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Robust generalized asymptotic regulation against non‐stationary sinusoidal disturbances with uncertain frequencies
Author(s) -
Köroğlu Hakan,
Scherer Carsten W.
Publication year - 2010
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1634
Subject(s) - control theory (sociology) , controller (irrigation) , relaxation (psychology) , mathematics , convex optimization , exponential stability , attenuation , optimization problem , stability (learning theory) , robust control , regular polygon , set (abstract data type) , mathematical optimization , computer science , control system , control (management) , nonlinear system , engineering , artificial intelligence , optics , biology , psychology , social psychology , geometry , quantum mechanics , machine learning , agronomy , physics , electrical engineering , programming language
Attenuation of sinusoidal disturbances with uncertain and arbitrarily time‐varying frequencies is considered in the form of a generalized asymptotic regulation problem. The disturbances are modeled as the outputs of a parameter‐dependent, unexcited and neutrally stable exogenous system that evolves from nonzero initial conditions. The problem is considered for a plant that depends partially on the uncertain parameters. Moreover, both the plant and the exogenous system are allowed to have dependence on another parameter vector that is measurable during online operation. The problem is then formulated as the synthesis of a controller that is scheduled on the measurable parameter in a way to guarantee robust internal stability and attenuate the disturbance according to a desired profile in steady state. The main result of the paper is a synthesis procedure based on a convex optimization problem, which is identified by a set of parameter‐dependent linear matrix inequalities and can be rendered tractable through standard relaxation schemes. It is also clarified how the transient behavior of the controller can be improved by some additional constraints. The order of the synthesized controller is equal to the order of the plant plus the order of the exogenous system. Copyright © 2010 John Wiley & Sons, Ltd.