Tracking control of underactuated mechanical systems based on controlled lagrangians

Tracking control of the underactuated mechanical system is investigated in this paper. First the system is linearized at its equilibrium, then the controlled Lagrangian method is used for the linearized system to design its tracking controller. The matching conditions satisfied for the controller are derived. At last, as examples, 2-DOF Acrobot and Pendubot are studied. The matching conditions for the two robots are solved and associate controllers are obtained. The simulation results verify effectiveness of the proposed method.