Robust Adaptive Learning Rate Neural Network State Observer based Fixed-Time Sliding Mode Control of a Permanent Magnet Synchronous Motor

This article proposes a robust controller based on fixed-time sliding mode control (FxTSMC) and a neural network to improve the speed tracking control performance of a permanent magnet synchronous motor (PMSM) under uncertainties and disturbances. First, a new reaching law is introduced, which offers a faster fixed-time convergence rate compared to existing methods. Second, to address the effects of parameter uncertainty and unknown disturbances, an adaptive learning rate neural network (NN) based on a fixed-time state observer (ALRNN-FxTSO) is designed to accurately estimate and compensate for these adverse factors. This ensures that the estimation error converges into a small predefined domain within a fixed time and is independent of the initial state. Furthermore, prior knowledge of the lumped disturbance is not required. By using the state estimation error, the learning rate and weights of the NN can be updated according to system dynamics, improving the capabilities of the ALRNN-FxTSO. Based on the proposed FxTSMC and ALRNN-FxTSO, a robust controller is developed to guarantee that tracking performance converges to a small neighborhood of the origin within a fixed time. The reaching time is not dependent on the initial state. The system stability is proven theoretically via Lyapunov analysis with fixed-time convergence. Finally, simulations and experiments are implemented on a PMSM system to demonstrate the practical effectiveness of the proposed method.