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

A fractional-order permanent magnet synchronous motor (PMSM) model is proposed and analyzed by phase portraits, bifurcation diagrams, Lyapunov exponents and Poincaré maps in this paper. Numerical simulations show that the proposed PMSM model with fractional integral of order α∈[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.