## 1 Introduction
Large and high frequency chattering of the controller is caused by the switching function in the traditional SMC algorithm, which affect the overall accuracy and stability of the system, and may lead to damage of experimental equipment [23]. Therefore, improving the traditional SMC algorithm to avoid sliding mode chattering is critical for the effective application of SMC algorithm in specific projects. Several algorithms have been proposed to improve the sliding mode control. The terminal sliding mode algorithm improves the sliding mode surface function design method, and eliminates sliding mode chattering of the controller output by design of a nonlinear sliding mode surface [24; 25; 26; 27]. A higher-order SMC algorithm is applied to extend the design method of traditional SMC output, which eliminates the sliding mode chattering by application of discontinuous control variables to the higher derivatives of sliding mode functions [28]. A robust adaptive second-order SMC was tested to address the tracking problem of uncertain linear systems with both matched and unmatched disturbances, and the results showed that the chattering was removed by applying the sign function for the time-derivative of the control signal [29]. A global SMC was applied to an uncertain chaotic system, and resulted in robustness to multiple delays, parametric uncertainties, and other nonlinear disturbances [30]. A composite nonlinear feedback technique based on a self-tuning integral SMC algorithm was proposed for the robust tracking control of switched systems with uncertainties and input saturation; this technique guaranteed robustness against uncertainties, removed reaching phase, and avoided the chattering problem of sliding mode [31]. A novel adaptive super-twisting-based global-SMC algorithm was proposed to remove the reaching interval and confer robustness and stability to underactuated systems; chatter-free operation was guaranteed by integration of the discontinuous sign function in the control signal [32]. Of these methods, the reaching law function directly defines the approaching movement and sliding mode, making it the most direct, effective, and simple method among the described improved sliding mode algorithms. In this work, a novel chatter-free reaching law algorithm with a disturbance compensation based on the exponential reaching law is proposed for the application in a ground-based laser communication rough tracking control system. This algorithm guarantees that the sliding mode chattering approaches zero and the system state is stabilized in the QSMD with O(\(T^{3}\)) (\(T\) is the sampling period) width, resulting in superior control that is robust to nonlinear disturbances and model parameter variations. The main findings of this work can be summarized as follows:  
1. The frequency domain characteristic of the turntable pitch axis is tested by the classical sweep method [33]. According to the frequency domain characteristic curve, the system model is obtained by the traditional identification method, which is the precondition for the design of SMC. 2. A novel reaching law with a disturbance compensator is proposed to solve the chattering problem, which is robust to system model identification error, friction, and other nonlinear disturbances. Both mathematical calculation and simulation support the effectiveness of the algorithm. 3. The proposed digital SMC algorithm, the traditional digital PID algorithm, and the existing chatter-reduced SMC algorithm were compared. The experimental results show that the proposed algorithm provides higher control accuracy, stronger anti-interference ability, better frequency domain characteristics, and also suppresses chattering for an improved ground-based laser communication servo turntable control system.