ANALYTIC ROOT LOCUS AND LAMBERT W FUNCTION IN CONTROL OF A PROCESS WITH TIME DELAY

被引:5
作者
Cogan, Brian [1 ]
de Paor, Annraoi M. [2 ]
机构
[1] Commissioners Irish Lights, Dun Laoghaire, Dublin, Ireland
[2] Natl Univ Ireland, Sch Elect Elect & Mech Engn, Dublin 4, Ireland
来源
JOURNAL OF ELECTRICAL ENGINEERING-ELEKTROTECHNICKY CASOPIS | 2011年 / 62卷 / 06期
关键词
Lambert W function; root locus; time-delay system; stability; eigenvalues; STABILITY ANALYSIS; SYSTEMS;
D O I
10.2478/v10187-011-0052-9
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
Recently, the Lambert W function has arisen in the analysis of many systems including a. restricted class of time-delay systems. An alternative approach to this analysis, based on the well-established root locus method, is shown here to contain the Lambert W function as a special case. As a purely illustrative example of the equivalence between the Lambert W function and analytic root locus a system comprising a Proportional controller with a time-delay process is analysed. Controller designs based on rightmost eigenvalue location and the dominant eigenvalue method are described.
引用
收藏
页码:327 / 334
页数:8
相关论文
共 27 条
[1]  
Andersen Kirsti., 2007, The Geometry of an Art: The History of the Mathematical Theory of Perspective from Alberti to Monge
[2]  
[Anonymous], Maple
[3]  
Bendrukov G.A., 1959, AUTOMAT REM CONTR+, V20, P340
[4]   Analytical stability bound for delayed second-order systems with repeating poles using Lambert function W [J].
Chen, YQ ;
Moore, KL .
AUTOMATICA, 2002, 38 (05) :891-895
[5]   Use of the analytic method and computer algebra to plot root loci [J].
Cogan, B .
INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING EDUCATION, 1998, 35 (04) :350-356
[6]  
COGAN B., 2006, THESIS TRINITY COLL
[7]   PI control of first-order lag plus time-delay plants: root locus design for optimal stability [J].
Cogan, Brian ;
de Paor, Annraoi M. ;
Quinn, Anthony .
TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL, 2009, 31 (05) :365-379
[8]   On the Lambert W function [J].
Corless, RM ;
Gonnet, GH ;
Hare, DEG ;
Jeffrey, DJ ;
Knuth, DE .
ADVANCES IN COMPUTATIONAL MATHEMATICS, 1996, 5 (04) :329-359
[9]   New views of the solar wind with the Lambert W function [J].
Cranmer, SR .
AMERICAN JOURNAL OF PHYSICS, 2004, 72 (11) :1397-1403
[10]  
D'Azzo JohnJ., 1988, LINEAR CONTROL SYSTE, V3rd