Adaptive neural network control for fractional-order PMSM with time delay based on command filtered backstepping

In this paper, an adaptive neural network (NN) control based on command filtered backstepping approach is presented for fractional-order permanent magnet synchronous motor (PMSM) with parameter uncertainties and unknown time delays. For the convenience of controller design, the state trajectories and phase portrait of the system are investigated to analyze the dynamics of the fractional-order PMSM. The unknown parameters and load torque disturbance in the system dynamics are approximated by using NNs, and the number of adaptive laws for the weight vector is curtailed to just one. To ensure orderly decay of the desired error trajectory, a model reference technique is also introduced to backstepping approach. The command filter technique, which can solve the “explosion of complexity” issue of backstepping, is extended to fractional-order nonlinear systems, and the error compensation mechanism is designed to overcome the shortcoming of the classical dynamics surface filter. The effects of time delays uncertainties are suppressed by employing proper Lyapunov-Krasovskii functions. From the Lyapunov stability theory, the design of the controller ensures all signals in the fractional-order PMSM system remain bounded, while the output error converges to a small region of the origin. Numerical simulations are given to show the correctness and effectiveness of the new design technique.