Nonlinear behavior for periodically excited brushless motor

Abstract

Purpose Due to the coupling between the direct-axis current, quadrature-axis current and rotor speed, the dynamic response could be strongly nonlinear. Besides, if the working condition is severe, the loading is no longer constant and multiple harmonics could be introduced. In this paper, the periodic motions for brushless motor will be solved, and accurate analytic solution will be obtained through the proposed method. The purpose of this study is to provide accurate analytic solution of periodic motions for brushless motor with fluctuated loading, which is a dynamic system with strong nonlinearity. Design/methodology/approach A newly developed semi-analytic algorithm called discrete implicit maps is used to give analytic solutions for both stable and unstable motions for such a motor. Findings The accurate analytic expressions for stable and unstable periodic motions have been obtained. For unstable motion, it can stay on the unstable orbit for many periods without any controller. Through bifurcation analysis, the parameter sensitivity has been obtained which can be a suggestion for design and operation. Originality/value This paper provides all possible analytical solutions for period-1 motion as well as the unstable motions in a range of system parameters. It offers a chance to control the unstable motion for such a motor.

Period-1 Motions and Bifurcations of a 3D Brushless DC Motor System with Voltage Disturbance

“…The frequency-amplitude characteristics of periodic motions were analyzed. Huang et al [21,22] analyzed the same brushless DC motor model using a discrete mapping method and obtained semi-analytical periodic currents and voltages. The stability and bifurcations of the semi-analytical currents and voltages were analyzed through the eigenvalues.…”

Analytical Bifurcation Tree of Period-1 to Period-4 Motions in a 3-D Brushless DC Motor With Voltage Disturbance

“…In 2017, Fasil et al [11] proposed a nonlinear phase variable model to simulate a permanent magnet brushless DC motor. In 2018, Huang and Xiong [12] applied a discrete mapping method to periodically excited brushless DC motor. Analytical expression in terms of finite Fourier series terms is obtained based on semi analytical results.…”