Optimal and robust control for linear state-delay systems

被引:63
作者
Basin, Michael
Rodriguez-Gonzalez, Jesus
Fridman, Leonid
机构
[1] Autonomous Univ Nuevo Leon, Dept Phys & Math Sci, Nuevo Leon 66450, Mexico
[2] Univ Nacl Autonoma Mexico, Dept Engn, Mexico City 04510, DF, Mexico
来源
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS | 2007年 / 344卷 / 06期
关键词
optimal control; robust control; integral sliding mode; linear time-delay system;
D O I
10.1016/j.jfranklin.2006.10.002
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
This paper presents the optimal regulator for a linear system with state delay and a quadratic criterion. The optimal regulator equations are obtained using the maximum principle. Performance of the obtained optimal regulator is verified in the illustrative example against the best linear regulator available for linear systems without delays. Simulation graphs demonstrating better performance of the obtained optimal regulator are included. The paper then presents a robustification algorithm for the obtained optimal regulator based on integral sliding mode compensation of disturbances. The general principles of the integral sliding mode compensator design are modified to yield the basic control algorithm oriented to time-delay systems, which is then applied to robustify the optimal regulator. As a result, the sliding mode compensating control leading to suppression of the disturbances from the initial time moment is designed. The obtained robust control algorithm is verified by simulations in the illustrative example. (c) 2006 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
引用
收藏
页码:830 / 845
页数:16
相关论文
共 29 条
[1]   QUADRATIC PROBLEM FOR SYSTEMS WITH TIME DELAYS [J].
ALEKAL, Y ;
BRUNOVSKY, P ;
CHYUNG, DH ;
LEE, EB .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1971, AC16 (06) :673-+
[2]  
[Anonymous], DETERMINISTIC STOCHA
[3]   Optimal filtering for linear state delay systems [J].
Basin, M ;
Rodriguez-Gonzalez, J ;
Martinez-Zuñiga, R .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2005, 50 (05) :684-690
[4]   Integral sliding mode design for robust filtering and control of linear stochastic time-delay systems [J].
Basin, M ;
Rodriguez-Gonzalez, J ;
Fridman, L ;
Acosta, P .
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 2005, 15 (09) :407-421
[5]   A closed-form optimal control for linear systems with equal state and input delays [J].
Basin, M ;
Rodriguez-Gonzalez, J .
AUTOMATICA, 2005, 41 (05) :915-920
[6]   Optimal control for linear systems with time delay in control input [J].
Basin, M ;
Rodriguez-Gonzalez, J ;
Martinez-Zuniga, R .
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2004, 341 (03) :267-278
[7]  
Basin MV, 2005, DYNAM CONT DIS SER B, V12, P1
[8]  
Cao WJ, 2001, P AMER CONTR CONF, P4369, DOI 10.1109/ACC.2001.945665
[9]   THE LINEAR-QUADRATIC OPTIMAL-CONTROL PROBLEM WITH DELAYS IN STATE AND CONTROL VARIABLES - A STATE-SPACE APPROACH [J].
DELFOUR, MC .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1986, 24 (05) :835-883
[10]  
Dion JM., 1999, LINEAR TIME DELAY SY