Dynamic Analysis of the Chaotic Fractional-order Synchronous Reluctance Motor System

A fractional-order system of reluctance synchronous motor is proposed in this paper. By considering equilibrium points and eigenvalues, the chaotic state of double scrolls under a specific set of parameters is verified by combining the dynamic theory of Lyapunov exponents and bifurcation diagrams. The theories are used to study the influence of the viscous friction coefficient on the system, and the parameters range of the system working in the chaotic state are obtained. Through bifurcation diagrams of the system varying with fractional-order and phase diagrams under different fractional orders, the influence of fractional-order on the system is verified by numerical simulation.