Global stabilization of 2-DOF underactuated mechanical systems—an equivalent-input-disturbance approach

This paper presents a new method of globally stabilizing a non-linear underactuated mechanical system with two degrees of freedom (DOF). It is based on the idea of equivalent input disturbance (EID), and designing the controller requires only the state variables of position, not velocity. The design procedure has two steps: (1) Use a global homeomorphic coordinate transformation to convert the original system into a new non-linear system. This changes the problem of stabilizing the original system into one of stabilizing the new system. (2) Divide the new system into linear and non-linear parts and take the non-linear part to be an artificial disturbance, thereby enabling use of the EID approach to globally asymptotically stabilize the new system at the origin. The new method was tested through numerical simulations on three well-known 2-DOF underactuated mechanical systems (TORA, beam ball, inertia wheel pendulum). The results demonstrate its validity and its superiority over others.