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Robust adaptive vibration control for a string with time‐varying output constraint
Author(s) -
He Wei,
Jing Zhe,
He Xiuyu,
Liu JinKun,
Sun Changyin
Publication year - 2018
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.4300
Subject(s) - control theory (sociology) , string (physics) , constraint (computer aided design) , ordinary differential equation , parametric statistics , lyapunov function , boundary (topology) , mathematics , partial differential equation , distributed parameter system , stability (learning theory) , adaptive control , function (biology) , computer science , differential equation , control (management) , mathematical analysis , nonlinear system , physics , statistics , geometry , quantum mechanics , artificial intelligence , machine learning , evolutionary biology , mathematical physics , biology
Summary In this paper, we present the vibration control design for a string with the boundary time‐varying output constraint. The dynamics of the string is a distributed parameter system described by a partial differential equation and two ordinary differential equations. A barrier Lyapunov function with a logarithmic function is adopted to prevent the time‐varying constraint violations. Adaptive control is designed to handle the system parametric uncertainties. Stability analysis and the solvability of the inequality equations are provided. Numerical simulations are provided to illustrate the effectiveness of the proposed control design.