Tracking control for boundary controlled parabolic PDEs with varying parameters: Combining backstepping and differential flatness

被引:151
作者
Meurer, Thomas [1 ]
Kugi, Andreas [1 ]
机构
[1] Vienna Univ Technol, Automat & Control Inst, Complex Dynam Syst Grp, A-1040 Vienna, Austria
关键词
Tracking control; Distributed-parameter systems; Diffusion-convection-reaction systems; Backstepping; Stabilization; Differential flatness; Trajectory planning; FEEDBACK; SYSTEMS; STABILIZATION; EQUATIONS; FEEDFORWARD; ASSIGNMENT; DESIGN; BEAM;
D O I
10.1016/j.automatica.2009.01.006
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
The combination of backstepping-based state-feedback control and flatness-based trajectory planning and feedforward control is considered for the design of an exponentially stabilizing tracking controller for a linear diffusion-convection-reaction system with spatially and temporally varying parameters and nonlinear boundary input. For this, in a first step the backstepping transformation is utilized to determine a state-feedback controller, which transforms the original distributed-parameter system into an appropriately chosen exponentially stable distributed-parameter target system of a significantly simpler structure. In a second step, the flatness property of the target system is exploited in order to determine the feedforward controller, which allows us to realize the tracking of suitably prescribed trajectories for the system output. This results in a systematic procedure for the design of an exponentially stabilizing tracking controller for the considered general linear diffusion-convection-reaction system with varying parameters, whose applicability and tracking performance is evaluated in simulation studies. (C) 2009 Elsevier Ltd. All rights reserved.
引用
收藏
页码:1182 / 1194
页数:13
相关论文
共 43 条
[1]   Nonlinear boundary control of semilinear parabolic systems [J].
Ahmed, NU ;
Xiang, X .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1996, 34 (02) :473-490
[2]   PARABOLIC EVOLUTION-EQUATIONS AND NONLINEAR BOUNDARY-CONDITIONS [J].
AMANN, H .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1988, 72 (02) :201-269
[3]  
[Anonymous], 2003, BERICHTE STEUERUNGS
[4]  
[Anonymous], FORTSCHR BER VDI 8
[5]  
Baehr H.D., 2006, Heat and Mass Transfer
[7]   ACTIVE CONTROL OF FLEXIBLE SYSTEMS [J].
BALAS, MJ .
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1978, 25 (03) :415-436
[8]   Feedforward tracking control for non-uniform Timoshenko beam models: combining differential flatness, modal analysis, and FEM [J].
Becker, Jens ;
Meurer, Thomas .
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2007, 87 (01) :37-58
[9]  
Christofides P. D., 2001, SYS CON FDN
[10]   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