Active Disturbance Rejection Control and Disturbance Observer-Based Control Approach to 1-d Flexible String System

In this paper, we pay attention to the boundary feedback stabilization of a one-dimensional flexible string system with the exogenous disturbance that acts on the control end. The active disturbance rejection control (ADRC) and disturbance observer-based control (DOBC) are introduced to reduce the vibration caused by external disturbance. By utilizing Lyapunov method and constructing a suitable Lyapunov functional, we conclude that system is uniformly bounded stable. The numerical simulations are also presented to demonstrate the validity of both methods.