Chaotic behavior and circuit implementation of a fractional-order permanent magnet synchronous motor model

摘要

A fractional-order permanent magnet synchronous motor (PMSM) model is proposed and analyzed by phase portraits, bifurcation diagrams, Lyapunov exponents and Poincare maps in this paper. Numerical simulations show that the proposed PMSM model with fractional integral of order alpha is an element of [0.94, 1] is chaotic on the condition of great changes of parameter. Further, through a transfer function approximation of fractional-order operator, an experimental circuit composed of resistors, capacitors, operational amplifiers and analog multipliers is presented to realize the fractional-order PMSM model, and whose chaotic behavior is also recorded by a digital oscilloscope in experiment. (C) 2015 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.