Optymalizacja parametryczna regulatora niecałkowitego rzędu typu PD^alfa

pol Article in Polish DOI: 10.14313/PAR_218/5

send Marta Zagórowska AGH Akademia Górniczo-Hutnicza im. Stanisława Staszica, al. Mickiewicza 30, 30-059 Kraków

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Streszczenie

W artykule przeanalizowano zachowanie układu całkowitego rzędu ze sprzężeniem zwrotnym niecałkowitego rzędu. Przedstawiono nową metodę doboru optymalnych parametrów dla regulatorów typu PDα we wspomnianych układach z nieskończonym horyzontem. Zaprezentowano wykorzystaną metodę aproksymacji układów niecałkowitego rzędu z wykorzystaniem funkcji Laguerre’a oraz sformułowano problem w postaci zagadnienia minmax. Pokazano również przykładowy przebieg optymalizacji ze względu na parametry związane z typem aproksymacji.

Słowa kluczowe

funkcje Laguerre’a, optymalizacja, PD^alfa, sprzężenie zwrotne, sterowanie niecałkowitego rzędu, układ niecałkowitego rzędu

Parametric optimization of non-integer order controller PD^alfa

Abstract

In this paper we analysed the behaviour of an integer order system with non-integer control function. We presented a new method for tuning the non-integer order controllers PDa for use in systems with infinite horizon. An approximation method for non-integer order systems was presented (using Laguerre functions) along with the definition of the issue in form of minmax problem. Finally some examples were analysed with respect to parameters specific for this approximation.

Keywords

feedback, Laguerre functions, non-integer order systems, optimization, PD^alfa controller

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