Boundary control for a flexible string system with input saturation constraint

In this study, we focus on the boundary control problem for a vibrating string system with saturated input under the condition of external disturbances. Based on the backstepping approach, a boundary vibration control scheme is proposed to globally stabilize the string around the equilibrium position. A smooth hyperbolic tangent function is exploited to restrict the control input, an auxiliary system and a Nussbaum function are adopted to cope with the nonlinear term derived from the input saturation, and a disturbance observer is employed to tackle the boundary disturbance. The developed controller can assure the convergence of the closed-loop system state to a small neighbourhood of zero. By the appropriate choice of control design parameters, numerical simulation is conducted to show the effectiveness of the derived control.