Control of nonlinear mechanical systems

Control design methods for some underactuated mechanical systems are presen ted. A first control algorithm is based on the energy of the system and its passivity properties. It has been applied on the reaction wheel pendulum a nd on a convey-crane system. Then, a smooth control Lyapunov function for t he planar vertical take-off and landing (PVTOL) aircraft is proposed. Its c onstruction relies on the nonlinear stabilization technique called forwardi ng. The PVTOL aircraft model represents a particular example which illustra tes well "Lyapunov forwarding" technique.