Fixed-Time Backstepping RLC of PMSMs

In this paper, a fixed-time backstepping repetitive learning control approach is proposed for PMSMs. A simple nonsingular fixed-time virtual controller is constructed to directly avoid the singularity caused by the differentiation of the virtual controller. In order to achieve the high precision steady-state tracking performance, the nonparametric uncertainty of the motor is separated into periodic and non-periodic parts, and a fully saturated repetitive learning law is constructed to accurately estimate and compensate for the periodic uncertainty. With the proposed control scheme, the fixed-time error convergence in the transient process and high precision tracking performance in the steady-state process can be both guaranteed simultaneously. The validity of the control method we proposed have been verified by simulation results.