Modeling and Control of a Nonuniform Vibrating String under Spatiotemporally Varying Tension and Disturbance

Abstract

AbstractIn 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. By using Hamilton's principle, the nonuniform vibrating string system is represented by a nonlinear nonhomogeneous partial differential equation (PDE) and two ordinary differential equations (ODEs). Robust adaptive boundary control is developed to suppress the vibration of the flexible nonuniform string and compensate the system parameter uncertainties and the disturbance uncertainties. With the proposed control, the state of the string system is proven to converge to a small neighborhood of zero by choosing the design parameters. Simulations are provided to illustrate the effectiveness of the proposed control.