Finite-time sliding mode speed control using an adaptive three-stage reaching law for PMSM

To address the challenge of balancing finite-time convergence and chattering suppression in sliding mode control for permanent magnet synchronous motors, this paper proposes a composite control scheme based on an adaptive three-stage reaching law (ATSRL) and an enhanced super-twisting sliding mode observer (ESTSMO). First, according to the distinct characteristics of system state, the ATSRL incorporates a clamped exponential term, a state-dependent adaptive term, and a nonlinear power term. It adaptively adjusts the reaching speed by system state and reduces the switching gain near the sliding surface, enabling fast finite-time convergence while effectively suppressing chattering. Second, to mitigate the deterioration of control performance caused by inertia mismatch, an extended sliding mode observer is employed for offline identification of system inertia, and then the ESTSMO is devised to estimate lumped disturbance online as a feedforward compensation term, which is directly embedded into the ATSRL-based control law. Interestingly, the offline-then-online framework provides accurate offline inertia identification via the ESMO, which is incorporated into the ESTSMO to significantly reduce disturbance estimation bias caused by inertia mismatch. Finally, simulation and experimental results validate the advantages of the proposed scheme.