values. From a practical point of view, this is an important aspect since the probabilities are often determined empirically and hence they are inherently imprecise. We show that the existence of robust controllers is also decidable, and that such controllers are effectively computable if they exist.

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Linear controller synthesis by a use of a "quasi" non-integer continuous-time integrator

Ostalczyk P., Kacerka J., Rybicki T.

Zeszyty Naukowe. Elektryka / Politechnika Łódzka

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2005

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z. 106

65-86

PL

W prezentowanej pracy rozważa się możliwości wykorzystania charakterystyk częstotliwościowych "fikcyjnych" elementów całkujących niecałkowitych rzędów do projektowania zamkniętych układów regulacji odpornych na zmiany parametrów obiektu regulacji. Sformułowanie "fikcyjny" odnosi się do rozerwania charakterystycznych związków pomiędzy stałą fazą elementów całkujących niecałkowitych rzędów i ich amplitudami. Zaproponowane elementy, spełniające tylko graniczne warunki określone wzorem (4) przedstawiają ciekawe związki pomiędzy charakterystykami częstotliwościowymi i odpowiedziami skokowymi. Badanie tego typu elementów i ich związków z odpowiedziami w układach zamkniętych pozwala określić wzorce zachowań układów realizowalnych fizycznie opisanych typowymi transmitancjami.

EN

In this paper a physically realizable linear controller approximating a continuous-time "quasi" non-integer integrator is presented. Such integrator is characterised by a constant phase angle over the whole frequency range and any magnitude characteristic satisfying only two boundary conditions. It is known that unity-feedback systems with such "quasi" integrators Nyquist characteristics are only functions of an integration order n [7]. A DC motor drive with a flexible arm and proposed controller is robust due to some transient characteristics parameters. A numerical example is presented.