Nonlinear control for a class of underactuated mechanical systems

A mathematical model of a class of underactuated mechanical systems is analyzed and a nonlinear control scheme based on partial feedback linearization is presented. In the underactuated mechanical system, the dynamics corresponding to the active degrees of freedom are linearized based on the exact linearization design technique, while the dynamics corresponding to the passive degrees are taken as the internal dynamics of the system. The trajectory tracking control of the linearized system is studied by choosing the active degrees as the system outputs. The analysis of the system internal dynamics shows that the stability of the zero dynamics guarantees the stability of the control system. Finally, simulation is done for the anti-swing control of an overhead crane system.