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).
Effect of Integral Feedback on a Class of Uncertain Nonlinear Systems: Stability and Induced Limit Cycles
University of Central Florida,
Orlando, FL 32816
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 8, 2016; final manuscript received August 18, 2017; published online November 23, 2017. Assoc. Editor: Beshah Ayalew.
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Abeysiriwardena, S., and Das, T. (November 23, 2017). "Effect of Integral Feedback on a Class of Uncertain Nonlinear Systems: Stability and Induced Limit Cycles." ASME. J. Dyn. Sys., Meas., Control. April 2018; 140(4): 041009. https://doi.org/10.1115/1.4037837
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