Vibration control design for a flexible string with input saturation

In this paper, we consider the vibration control problem of a flexible string system in the presence of input saturation. The dynamics of the string system are represented by the coupled partial differential equation (PDE) and ordinary differential equation (ODE). In order to suppress the transverse vibration of the flexible string system, boundary control is proposed by introducing a well-defined integral Lyapunov function. An auxiliary system is introduced to handle the effect of input saturation, and the proof for the existence and the uniqueness of the solution of the closed-loop system is presented. The exponential stability is achieved through rigorous analysis without any simplification of the dynamics. The results are illustrated with numerical simulations for verifying the control performance.