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An upper bound on structurally stable linear regulation of a parameter-dependent family of control systems
Journal article   Peer reviewed

An upper bound on structurally stable linear regulation of a parameter-dependent family of control systems

Jordan Berg and Harry G. Kwatny
Systems & control letters, v 23(2)
1994
DOI: https://doi.org/10.1016/0167-6911(94)90038-8
Featured in Collection :   UN Sustainable Development Goals @ Drexel

Abstract

Linear control regulation robustness
We investigate the use of a linear compensator to regulate a parameter-dependent control system. This system may be linear or nonlinear. Our goal is to design a compensator that will ensure stable regulation over a wide range of parameter values. This paper reports a fundamental limitation on achieving this aim. In particular, we show that systems with a special, unregulatable, structure form hypersurfaces on the open-loop equilibrium manifold. Such systems include, but are not restricted to, those with transmission zeros at the origin. These surfaces partition the open-loop equilibrium manifold into disjoint open sets. We show that a linear compensator designed to regulate a system in some such partition must fail to regulate almost all systems in an adjacent partition. Therefore, by consideration of the open-loop system only, we derive upper bounds on the robustness of any linear regulator. We discuss some other qualitative aspects of the closed-loop dynamics.

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5 citations in Web of Science
13 citations in Scopus

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Web of Science research areas
Automation & Control Systems
Operations Research & Management Science
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