Nonlinear dynamic analysis and modeling of fractional permanent magnet synchronous motors

Abstract

This paper is a step forward to generalize the fundamentals of the relationship between fractional-order system modeling and integer order system modeling. First, we establish a fractional-order mathematical modeling of permanent magnet synchronous motor from the view of engineering applications. Obviously, the effect of fractional order is the key factor for extra freedom, more flexibility and novelty. As a pioneering work, we analyze the effect of fractional order on the bifurcation point, and give its basic law, which is a fundamental work to optimize the use of the previous integer-order research results, and a bridge between fractional-order system and integer order system. Furthermore, we discuss the beginning point and ending point of chaos and the size of the attractors with varying fractional-order, respectively. In addition, nonlinear dynamics analyses of the presented fractional order system are also given. Finally, numerical simulations are given which match the analytical discussion.