Vibration control of flexible manipulator with unknown control direction

The vibration control problem of the flexible manipulator with unknown control direction is studied in this paper. Using Hamilton's principle, we derive the partial differential equation (PDE) dynamic model of the system, which can accurately characterise the flexible manipulator. On this basis, a boundary control approach is proposed, and Nussbaum function is adopted in the controller design to circumvent the problem of unknown control directions. Under the action of the proposed controller, the flexible manipulator can reach the desired angle and eliminate vibration without knowing the control direction. The asymptotic stability of the whole closed-loop system is verified by Lyapunov's direct method in detail, and the effectiveness of the designed control scheme is validated by numerical simulations.