Practical Prescribed-Time Super-Twisting Sliding Mode Control of PMSM Drives via Generalized Lyapunov Stability Theory

Abstract

Fast transient response with a prescribed convergence time is essential for high-performance permanent magnet synchronous motor (PMSM) drives. Existing finite-gain prescribed-time (PT) results mainly use smooth Lyapunov analysis and cannot directly cover the non-smooth dynamics of super-twisting sliding mode (STSM) control. This paper develops a time-regularized practical PT stability framework using generalized derivatives for Filippov differential inclusions. A deterministic time-triggered regularization keeps the control gain bounded, while the framework guarantees semi-global convergence to a residual set within the prescribed time. Based on this result, an observer-free PT-STSM controller is designed for PMSM speed regulation. Unlike PT sliding mode control methods using discontinuous switching, the proposed controller generates a continuous control signal. Unlike conventional STSM, its convergence bound is independent of initial conditions. Experiments show that, compared with conventional STSM, the proposed method reduces overshoot by 34.9% and 26.0% at 900 and 1600 rpm, respectively, shortens the step-load recovery time by 39.7%, and reduces speed fluctuation under sinusoidal loading by 28.9%. Note to Practitioners—This work is motivated by the stringent timing and precision requirements in modern automated systems, such as high-speed robotic manipulators, autonomous vehicles, and precision machines driven by PMSMs. In these applications, fast transient response and strict temporal determinism are critical for multi-axis coordination and task scheduling. Traditional PT control methods guarantee exact convergence but often suffer from infinite-gain singularities and severe chattering, making them unsafe or difficult to implement in physical digital drives. Meanwhile, conventional STSM algorithms struggle to pre-specify exact settling times independent of initial conditions. To overcome these bottlenecks, this paper proposes a practical PT-STSM controller. By intrinsically bounding the control gain and eliminating the need for complex auxiliary disturbance observers, it generates a safe, chattering-free continuous control signal. Experimental results on a DSP-based PMSM platform show that the proposed method is effective in practical scenarios requiring fast and precise convergence.