Dynamic analysis and bursting oscillation control of fractional-order permanent magnet synchronous motor system

Abstract

In fractional-order permanent magnet synchronous motor (FPMSM) systems, hidden bursting oscillation behaviors are found and a bursting oscillation suppression method is proposed for the first time. First, a FPMSM system model with the mismatched external load disturbance is established, and an auxiliary parameter is introduced to ensure that it have the correct time dimensionality. Second, when there is an order gap difference between the frequency of the external load disturbance and the natural frequency of the FPMSM system, it is found that the system undergo bursting oscillation behavior through bifurcation analysis and numerical simulations, and the evolution mechanism of the bursting oscillations is revealed by the fast-slow dynamics analysis method. Based on immersion and invariance (I&I) theory and fractional calculus theory, an adaptive backstepping super-twisting sliding mode control method with fractional I&I observer (I&I ABSSMC) is proposed to maintain the stable operation of the FPMSM system. The effectiveness of the I&I observer is verified by comparing with the adaptive method and disturbance observer under different forms of disturbances. Finally, comparisons of the I&I ABSSMC and other related methods show that the angular velocity tracking error accuracy and response speed of the I&I ABSSMC are superior. The proposed control method is easy to implement in practical applications.