Effect Of Integral Feedback On A Class Of Uncertain Nonlinear Systems: Stability And Induced Limit Cycles

Abstract

The theoretical problem addressed in the present work involves the effect of integral feedback on a class of uncertain nonlinear systems. The intriguing aspects of the problem arise as a result of transient constraints combined with the presence of parametric uncertainty and an unknown nonlinearity. The motivational problem was the state-of-charge (SOC) control strategy for load-following in solid oxide fuel cells (SOFCs) hybridized with an ultracapacitor. In the absence of parametric uncertainty, our prior work established asymptotic stability of the equilibrium if the unknown nonlinearity is a passive memoryless function. In contrast, this paper addresses the realistic scenario with parametric uncertainty. Here, an integral feedback/parameter adaption approach is taken to incorporate robustness. The integral action, which results in a higher-order system, imposes further restriction on the nonlinearity for guaranteeing asymptotic stability. Furthermore, it induces a limit cycle behavior under additional conditions. The system is studied as a Lure problem, which yields a stability criterion. Subsequently, the describing function method yields a necessary condition for half-wave symmetric periodic solution (induced limit cycle).

Publication Date

4-1-2018

Publication Title

Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

Volume

140

Issue

4

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1115/1.4037837

Socpus ID

85035085645 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85035085645

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