I. Introduction
The double-sided linear synchronous motor comprises two primary elements and one secondary element (or one primary component and two secondary components). It is widely utilized in various transportation applications [1], [2], [3], [4]. Nevertheless, the motor’s primary, characterized by finite length and slots, introduces detent force and thrust fluctuations [5], [6], resulting in vibrations and noise. This, in turn, has a detrimental impact on the control precision and the overall reliability of transportation systems.