A1-7 - Sedma Nacionalna Konferencija so Me|unarodno U~estvo...

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VARIABLE STRUCTURE CONTROL FOR A CLASS OF DISCRETE-TIME UNCERTAIN SYSTEMS Wenlin Li 1 , Yang Mi 2 , Yuanwei Jing 2 , and Georgi M. Dimirovski 3, 4 1 Henan Normal University, Department of Mathematics – Henan, Liaoning, P. R. of China 2 Northeastern University, Institute of Control Science School of Information Science & Engineering, Shenyang – Liaoning, 110004, P. R. of China E-mails: [email protected] ; [email protected] 3 Dogus University, Department of Computer Engineering Faculty of Eng., Acibadem – Kadikoy, 34722 Istanbul, Turkey FAX: +90-216- 327-9631; E-mail: [email protected] 4 SS Cyril & Methodius University, Institute of ASE Faculty of Electrical Engg., 1000 Skopje, R. of Macedonia Abstract – In this paper, to the synthesis design of variable structure control for a class of discrete- time uncertain systems is studied further. In particular, the variable law of the ratio between the change of the uncertainty and the sampling interval is presented, using the approximate uncertainty in different region. The estimation of the uncertainty is properly solved. Compared to the conventional design the effects of the variable structure control are improved. It is shown that the drawback of the conventional design method is overcome by using of the controller design presented in this paper. Keywords – Discrete-time systems; variable structure control, sliding mode; uncertainty estimation; uncertainty reaching law. 1. INTRODUCTION Theory of variable structure control has undergone a considerable development (Hung and c-authors, 1993) since the 1974 monograph by V. I. Utkin was re-published in English (1978). Nevertheless, variable structure control theory for discrete-time and uncertain systems was developed during recent times mainly (Dot and Holf, 1980; Furuta, 1990. Milosavljevic, 1985; Moura and Olgac, 1998; Sapturk and co-authors, 1987; Yoo and Chung, 1992; Yu, 2000). In this regard, the respective conventional approach (Dot and Holf, 1980; Furuta, 1990; Milosavljevic, 1985; Yoo and Chung, 1992; Gao, 1995) requires the bound of the uncertainty known as a premise to assure the existence of the quasi-sliding mode. The bound of uncertainty is used in the control law which, in turn, can compensate the impact of the system uncertainties. This method, however, has an obvious shortcoming: Many strong limit conditions (e.g., matching condition, the limit condition of the boundary, etc.) should be imposed on the uncertainty, at the same time the control law based on the upper boundary of the uncertainty’s norm must be over conservative and has large chattering. In the fairly recent study by Yu (2000), on the grounds of the work by Moura and Olgac (1998), he attributed the uncertainty to equivalent disturbance () k ϕ and took (1 ) k instead of () k to deduce control law in order to overcome the above shortcoming. Due to exploring the estimation of uncertainty instead of the boundary, the controller proposed by Yu overcome the conservativeness of the standard variable-structure controller and eliminated a set of complex limiting conditions. However, Yu’s approach needs a key assumption that the dynamic
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  • Spring '10
  • PopovskiBorislav
  • Sliding mode control, K T, Variable structure control, variable structure, Variable structure system

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A1-7 - Sedma Nacionalna Konferencija so Me|unarodno U~estvo...

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