Abstract
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.
Highlights
The integral and derivative of arbitrary order, namely, fractional calculus, which can be considered as a generalization of classical integer-order calculus
We will present a model reference adaptive neural network (NN) control method based on command filtered backstepping approach for fractional-order permanent magnet synchronous motor (PMSM) with parameter uncertainties and unknown time delays
Compared with previous dynamic surface control (DSC) PMSM system designed in Ref. 26, some differences of our method are that we employ fractional-order command filter and design compensation mechanism to compensate the errors of filter. (26) and (33) show how the compensating mechanism works
Summary
The integral and derivative of arbitrary order, namely, fractional calculus, which can be considered as a generalization of classical integer-order calculus. For parameter uncertainties and load torque disturbance, Ref. 17 proposed adaptive NN method to guarantee the boundedness of all the signals in the PMSM system. In Ref. 20, a model reference adaptive control method is employed to track trajectory, which includes an adaptive compensating term and a feedback control term These studies mainly focus on integer-order system. For the PMSM system with parameter uncertainties and time delay, an adaptive SMC scheme based on DSC is presented in Ref. 26. Motivated by the aforementioned investigations, this work presents a novel control scheme for the fractional-order PMSM with parameter uncertainties and unknown time delays. 3) Integrating model reference, adaptive NN, command filter and backstepping technique into controllers in the domain of fractional-order, which suppresses chaotic oscillation, and guarantees the boundedness of all signals.
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