Nonlinear simulation of a string system under boundary robust control

In this paper, a new boundary robust vibration control is designed for a nonlinear string system using the Lyapunov direct method. Simulations are carried out using the finite difference approach, and open-loop and closed-loop responses of the nonlinear system are compared to demonstrate the effectiveness and robustness of the proposed boundary control. Uncertainties considered in the design and simulation include such dynamics as nonlinear string tension, string non-uniformity, and nonlinear friction. The simulation results demonstrate that, in the presence of significant uncertainties, any vibration of the string can be exponentially suppressed by the proposed robust control