Second-Order Predefined-Time Terminal Sliding Mode Control for Speed Regulation System of Permanent Magnet Synchronous Motor

In this paper, a second-order predefined-time terminal sliding mode (SPTSM) is proposed, which is investigated for the practical applications of the speed regulation system of a permanent magnet synchronous motor (PMSM) by using predefined-time stability theory and Lyapunov stability theory. At first, we propose the SPTSM, which involves the controller’s design by using the novel reaching law with predefined-time terminal sliding mode (PTSM) and the novel sliding mode surface with PTSM. Second, we derive the novel SPTSM controller for the universal second-order nonlinear single-input single-output (SISO) system and the practical applications of the speed regulation system of the PMSM separately. Then, numerical simulation results of the speed regulation system of the PMSM are also included to check the effect of the theoretical results and the corresponding parameters on the convergence rates, so that the results can be guidance for the selection of SPTSM controller parameters. Finally, the dynamic responsiveness and robustness of the system are validated through numerical simulations and experimental results. It has been observed that the robust SPTSM controller, which is designed with the PTSM-PTSM, referring to the sliding mode that involves a reaching law with PTSM and a sliding mode surface with PTSM, exhibits superior performance.