Boundary Control of a Vibrating String Subject to Input Saturation and Output Constraint

Abstract

This paper presents a control framework of a vibrating flexible string system subject to input saturation and output constraint. By integrating the backstepping technique and Lyapunov theory, a smooth function, a Nussbaum function, a barrier function, and an auxiliary system are exploited to establish a constrained boundary control for tacking the output and input constraints as well as stabilizing the system. The derived control can assure the bounded stability in controlled systems depending on Lyapunov criteria. The simulation study and analysis verify the effectiveness of the presented scheme.

A time-varying string length method for a suppression string vibration

“…Therefore, the remarkable achievements have been made in the research of the boundary controller of string vibrations [6][7][8][9][10][11][12]. For the string vibration problems with the input saturation, the boundary controller was constructed by using the backstepping technique, the hyperbolic tangent function was used to control the input [6][7]; and a Nussbaum function and the auxiliary system can deal with the nonlinear terms in the control [7] [13]. The designed boundary controller can achieve the convergence of the controlled system and ensure the stability of the controlled system.…”