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Technical Brief

Analysis of multi-dimensional time delay systems using Lambert W function

[+] Author and Article Information
Niraj Choudhary

Department of Electrical Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India
niraj.choudhary@ee.iitd.ac.in

Sivaramakrishnan Janardhanan

Department of Electrical Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India
janas@ee.iitd.ac.in

Indra Narayan Kar

Department of Electrical Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India
ink@ee.iitd.ac.in

1Corresponding author.

ASME doi:10.1115/1.4036874 History: Received November 11, 2016; Revised May 10, 2017

Abstract

In this note, the analysis of time delay systems using Lambert W function approach is reassessed. A common canonical form of time delay systems is defined. We extended the recent results of [1] for second order into nth order system. The eigenvalues of a time delay system are either real or complex conjugate pairs and therefore, the whole eigenspectrum can be associated with only two real branches of the Lambert W function. A new class of time delay systems is characterized to extend the applicability of the above said method. Moreover, this approach has been exploited to design a controller which places a subset of eigenvalues at desired locations. Stability is guaranteed by using a new algorithm developed in this paper which is based on the Nyquist plot. The approach is validated through numerical examples.

Copyright (c) 2017 by ASME
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