In this paper, observer-based command filtered adaptive neural network tracking control problem is addressed for fractional-order chaotic permanent magnet synchronous motor (PMSM) with immeasurable state, parameter uncertainties and external load disturbance. First, Chebyshev neural networks are introduced to approximate the nonlinear and unknown functions. Next, a neural network reduced-order state observer is designed to obtain the unmeasured state. Then, the command filtering approach based on first-order Levant differentiator is developed to solve the “explosion of complexity” issue of backstepping, and a novel fractional-order error compensation mechanism is employed, which can remove the filtering errors in finite-time. After that, the continuous frequency distributed model is investigated to design proper Lyapunov function, it is demonstrated that the proposed control method not only ensures all signals in the fractional-order PMSM system are bounded, but also suppresses chaotic oscillation. Finally, simulation studies are provided to verify the correctness and effectiveness of the proposed scheme.

The automatic train operation (ATO) system of urban rail trains includes a two-layer control structure: upper-layer control and lower-layer control. The upper-layer control is to optimize the target speed curve of ATO, and the lower-layer control is the tracking by the urban rail train of the optimal target speed curve generated by the upper-layer control according to the tracking control strategy of ATO. For upper-layer control, the multi-objective model of urban rail train operation is firstly built with energy consumption, comfort, stopping accuracy, and punctuality as optimization indexes, and the entropy weight method is adopted to solve the weight coefficient of each index. Then, genetic algorithm (GA) is used to optimize the model to obtain an optimal target speed curve. In addition, an improved genetic algorithm (IGA) based on directional mutation and gene modification is proposed to improve the convergence speed and optimization effect of the algorithm. The stopping and speed constraints are added into the fitness function in the form of penalty function. For the lower-layer control, the predictive speed controller is designed according to the predictive control principle to track the target speed curve accurately. Since the inflection point area of the target speed curve is difficult to track, the softness factor in the predictive model needs to be adjusted online to improve the control accuracy of the speed. For this paper, we mainly improve the optimization and control algorithms in the upper and lower level controls of ATO. The results show that the speed controller based on predictive control algorithm has better control effect than that based on the PID control algorithm, which can meet the requirements of various performance indexes. Thus, the feasibility of predictive control algorithm in an ATO system is also verified.

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.