## 1 Introduction  
A linear motor is widely used in industrial production because it can provide linear motion without mechanical conversion [1]. However, if we want to achieve excellent control accuracy in practical applications, there are indeed many difficulties [2]. The parameters of the model are not fixed, and the parameters are different under different motion conditions [3]. This difference in parameter changes will have a greater impact on the control accuracy, such as the change of moveer mass [4], and friction and ripple forces also have a direct impact on control performance [5]. In addition, exterior interferences with uncertainties and nonlinear unmodeled dynamics are also common in the linear motor systems, which have a negative impact on the control accuracy [6]. In order to deal with the above problems at the same time, the most common method is adaptive robust control [7]. Combining the adaptive control idea and robust control theory, adaptive robust control has the ability of parameter adaptive adjustment and robust characteristics to deal with uncertain disturbances. After a long period of development, its stability and logicality have been fully proved. Moreover, it has been verified in many specific practices, such as linear motor [8], pneumatic artificial muscle [9], hydraulic manipulator [10] and planar motor [11], etc. As in [12], an adaptive sliding mode robust tracking controller based on barrier function is designed to deal with the influence of payload uncertainty and external time-varying disturbance. Through the combination of adaptive technology and backstepping method based on command filter, a new adaptive tracking controller is designed to achieve asymptotic tracking, and the relevant stability is proved in [13]. In [14], by designing different control algorithms and aiming at the given reference signal, three stable adaptive tracking schemes are proposed to complete the tracking control problem for a class of uncertain multiple-input multiple-output nonlinear systems although there are time-varying parameters and time-varying disturbances in the system. The traditional adaptive robust control is designed on account of the well-known model. In addition, the uncertain parameters in the system dynamic equation can be estimated by system identification or nonlinear regression function [15]. However, when dealing with unknown disturbances, it is only replaced by the product of time-varying parameters and weights, which limits the practicability of adaptive robust control to a certain extent. Most of the existing adaptive robust control results are carried out under the condition of step disturbance, which cannot fully reflect the ability of antidisturbance. In order to suppress the interference in the control process, a variety of corresponding control methods have been developed. An integral part of the classical PID control algorithm is the traditional antidisturbance method [16]. The basic idea of the active antijamming control method developed on this basis is to make a general estimation of the uncertainties inside and a broad sense of interference through additional instruments of observation so that it can inherit the error-based control concept of PID control. This control method is widely used in mechatronics systems due to its convenient implementation steps and effectiveness in practical applications. As in [17], an output feedback controller is designed to realize the accurate trajectory tracking and state estimation of a class of electromechanical systems, and the chattering problem is effectively alleviated. The robust stability and performance of the digital motion control system based on disturbance observer are analyzed in [18]. There is also one other tactic which is used to mitigate interference on a wide scale: the construction of an interference observer. It compensates the control action by using the difference between the actual system output and the resulting nominal model.