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Considering the variations of inertia in real applications, an adaptive control scheme for the permanent-magnet synchronous motor speed-regulation system is proposed in this paper. First, a composite control method, i.e., the extended-state-observer (ESO)-based control method, is employed to ensure the performance of the closed-loop system. The ESO can estimate both the states and the disturbances simultaneously so that the composite speed controller can have a corresponding part to compensate for the disturbances. Then, considering the case of variations of load inertia, an adaptive control scheme is developed by analyzing the control performance relationship between the feedforward compensation gain and the system inertia. By using inertia identification techniques, a fuzzy-inferencer-based supervisor is designed to automatically tune the feedforward compensation gain according to the identified inertia. Simulation and experimental results both show that the proposed method achieves a better speed response in the presence of inertia variations.