Effect of Integral Feedback on a Class of Uncertain Nonlinear Systems: Stability and Induced Limit Cycles

[+] Author and Article Information
Singith Abeysiriwardena

Mech. & Aero. Engg. Dept., University of Central Florida, Orlando, Fl 32816

Tuhin Das

Mech. & Aero. Engg. Dept., University of Central Florida, Orlando, Fl 32816

1Corresponding author.

ASME doi:10.1115/1.4037837 History: Received August 08, 2016; Revised August 18, 2017


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 ultra-capacitor. 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 feed-back/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).

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