Prescribed-Time Nonsingular Terminal Sliding Mode Control and Its Application in PMSM Servo Systems

This study investigates the design of prescribed-time nonsingular terminal sliding mode (TSM) control and its utilization in position tracking control of permanent magnet synchronous motors (PMSM) servo systems. First, we propose a novel continuously differentiable and bounded time-varying scaling function, which avoids the issues of infinite gain and singularity in differentiation. Building upon this newly proposed time-varying function, a new prescribed-time Lyapunov theorem is presented, providing a theoretical foundation for controller design and stability analysis. Subsequently, we introduce a unique time-varying nonsingular TSM manifold and controller equipped with bounded time-varying gains. A comprehensive Lyapunov analysis confirms that the time required to reach the sliding mode manifold and equilibrium point can be predetermined, independent of initial system conditions or other related control parameters. Finally, the superiority of our theoretical findings is validated through experimental comparisons with existing studies, demonstrating the advantages of prescribed-time convergence and enhanced accuracy in position tracking control of PMSM servo systems.