Mixed VSS swining-up/balancing stabilisation of a rotating pendulum

This paper describes the development of a mixed VSS swinging-up/ balancing controller for the stabilisation of an underactuated mechanical system, the rotating pendulum. The control design is achieved through two stages. The first deals with the swinging-up of the pendulum and the second deals with the balancing of the pendulum about its equilibrium unstable position. The swing-up controller is based on a non-collocated partial feedback linearisation of the underactuated system with a particular choice of the additional control, for which the design is made using the VSS approach. On the other hand, the balancing control is based on the linearised model of the pendulum about its equilibrium unstable position. Simulation results made on a 2-DOF rotating pendulum are given to illustrate the proposed approach.