1. Introduction Many control systems are sensitive to parameter changes and load perturbations. Using variable control theory, it is possible to obtain a state trajectory in the phase plane sliding along the switching surface, thus keeping the system response to parameters and perturbations constant. However, in the sliding state, the trajectory near the switching surface causes high-frequency chattering. A feasible remedy is to replace the intermittent switching law with an appropriate continuous switching law, thereby keeping the system response within a given accuracy range. The perturbation compensator presented in this paper can reduce the impact of modeling errors and chattering on the system output. A simple yet novel method for estimating dynamic perturbation signals is proposed, and the determined robust control law ensures that the control system reaches the sliding state within a limited time. [b]2 Perturbation Compensation[/b] This study examines a system with uncertain parameters and external perturbations: [img=348,80]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhjsyyy/2002-4/3-1.jpg[/img] [font=SimSun][img=360,231]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhjsyyy/2002-4/3-2.jpg[/img][/font] Clearly, ΔU's role is to overcome the influence of D(·)F(·). Conventionally, appropriately selecting the amplitude of ΔU can improve the system's robustness to perturbations. It is noteworthy that the control law (2) intermittently crosses the sliding surface, causing chattering in the control signal. The purpose of this study is to utilize perturbation compensation to reduce unwanted chattering. In fact, direct measurement of perturbation in any system is very difficult. Some literature has proposed methods for estimating or observing perturbation in a system. None of these methods achieve this goal by studying the characteristics of variable structure systems, which is the innovation of this paper. Theorem 1: By using the control signal U from the compensator, the effect of perturbation on the dynamics of equation (1) can be eliminated. [img=357,160]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhjsyyy/2002-4/4-1.jpg[/img] Substituting the compensator represented by equation (5) into equation (1), the dynamic perturbation signal (6) can be obtained from equation (4). 3. Variable Structure Controller The compensation signal is fed back to the input of the control system, so that [img=357,107]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhjsyyy/2002-4/4-2.jpg[/img] Obviously, equation (9) is independent of the perturbation of the system. Theorem 2: If the variable structure control law shown in equation (10) is adopted, the compensated system (9) can obtain the desired sliding state. The transient response of the system is determined by the following equation: [img=345,256]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhjsyyy/2002-4/4-5.jpg[/img][/font] It indicates that within a limited time, V=0, i.e., S=0. In addition, according to equation (16), the transient response is determined by equation (14). By setting the right half of equation (9) to zero, the upper limit of the arrival time tr can be obtained, and tr is given by equation (12).  From equation (12), it can be seen that the maximum value of tr is inversely proportional to e and λmin(K). The appropriate choice is to take a small e and a large λmin(K) so that it can reach the transient quickly, while reducing chattering. An extreme case is to choose e equal to zero, which will weaken the transient to approximately the sliding family, so that the control law equation (10) continuously passes through the sliding surface, thus not exhibiting any chattering. [b]4 Conclusions[/b] This paper proposes a simple method for estimating system perturbation signals, introduces positive compensation, and reduces unwanted chattering. The compensator has been applied to the servo system of a certain type of naval gun simulator. The results show that the method has a good compensation effect. References [1] Lin Yan, et al. Design of reference adaptive controller for low-gain variable structure model [J]. Control Theory and Applications, 2001(6) [2] Yu Liming, et al. Research on optimal predictive compensation tracking control of human-machine system [J]. Acta Automatica Sinica, 2001, (3) [3] Hu Jianbo, et al. Approximate variable structure output tracking control of mismatched uncertain system [J]. Control and Decision, 2001, (1)