This paper focuses on an adaptive dynamic surface control based on the Radial Basis Function Neural Network for a fourth-order permanent magnet synchronous motor system wherein the unknown parameters, disturbances, chaos, and uncertain time delays are presented. Neural Network systems are used to approximate the nonlinearities and an adaptive law is employed to estimate accurate parameters. Then, a simple and effective controller has been obtained by introducing dynamic surface control technique on the basis of first-order filters. Asymptotically tracking stability in the sense of uniformly ultimate boundedness is achieved in a short time. Finally, the performance of the proposed control has been illustrated through simulation results. 1. Introduction Recently, the permanent magnet synchronous motor (PMSM) is the most widely used driven mechanism because of the advantageous merits of cost, reliability, and performances. The PMSM is characterized by complexity, high nonlinearity, time-varying dynamics, inaccessibility of some states, and output for measurements; hence, it can be considered as a challenging engineering problem [1, 2]. It is found that the PMSM is experiencing chaotic behavior at specific parameters and working conditions [3, 4]. Then, the intermittent oscillation of torque and rotational speed, irregular current noise of the system, and unstable control performance appear in the PMSM, which seriously affect the stability and safety. Thus, it is difficult to accomplish the high-performance control of PMSM by using classic PID-type control methods. A neuron-fuzzy controller (NFC) [5] is suitable for control of systems with uncertainties and nonlinearities. The NFC approach can also achieve self-learning; however, it is unsuitable for online learning real-time control due to the drawback of time consuming [6, 7]. The sliding mode control (SMC) [8] can guarantee the robustness only under the bounds of the uncertainties and it has a shortage named chattering. The terminal sliding mode control (TSMC) method can assure convergence to the origin in finite time. Hence, the TSMC is successfully applied to PMSM driver system to improve control performance [9]. A position tracking control method via adaptive fuzzy backstepping is presented for the induction motors with unknown parameters [10]. Unfortunately, the traditional backstepping suffers from the “explosion of complexity” caused by the repeated differentiation of virtual control functions [11]. In order to overcome the above shortcomings, a backstepping approach combined with SMC technique is
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