Frequency domain modelling and control of fractional-order system for permanent magnet synchronous motor velocity servo system

This study presents fractional-order system modelling and control for a permanent magnet synchronous motor (PMSM) velocity servo system. Fractional-order model of the PMSM velocity servo system is obtained theoretically for an improved modelling precision. To identify the parameters of the proposed fractional-order model, an enhancement of the classic Levy identification method with weights is applied. In a real-time PMSM velocity servo plant, the fractional-order model is identified according to the experimental tests using the presented algorithm. The fact that the fractional model is more accurate than traditional integer-order model is substantiated using by the mean square error performance index. Two H ∞ stabilising output feedback controllers are designed for velocity servo using a simple scheme according to the identified fractional-order model and the traditional integer order one, respectively. The experimental test performance using these two designed H ∞ controllers is compared to demonstrate the advantage of the proposed fractional-order model of the PMSM velocity system.

[1]  Ivo Petras,et al.  A note on the fractional-order Chua’s system , 2008 .

[2]  Kim-Chuan Toh,et al.  SDPT3 -- A Matlab Software Package for Semidefinite Programming , 1996 .

[3]  Ying Luo,et al.  Authentic simulation studies of periodic adaptive learning compensation of cogging effect in PMSM position servo system , 2008, 2008 Chinese Control and Decision Conference.

[4]  Y. Chen,et al.  Fractional Order Motion Controls , 2012 .

[5]  Isabel S. Jesus,et al.  Development of fractional order capacitors based on electrolyte processes , 2009 .

[6]  Least-squares fitting of data by rational functions: Levy's method (Part 1) [By the Numbers] , 2009, IEEE Instrumentation & Measurement Magazine.

[7]  R. Bagley,et al.  On the Appearance of the Fractional Derivative in the Behavior of Real Materials , 1984 .

[8]  Y. Chen,et al.  Experimental study of fractional order proportional derivative controller synthesis for fractional order systems , 2011 .

[9]  Ying Luo,et al.  Fractional order modeling and control for permanent magnet synchronous motor velocity servo system , 2013 .

[10]  Christophe Farges,et al.  H∞ output feedback control of commensurate fractional order systems , 2013, 2013 European Control Conference (ECC).

[11]  Manuel Duarte Ortigueira,et al.  Identifying a Transfer Function From a Frequency Response , 2007 .

[12]  Tom T. Hartley,et al.  Fractional-order system identification based on continuous order-distributions , 2003, Signal Process..

[13]  Miroslav Krstic,et al.  Quantized-Input Control Lyapunov Approach for Permanent Magnet Synchronous Motor Drives , 2013, IEEE Transactions on Control Systems Technology.

[14]  Christophe Farges,et al.  H∞ analysis and control of commensurate fractional order systems , 2013 .

[15]  Simin Yu,et al.  Design and Circuit Implementation of fractional-Order Multiwing Chaotic attractors , 2012, Int. J. Bifurc. Chaos.

[16]  Roberto Kawakami Harrop Galvão,et al.  Fractional Order Modeling of Large Three-Dimensional RC Networks , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[17]  James Lam,et al.  State feedback H ∞ control of commensurate fractional-order systems , 2014, Int. J. Syst. Sci..

[18]  C. F. Lorenzo,et al.  Chaos in a fractional order Chua's system , 1995 .

[19]  José António Tenreiro Machado,et al.  Fractional Order Calculus: Basic Concepts and Engineering Applications , 2010 .

[20]  J. Lam,et al.  H∞ Model Reduction for Positive Fractional Order Systems , 2014 .

[21]  E. C. Levy.  Complex-curve fitting , 1959, IRE Transactions on Automatic Control.

[22]  Peter J. Gawthrop,et al.  Frequency-domain identification of the human controller , 2012, Biological Cybernetics.

[23]  Alessandro Astolfi,et al.  Estimation of Rotor Position and Speed of Permanent Magnet Synchronous Motors With Guaranteed Stability , 2011, IEEE Transactions on Control Systems Technology.

[24]  B. M. V. Jara.  Modelado y control de sistemas caracterizados por ecuaciones íntegro-diferenciales de orden fraccional , 2001 .