Through introducing the concept of complex current and resetting cross-coupling term, this paper proposes a novel complex permanent magnet synchronous motor system and analyzes its properties. Based on a complex permanent magnet synchronous motor system, we design controllers and achieve lag synchronizations both in real part and imaginary part with backstepping method. In our study, we take complex current, time delay, and structure of complex system into consideration. Numerical simulation results demonstrate the validity of controllers.
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