Please use this identifier to cite or link to this item: https://doi.org/10.1109/TMECH.2011.2160960
Title: Modeling and control of a nonuniform vibrating string under spatiotemporally varying tension and disturbance
Authors: Zhang, S.
He, W. 
Sam Ge, S. 
Keywords: Adaptive control
boundary control
Lyapunovs direct method
ordinary differential equation (ODE)
partial differential equation (PDE)
Issue Date: 2012
Source: Zhang, S., He, W., Sam Ge, S. (2012). Modeling and control of a nonuniform vibrating string under spatiotemporally varying tension and disturbance. IEEE/ASME Transactions on Mechatronics 17 (6) : 1196-1203. ScholarBank@NUS Repository. https://doi.org/10.1109/TMECH.2011.2160960
Abstract: In this paper, robust adaptive boundary control is developed for a class of flexible string systems under unknown spatiotemporally varying distributed disturbance and time-varying boundary disturbance. The vibrating string is nonuniform since the spatiotemporally varying tension applied to the system. The nonuniform vibrating string system is represented by a nonlinear nonhomogeneous partial differential equation (PDE) and two ordinary differential equations (ODEs). Model-based control is first proposed at the right boundary of the string to suppress the vibration of the flexible nonuniform string system. To compensate for the system parametric uncertainties, robust adaptive boundary control is developed. With the proposed control, the uniformly ultimate boundness of the closed-loop system is demonstrated via Lyapunovs direct method. The state of the nonuniform string system is proven to converge to a small neighborhood of zero by appropriately choosing the design parameters. Simulations are provided to illustrate the effectiveness of the proposed control. © 2012 IEEE.
Source Title: IEEE/ASME Transactions on Mechatronics
URI: http://scholarbank.nus.edu.sg/handle/10635/56663
ISSN: 10834435
DOI: 10.1109/TMECH.2011.2160960
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