Researchers from the Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, together with collaborators at the University of Chinese Academy of Sciences and NIMTE, reported a robust speed-control strategy for permanent magnet synchronous motors (PMSMs) in IEEE Transactions on Power Electronics. The paper introduced a new sliding-mode reaching law (NSMRL) and a variable-parameter generalized super-twisting observer (VGSTO), forming an improved sliding-mode controller (ISMC) that enhanced transient response and disturbance rejection while suppressing chattering.

PMSMs are widely used in robots, CNC tools, and other precision systems, but their multivariable, strongly nonlinear behavior complicates speed regulation when parameters drift or loads fluctuate. Classical PI control often falls short under such uncertainty, prompting interest in modern approaches such as sliding-mode control (SMC) and extended-state-observer designs. The study positioned SMC as a promising foundation—owing to its robustness to modeling errors—while noting two persistent drawbacks in practice: slow convergence during the “reaching” phase and high-frequency chattering that degrades response and efficiency.

To address these issues, the team designed a controller around two technical ideas. First, the new reaching law embedded a terminal attractor into the exponential reaching formulation and coupled it with an adaptive gain. This structure accelerated convergence far from the sliding surface, then smoothly reduced gain near the surface to avoid exciting chatter—achieving finite-time convergence and continuity in the switching neighborhood. Second, the speed loop used an integral sliding-mode surface, which transferred discontinuities to an internal dynamic and allowed the external control path to remain continuous, further mitigating chattering while preserving rapid approach to the desired state.

Disturbance observation posed a separate challenge. Conventional extended state observers cannot simply raise bandwidth because stiffness and high-frequency noise limit stability and accuracy. The authors therefore proposed the VGSTO, which added linear and “extra” terms from super-twisting theory and introduced variable parameters that adapted to operating conditions. This observer maintained fast convergence without an excessively large bandwidth and reduced steady-state and dynamic estimation errors for the lumped disturbance entering the speed dynamics. The disturbance estimate was then fed forward in the control law, enabling the controller to react promptly to torque changes without resorting to large switching gains.

The research process followed a clear sequence. The team formulated the PMSM model under d–q coordinates and defined the speed-error state and its integral for the sliding surface. They derived the NSMRL, proved its faster-than-exponential reaching time, and showed finite-time properties using Lyapunov arguments. They then constructed the ISMC law, combined it with the VGSTO for disturbance estimation, and analyzed closed-loop stability with a Lyapunov criterion. Finally, they implemented the strategy on a 2.2-kW surface-mounted PMSM testbed with unified current-loop settings to ensure fair comparison across controllers. Throughout, experiments were designed to compare transient response, steady-state chattering, variable-speed tracking, and load-disturbance rejection.

Results indicated consistent advantages for the proposed strategy. Under step speed commands, the NSMRL-based controller reached target speeds faster than PI, conventional SMC, and a nonlinear exponential-term SMC baseline. In steady operation, phase-current quality improved and chattering amplitudes were markedly lower than all comparators. During variable-speed tracking, the controller maintained rapid response without overshoot. For disturbance rejection, the VGSTO reduced speed fluctuation peaks and shortened adjustment time compared with a standard ESO and a generalized super-twisting observer without variable parameters; under both light and heavy load changes, its observation errors were the smallest of the three. Across tests with changing set speeds, the VGSTO also exhibited the lowest dynamic estimation error, supporting its role in stabilizing the RSCS (ISMC+VGSTO) speed loop.

Taken together, the study showed that carefully balancing convergence speed, continuity near the sliding surface, and disturbance observation bandwidth can unlock higher PMSM speed-control performance without aggressive switching gains. The NSMRL improved the dynamics of the reaching phase, the integral sliding-mode surface reduced observable chattering, and the VGSTO provided accurate disturbance estimates at moderate bandwidth. This combination yielded fast transients and strong immunity to parameter drift and load torque variations—qualities that are valuable for factory automation, high-precision mechanisms, and mobile platforms where reliability and efficiency are paramount.