# Sliding Mode Control of Electro-Hydraulic Position Servo System Based on Adaptive Reaching Law
## 1 Introduction  
Electro-hydraulic servo systems have been widely used in excavators [1], hydraulic load simulators [2; 3], and industrial robots [4] due to their advantages of a high output power, high control precision, and fast response speed. However, the electro-hydraulic servo system itself has the characteristics of nonlinearity and parameter uncertainty and is affected by friction leakage and external disturbance during the movement of the hydraulic actuator, which is not conducive to the accurate control of the position of the servo system. Sliding mode control (SMC) has a strong antidisturbance ability and is widely used in electro-hydraulic servo systems. The basic idea of SMC is to drive the system states to an internally stable reduced-order system within finite time [5; 6; 7; 8], which means that the motion of the controlled system is divided into two stages: one is \"reaching\" and the other is \"sliding\" [9]. However, there are still some problems in SMC, especially the chattering problem [10]. Many scholars have conducted extensive research on the problem of sliding mode chattering. The methods to solve this problem include quasi-sliding mode method [11; 12; 13], high-order sliding mode method [14], adaptive fuzzy integral sliding mode velocity control [15], boundary layer method [16], and dynamic sliding mode method [17]. [PERSON] et al. [18] designed a new sliding mode controller, which could make the position error converge to zero in a certain period of time without external disturbances, but the controller output parameters still had chattering. [PERSON] et al. [19] proposed an adaptive reaching-law controller that reached the sliding surface at the fastest speed, thereby ignoring chattering. Most of the methods mentioned above combine the exponential reaching law and the constant velocity reaching law to weaken the chattering. Although the exponential reachinglaw can improve the dynamic characteristics of the system and reduce the chattering by adjusting the parameters of the reaching law, it cannot completely eliminate the chattering of the system. [PERSON] et al. [20] proposed a variable structure control with a neural network and an optimized fractional-order selection policy, which could suppress the combined error in the boundedness of approximating double Euler difference errors. [PERSON] et al. [21] proposed a new exponential reaching law method, which could speed up the convergence while adding power function terms. [PERSON] et al. [22] proposed a method combining the exponential reaching law and power reaching law, which could effectively solve the problem of the arrival time of the power reaching law being too long. [PERSON] et al. [23] proposed an exponential reaching law method, which combined with the mismatched uncertain system to weaken the buffeting of the system, and the stability of the system was ensured. [PERSON] et al. [24] combined the isokinetic reaching law with the bipower reaching law to accelerate the global convergence of the sliding mode variable structure. [PERSON] et al. [25] proposed a class of globally nonsingular SMC laws, called logarithmic sliding mode control, which led to a higher tracking precision and a faster local convergence rate than those of some classical SMCs. To attenuate the effect of parameter uncertainties and uncertain nonlinearities in the hydraulic system, other nonlinear control schemes have been proposed, such as the disturbance observer [26; 27; 28; 29; 30], state observer [31; 32; 33], and adaptive control [34; 35; 36; 37]. According to the characteristics of SMC, this paper proposes an improved adaptive reaching law SMC algorithm to control the position of the valve-controlled asymmetric cylinder system, so that it can quickly track the desired trajectory, reduce the system response time, and improve the robustness of the system.