NDLI: A Strict Control Lyapunov Function for a Diffusion Equation With Time-Varying Distributed Coefficients

Content Provider	IEEE Xplore Digital Library
Author	Bribiesca Argomedo, F. Prieur, C. Witrant, E. Bremond, S.
Copyright Year	1963
Abstract	In this paper, a strict Lyapunov function is developed in order to show the exponential stability and input-to-state stability (ISS) properties of a diffusion equation for nonhomogeneous media. Such media can involve rapidly time-varying distributed diffusivity coefficients. Based on this Lyapunov function, a control law is derived to preserve the ISS properties of the system and improve its performance. A robustness analysis with respect to disturbances and estimation errors in the distributed parameters is performed on the system, precisely showing the impact of the controller on the rate of convergence and ISS gains. This is important in light of a possible implementation of the control since, in most cases, diffusion coefficient estimates involve a high degree of uncertainty. An application to the safety factor profile control for the Tore Supra tokamak illustrates and motivates the theoretical results. A constrained control law (incorporating nonlinear shape constraints in the actuation profiles) is designed to behave as close as possible to the unconstrained version, albeit with the equivalent of a variable gain. Finally, the proposed control laws are tested under simulation, first in the nominal case and then using a model of Tore Supra dynamics, where they show adequate performance and robustness with respect to disturbances.
Sponsorship	IEEE Control Systems Society
Starting Page	290
Ending Page	303
Page Count	14
File Size	3032888
File Format	PDF
ISSN	00189286
Volume Number	58
Issue Number	2
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Equations Mathematical model Lyapunov methods Tokamaks Boundary conditions Convergence Toroidal magnetic fields tokamaks Distributed parameter systems fusion power generation Lyapunov method partial differential equations time-varying systems
Content Type	Text
Resource Type	Article
Subject	Control and Systems Engineering Electrical and Electronic Engineering Computer Science Applications

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