Optimal tracking control for discrete-time systems with multiple input delays under sinusoidal disturbances

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• 作者：Shi-Yuan Han (1)
  Dong Wang (1)
  Yue-Hui Chen (1)
  Gong-You Tang (2)
  Xi-Xin Yang (3)
  
  1. Shandong Provincial Key Laboratory of Network Based Intelligent Computing ; University of Jinan ; 336 Nanxinzhuang Road ; 2500 22 ; Jinan ; China
  2. College of Information Science and Engineering ; Ocean University of China ; 238 Songling Road ; Qingdao ; 266100 ; China
  3. College of Software Technical ; Qingdao University ; Qingdao ; 266100 ; China
  
• 关键词：Discrete ; time systems ; multiple input delays ; observer ; optimal tracking control ; sinusoidal disturabnces
• 刊名：International Journal of Control, Automation and Systems
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：13
• 期：2
• 页码：292-301
• 全文大小：1,230 KB
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• 刊物类别：Engineering
• 刊物主题：Control Engineering
  
• 出版者：The Institute of Control, Robotics and Systems Engineers and The Korean Institute of Electrical Engi
• ISSN：2005-4092

文摘

This study researches the tracking control problem for discrete-time systems with multiple input delays affected by sinusoidal disturbances. This study is organized around the expression of sinusoidal and disturbances and the delay-free transformation. First, based on the periodic characteristic of the sinusoidal disturbance, the sinusoidal disturbances are considered as the output of an exosystem. By proposing a discrete variable transformation, the discrete-time system with multiple input delays and the quadratic performance index are transformed into equivalent delay-free ones. Then, by constructing an augmented system that comprises the states of the exosystems of sinusoidal disturbances, the reference input, and the delay-free transformation systems, the original tracking problem is transformed into the optimal tracking problem for a delay-free system with respect to the simplified performance index. The optimal tracking control (OTC) law is obtained from Riccati and Stein equations. The existent and uniqueness of the optimal control law is proved. A reduced-order observer is constructed to solve the problem of physically realizable for the items of the reference input and sinusoidal disturbances. Finally, the feasibility and effectiveness of the proposed approaches are validated by numerical examples.