Dynamic feedback control for manipulators handling a flexible payload based on distributed parameters

The stabilization of a multivariable rigid-flexible coupling manipulator handling a flexible payload is studied. The dynamic behavior of the system is described by a distributed parameter model in terms of partial differential equations to avoid the drawbacks of the lumped parameter model. A dynamic feedback control method is given based on the Lyapunov function for the energy dynamics of the flexible payload using the positive real lemma. The controller includes compensation and dynamic feedback controllers, with the transfer function of the dynamic controller being strictly positive real. The asymptotic stability in the neighbor-hood of the desired states of the closed-loop system is proved using semigroups of linear operators and LaSalle's invariance principle.