Research Papers

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

[+] Author and Article Information
Singith Abeysiriwardena

Mechanical and Aerospace
Engineering Department,
University of Central Florida,
Orlando, FL 32816
e-mail: singith.abeysiriwardena@knights.ucf.edu

Tuhin Das

Mechanical and Aerospace
Engineering Department,
University of Central Florida,
Orlando, FL 32816

1Corresponding author.

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.

J. Dyn. Sys., Meas., Control 140(4), 041009 (Nov 23, 2017) (8 pages) Paper No: DS-16-1384; 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 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).

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Fig. 1

Schematic diagram of the hybrid SOFC system [5]

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Fig. 2

SOFC/UC hybrid as a cascaded system [5]

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Fig. 3

Generalized form of Fig. 2 [5]

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Fig. 4

A Lure problem formulation derived from Fig. 3

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Fig. 6

A lure problem formulation of third-order closed-loop dynamics

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Fig. 5

Generalized form of Fig. 3 with parametric uncertainty

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Fig. 8

Effect of relative gains in inducing stable equilibrium or limit cycles

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Fig. 9

A non K∞ nonlinearity yielding a locally stable equilibrium

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Fig. 10

A non K∞ nonlinearity yielding an unbounded response outside the region of attraction

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Fig. 7

Nonlinear functions f(e): (a) correspond to Fig. 8(b) correspond to Figs. 9 and 10



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