To suppress the vibration and improve the vibration control for a flexible manipulator with the system parametric uncertainty and unknown boundary disturbance uncertainty

a robust adaptive boundary control with boundary disturbance observer is proposed by using adaptive control and boundary control technologies based on the manipulator's parameter estimation to suppress the vibration of the manipulator. With the proposed control scheme

system parameter uncertainty can be compensated and the control spillover problem can be avoided

and the boundary disturbance observer can attenuate and track the unknown boundary disturbance. The stability and uniform boundedness of the control system are both proved by Lyapunov's synthesis method. Simulation results demonstrate the effectiveness of the proposed control method to suppress the manipulator's vibration.