Anti-swing control of underactuated overhead crane system using multiple Lyapunov functions

For a class of underactuated systems, a switching Lyapunov functions based nonlinear controller is given. Underactuated configuration space is split in to two subsets. Two simplified controllers with local guaranteed performances are derived. A direct controller is designed on actuated configuration space while another feedback controller is utilized indirectly to act on the unactuated configuration space. A switching algorithm between those controllers is based on maximum projection strategy. Direct controller is the passivity based and indirect controller is based on noncollocated feedback linearization. Unlike PD only controller, the suggested controller enables parametrization for anti-swing strategy. Concept is developed and illustrated on 2-DOF overhead gantry crane systems. Simulation results have shown effectiveness of the proposed controller.