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

被引：170

作者：

Cheng, Meng-Bi ^{[1
]}

Radisavljevic, Verica ^{[2
,3
]}

Su, Wu-Chung ^{[1
]}

机构：

[1] Natl Chung Hsing Univ, Dept Elect Engn, Taichung 402, Taiwan

[2] Calif State Univ Los Angeles, Dept Mech Engn, Los Angeles, CA 90032 USA

[3] Amer Univ Sharjah, Dept Mech Engn, Sharjah, U Arab Emirates

来源：

AUTOMATICA | 2011年 / 47卷 / 02期

基金：

美国国家科学基金会;

关键词：

Sliding mode control; Distributed parameter systems; Boundary control; Chattering reduction; Lyapunov function; VARIABLE-STRUCTURE CONTROL; EQUATION; STABILIZATION; FEEDBACK;

D O I：

10.1016/j.automatica.2010.10.045

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

080201 [机械制造及其自动化];

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.

引用

页码：381 / 387

页数：7

共 32 条

[1]

Boundary control of an unstable heat equation via measurement of domain-averaged temperature [J].

Boskovic, DM ;

Krstic, M ;

Liu, WJ .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2001, 46 (12) :2022-2028

[2]

Sliding Mode Boundary Control of Unstable Parabolic PDE Systems with Parameter Variations and Matched Disturbances [J].

Cheng, Meng-Bi ;

Radisavljevic, Verica ;

Su, Wu-Chung .

2009 AMERICAN CONTROL CONFERENCE, VOLS 1-9, 2009, :4085-+

[3]

Christofides P. D., 2001, SYS CON FDN

[4]

SOLUTION OF INITIAL-BOUNDARY VALUE-PROBLEMS FOR PARABOLIC EQUATIONS BY METHOD OF INTEGRAL-OPERATORS [J].

COLTON, D .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1977, 26 (02) :181-190

[5]

Curtain RF, 2012, An Introduction to Infinite-dimensional Linear Systems Theory, V21

[6]

Sliding mode control of a heat equation with application to are welding [J].

Drakunov, S ;

Barbieri, E ;

Silver, DA .

PROCEEDINGS OF THE 1996 IEEE INTERNATIONAL CONFERENCE ON CONTROL APPLICATIONS, 1996, :668-672

[7]

SLIDING MODE CONTROL IN DYNAMIC-SYSTEMS [J].

DRAKUNOV, SV ;

UTKIN, VI .

INTERNATIONAL JOURNAL OF CONTROL, 1992, 55 (04) :1029-1037

[8]

Edwards C, 1998, Sliding mode control: theory and applications

[9]

From PDEs with boundary control to the abstract state equation with an unbounded input operator: A tutorial [J].

Emirsjlow, Z ;

Townley, S .

EUROPEAN JOURNAL OF CONTROL, 2000, 6 (01) :27-49

[10]

Ge SS, 2001, J ROBOTIC SYST, V18, P17, DOI 10.1002/1097-4563(200101)18:1<17::AID-ROB2>3.0.CO

← 1 2 3 4 →