Sliding mode boundary control of a parabolic PDE system with parameter variations and boundary uncertainties

作     者：Cheng, Meng-Bi Radisavljevic, Verica Su, Wu-Chung 

作者机构：Natl Chung Hsing Univ Dept Elect Engn Taichung 402 Taiwan Calif State Univ Los Angeles Dept Mech Engn Los Angeles CA 90032 USA Amer Univ Sharjah Dept Mech Engn Sharjah U Arab Emirates 

出 版 物：《AUTOMATICA》 (自动学)

年 卷 期：2011年第47卷第2期

页      面：381-387页

核心收录：

学科分类：0711[理学-系统科学] 0808[工学-电气工程] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 0701[理学-数学] 071101[理学-系统理论] 

基　　金：National Science Council, Taiwan, ROC [NSC98-2221-E-005-042] Direct For Education and Human Resources Division Of Human Resource Development Funding Source: National Science Foundation 

主　　题：Sliding mode control Distributed parameter systems Boundary control Chattering reduction Lyapunov function 

摘      要：This paper considers the stabilization problem of a one-dimensional unstable heat conduction system (rod) modeled by a parabolic partial differential equation (PDE), powered with a Dirichlet type actuator from one of the boundaries. By applying the Volterra integral transformation, a stabilizing boundary control law is obtained to achieve exponential stability in the ideal situation when there are no system uncertainties. The associated Lyapunov function is used for designing an infinite-dimensional sliding manifold, on which the system exhibits the same type of stability and robustness against certain types of parameter variations and boundary disturbances. It is observed that the relative degree of the chosen sliding function with respect to the boundary control input is zero. A continuous control law satisfying the reaching condition is obtained by passing a discontinuous (signum) signal through an integrator. (C) 2010 Elsevier Ltd. All rights reserved.