## 1 Introduction
A noncascade structure speed tracking controller based on improved disturbance observer is proposed in [19], which is used to deal with multiple disturbances and improve tracking performance. A novel disturbance suppression framework based on a noncascaded structure is proposed in [20] to deal with typical disturbances common in industrial applications. Generally, under the condition of accurate modeling, this kind of model-based control strategy has a wide range of applications. Moreover, some data-driven neural network control strategies can also be applied to suppress interference. Through machine learning, arbitrary nonlinear mapping is approximated by input-output data [21]. This control method has been successfully applied to robots [22], permanent magnet synchronous motor motion control [23] and so on. As in [24], an adaptive fuzzy fractional-order sliding mode control strategy is designed to control the motion position of a permanent magnet linear synchronous motor system. For a two-axis motion control system, a robust fuzzy neural network sliding mode control method based on computational torque control design is proposed in [25]. These studies confirm that the neural networks' nonlinear approximation capacity can enhance the controlling ability [26]. In conclusion, the anti-interference ability of adaptive robust control can be further improved. Recently, there have been some achievements that combine adaptive robust control with the neural network method. The external disturbances further complicate the control process that must be addressed. The authors present the computed torque control (CTC) scheme compensated by a radial basis function neural network (RBFNN) in [27]. In [28], the authors propose a novel hybrid metaheuristic technique based on a nonsingular terminal sliding mode controller, a time-delay estimation method, an extended grey wolf optimization algorithm and an adaptive super-twisting control law. However, there are some defects: In general, the selection of the activation function of a neural network should establish an adequate comprehension of the existing model, making the controller's design very tough. Secondly, the activating feature established on the already-known dynamic model will impair the approximation ability with respect to the unknown state nonlinearity. Thirdly, the multilayer neural network used in the existing neural network adaptive robust control can theoretically achieve the global optimization approximation, but it ignores the accuracy of detail approximation, which may be against disturbance suppression. Lastly, the neural network control methods need to be based on the huge number of neurons, and the corresponding calculation will inevitably increase geometrically. In recent years, a multidimensional Taylor network control method has been proposed, which benefits from the fixed structure and the convenience of parameter adjustment, and has achieved many good application results. As in [29], for a class of nonlinear systems with unknown output dead zones, an adaptive multidimensional Taylor network control method is proposed. An output feedback control strategy based on MTN is proposed to control nonlinear systems with input saturation constraints in [30]. However, these control methods require a multidimensional Taylor network to take into account the requirements of stability, speed and error, and the internal parameter adjustment inevitably has a competitive relationship. In [31] and [32], the authors focus on the role of a multidimensional Taylor network for stochastic nonlinear systems, and in order to make the theory more rigorous, more stringent assumptions are usually required. In order to design a motion controller for a linear motor with both parameter adaptation and disturbance rejection, an adaptive robust control strategy based on a multidimensional Taylor network is proposed in this paper.