Sliding Mode Preview Control for a Class of Continuous-Time Linear Systems
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RESEARCH PAPER
Sliding Mode Preview Control for a Class of Continuous-Time Linear Systems Chen Jia1 Received: 3 September 2019 / Accepted: 28 February 2020 Ó Shiraz University 2020
Abstract In this paper, the sliding mode preview control problem for a class of continuous-time linear systems is studied. Firstly, an extended error system consisting of the error equation and the state equation of the original system is constructed, and the tracking problem is transformed into the regulation problem. Secondly, a quadratic performance index function is introduced for the state variables of the extended error system, and the preview sliding surface is designed based on the existing conclusions of the optimal preview control. Thirdly, the sliding mode controller with preview effect for the extended error system is designed by using the reaching law method; then, the desired sliding mode preview controller of the original system can be obtained through the integral. The numerical simulation verifies the feasibility of the proposed method. Keywords Preview control Sliding mode control Optimal control Linear systems theory Reaching law
1 Introduction Sliding mode control is a variable structure control strategy. The basic difference between sliding mode control and conventional control strategy is the discontinuity of control. Controllers play different roles in different stages of system motion: At the arrival stage, the system can reach the sliding surface from any initial state; at the sliding stage, the system can enter the sliding surface and move along the sliding surface. In the 1950s, Emelyanov et al. (1962, 1963, 1964) proposed the concept of sliding mode control, in which basic research object was second-order linear systems. In 1977, the research on sliding mode control theory proposed by Utkin (1977) was widely concerned by scholars, and many studies were carried out (Doffing and Zinober 1986; Utkin and Shi 1996; Gao 1990). Doffing and Zinober (1986) applied the quadratic performance index optimal control to sliding surface design. Utkin and Shi (1996) proposed the design method
& Chen Jia [email protected] 1
Department of Information and Computing Science, School of Mathematics and Physics, University of Science and Technology Beijing, No. 30, College Road, Haidian District, Beijing 100083, China
of integral sliding surface. Academician Gao (1990) studied the motion of the system before entering sliding surface, and put forward the concept of reaching law, which provided an effective way to shorten the time of reaching process and reduce chattering. In recent years, sliding mode control has been used to study complex systems such as time-delay systems, singular systems, stochastic systems and Markov switching systems. It has been widely used in vehicle control, robot control, network control, etc. (Wu et al. 2017; Han et al. 2017; Wang et al. 2016; Guo and Ma 2019; Liu et al. 2016). Wu et al. (2017) considered a class of uncertain stochastic systems with limited communication network from se
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