Dynamical Analysis of Fractional-order Permanent Magnet Synchronous Motor Based on Current Time-delayed Feedback

Abstract This paper investigates the nonlinear dynamics of a fractional-order PMSM depends on current time-delayed feedback. Firstly, model parameters of fractional- order PMSM are selected to display bifurcation and chaos in the case of no feedback. Secondly, the stability of equilibrium points and emergence of Hopf bifurcation in the system with feedback gain and time delay are derived. It is found that a smaller fractional-order can enhance the stability of fractional-order PMSM if all parameters are fixed in some cases. In addition, the research indicates that time delay can vary the stability interval, the properties of stability and Hopf bifurcation show chaos vanishes as the time delay reaches a certain value. Finally, numerical simulations are provided to illustrate the theoretical results and demonstrate the complex dynamic behaviors.