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Robust tracking control design for uncertain robotic systems with persistent bounded disturbances
Author(s) -
Tseng ChungShi
Publication year - 2008
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.41
Subject(s) - control theory (sociology) , bounded function , nonlinear system , tracking error , tracking (education) , robust control , mathematics , domain (mathematical analysis) , automatic gain control , computer science , control (management) , artificial intelligence , psychology , mathematical analysis , pedagogy , amplifier , computer network , physics , bandwidth (computing) , quantum mechanics
Abstract In this study, a robust nonlinear L ∞ ‐ gain tracking control design for uncertain robotic systems is proposed under persistent bounded disturbances. The design objective is that the peak of the tracking error in time domain must be as small as possible under persistent bounded disturbances. Since the nonlinear L ∞ ‐ gain optimal tracking control cannot be solved directly, the nonlinear L ∞ ‐ gain optimal tracking problem is transformed into a nonlinear L ∞ ‐ gain tracking problem by given a prescribed disturbance attenuation level for the L ∞ ‐ gain tracking performance. To guarantee that the L ∞ ‐ gain tracking performance can be achieved for the uncertain robotic systems, a sliding‐mode scheme is introduced to eliminate the effect of the parameter uncertainties. By virtue of the skew‐symmetric property of the robotic systems, sufficient conditions are developed for solving the robust L ∞ ‐ gain tracking control problems in terms of an algebraic equation instead of a differential equation. The proposed method is simple and the algebraic equation can be solved analytically. Therefore, the proposed robust L ∞ ‐ gain tracking control scheme is suitable for practical control design of uncertain robotic systems. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society