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

Brian COGAN – Annraoi M de PAOR

   Recently, the Lambert W function 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.

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

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