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Warianty tytułu
Języki publikacji
Abstrakty
The paper presents a new method applicable in determining the settings of PI and PID controllers for models of controlled systems given by the following transfer functions [wzór] and [wzór]. Using the capabilities of computer operations with symbolic variables, the closed system transfer function is expanded into a chain-type fraction, type V (Bultheel, 1978; Khovanskii, 1956; Halawa and Trzmielak-Stanislawska, 1986; Wall, 1973) and the second order convergent method is used as a simplified model. Denominator of this convergent M(s), is the following polynomial [wzór] with coefficients being the functions of controlled system parameters and unknown controller settings. Diagrams of step responses for systems given by second-order transfer functions are well known. Assuming the values of [wzór] and [wzór], we get a set of non-linear equations used to determine controller settings. The set of equations has been determined and resolved by means of Mathematica language which allows calculations with symbolic variables.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
1075--1091
Opis fizyczny
Bibliogr. 16 poz., wykr.
Twórcy
autor
- Wroclaw University of Technology, Institute of Technical Cybernetics, Janiszewskiego 11-17, 50-372 Wroclaw, Poland
Bibliografia
- Baker, G.A. and Graves-Morris, P. (1981) Pade’Approximants. Addison-Wesley Publishing.
- Bultheel, A. (1978) Division algorithms for continued fractions and Pade’table. Report TW 41, August, Applied Mathematics and Programming Division, Katholieke Universitet Leuven (Belgium).
- Chu, S.Y. and Teng, C.C. (1999) Tuning of PID controllers Based on Gain and Phase Margin Specifications Using Fuzzy Neutral Network. Fuzzy Sets and Systems 101, 21-30.
- Danilow, W.C., Iwanowa, A.N. and Isakowa, I.K.I. (1970) Funkcje, granice, szeregi, ułamki łańcuchowe. PWN, Warszawa.
- Halawa, J. (1989) Determination of Simplified Transfer Functions by Means of the Moment Method. Transactions of the Society for Computer Simulation 6 (1), 17-29.
- Halawa, J. (1991) Metody wyznaczania transmitancji uproszczonych i ich zastosowanie w automatyce i elektroenergetyce. Prace Naukowe Instytutu Cybernetyki Technicznej Politechniki Wrocławskiej 88, Seria: Monografie 21, Wrocław.
- Halawa, J. (2002) Wyznaczanie parametrów regulatorów PI i PID metodą reduktorów za pomocą wspomagania komputerowego. Raport Instytutu Cybernetyki Technicznej Politechniki Wrocławskiej. Seria Reprinty, 1.
- Halawa, J. (2005) Dobór nastaw regulatorów dla obiektów bez wyrównania z inercją pierwszego rzędu. Kwartalnik Elektroniki i Telekomunikacji 1.
- Halawa, J. and Trzmielak-Stanisławska, A. (1986) Properties of Simplified Transfer Functions as Acquired with aMethod of Continued Fractions. Archiwum Automatyki i Telemechaniki XXXI, 1-2, 117-132.
- Ho, W.K., Lee, T.H., Han, H.P and Hong, Y. (2001) Self tuning IMC-PID control with interval gain and phase margins assignment. IEEE Trans. Contr. Syst. Technol. 9, 535-541.
- Ho, W.K., Lim, K.W., Hang, C.C. and Ni, L.Y. (1999) Getting more phase margin and performance out of PID controllers. Automation 35, 1579-1985.
- Khovanskii, A. (1956) Prilozheniye tsepnykh drobiei i ikh obobshcheniy k voprosam priblizhennogo analiza. Izdatelstvo Tekhnika – Teoreticheskoi Literatury, Moskva.
- Narendra, K.S. and Parthasarathy, K. (1990) Identification and Control of Dynamical Systems Using Neural Networks. IEEE Transaction on Neural Networks 1 (1), 8-26.
- Phama, S. and Singh, H. (1993) Single Layer Neutral Networks for Linear System Identification Using Gradient Descent Technique. IEEE Transactions on Neural Networks, 4 (5), 88-92.
- Wall, H.S. (1973) Analytic Theory of Continued Fractions. Chelsea Publ. Co.
- Zhung, M. and Atherton, D.P. (1993) Automatic tuning of optimum PID controllers. IEE Proc., Part D 140, 216-224.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0010-0016