Tracking control of 2-DOF underactuated mechanical systems

The tracking controller design of 2-DOF underactuated mechanical systems is investigated in this paper. First the system is linearized at its equilibrium, then the controlled Lagrangian and asymmetric damping force to get desired closed-loop system are constructed, and asymptotical stability conditions of the closed-loop system are derived from its characteristic equation. By solving matching conditions satisfied by the close-loop system, tracking controller for the underactuated system can be obtained. At last, as examples, 2-DOF Acrobot and Pendubot are studied. The matching conditions for the two robots are solved and associate controllers are designed. The simulation results verify effectiveness of the proposed method.