Nonlinear behavior for periodically excited brushless motor

Abstract

PurposeDue 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/approachA 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.FindingsThe 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/valueThis 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.