In this paper, the flexible robotic manipulator is modelled as a distributed parameter system, represented by a group of partial differential equations and ordinary differential equations. Control is designed at the boundary of the robotic manipulator based on integral-barrier Lyapunov function to suppress the vibration of the elastic deflection and track the desired angular position. With the proposed boundary control, the manipulator can be driven to the desired set-point with angular position and elastic deflection stay under the former setting constraint. Uniformed boundedness of the closed-loop system under the unknown time-varying disturbance is achieved. Stability analysis of the closed-loop system is given by employing the Lyapunov stability theory. Simulation results illustrate the effectiveness of the proposed boundary controller for ensuring output constraint and suppressing vibrations.