<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>Recently, the Lambert <italic>W</italic> 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.</p><p>As a purely illustrative example of the equivalence between the Lambert <italic>W</italic> 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.</p></abstract>

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.

Analytic Root Locus and Lambert <italic>W</italic> Function in Control of a Process with Time Delay

Commissioners of Irish Lights, Dun Laoghaire, Co., Harbour Road, Dublin, Ireland

School of Electrical, Electronic and Mechanical Engineering, National University of Ireland, Dublin, Belfield, Dublin 4, Ireland

Journal of Electrical Engineering

Analytic Root Locus and Lambert  Function in Control of a Process with Time Delay

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...

Analytic Root Locus and Lambert W Function in Control of a Process with Time Delay

Published Online: Dec 21, 2011

Page range: 327 - 334

DOI: https://doi.org/10.2478/v10187-011-0052-9

Keywords
Lambert function, root locus, time-delay system, stability, eigenvalues

This content is open access.