Vibration Control of a Flexible String With Both Boundary Input and Output Constraints

This paper investigates control design for a flexible string system with both boundary input and output constraints. Dynamics of the string system are represented as a homogeneous partial differential equation describing the vibrations of the system. First, model-based boundary control is proposed by employing an auxiliary system for handling the input saturation and an integral barrier Lyapunov function for eliminating the effect of output constraint. The exponential stability is achieved through rigorous analysis without any simplification of the dynamics. Subsequently, because the system parameters are unknown, adaptive boundary feedback control is proposed and uniform ultimate boundedness is guaranteed. Finally, the simulation results are provided for demonstrating the effectiveness of the proposed control, where all the signals in the control inputs can be measured using the most common sensors.