Nonlinear Dynamic Analysis of Fractional-Order Permanent Magnet Synchronous Motor

This paper aims to study the nonlinear dynamic behavior of fractional-order PMSM systems and the subordination between integer-order and fractional-order systems. Firstly, the fractional-order PMSM model is established, and the fractional-order calculus numerical calculation method is used to draw the bifurcation diagram of the system as order changes. Combined with the time response curves and phase diagrams of the models in different states, the nonlinear dynamic characteristics of the same and different order systems are analyzed. Next, by observing the non-linear dynamic behavior with the increase of order under the same conditions, the subordination relationship between integerorder and fractional-order is analyzed. Studies have shown that the operation of PMSM undergoes changes in equilibrium, periodic and chaotic states as the order of the system changes. At the same time, fractional-order system is a total set including the integer-order, and the dynamic characteristics of the system change due to the effect of order.