Disturbance-Derivative-Driven Gain Scheduling for Adaptive Super-Twisting Sliding Mode Control of PMSM

This paper addresses a specific dynamic limitation in conventional adaptive super-twisting sliding mode control (ASTSMC) for permanent-magnet synchronous motor (PMSM) speed regulation: the reactive lag of gain adaptation. In standard ASTSMC, controller gains are adjusted based solely on the sliding variable, which grows only after a disturbance has already induced a tracking error. This reactive behavior may produce a non-negligible transient speed droop during abrupt load variations. To alleviate this limitation, a proactive gain-scheduled ASTSMC (PDG-ASTSMC) strategy is proposed. A second-order nonlinear extended state observer (NESO) is employed to estimate the lumped disturbance and to extract its time derivative ${\dot{\widehat{d}}}_l$. This disturbance-derivative signal is incorporated into the gain adaptation law to increase the controller gains during the incipient phase of a load change, before significant speed error accumulates. Stability analysis based on a composite Lyapunov function establishes uniformly ultimately bounded convergence of the closed-loop system, and a quantitative relationship between the proactive index and transient droop reduction is derived. Experimental validation on a 1.42 kW PMSM platform shows that, compared with conventional reactive ASTSMC, the proposed PDG-ASTSMC reduces transient speed droop by over 17% (from 10.5 rpm to 8.7 rpm) and shortens load recovery time by approximately 69% (from 140 ms to 44 ms), without increasing steady-state chattering or current ripple.