Observer design for a flexible manipulator model with a payload

In this paper, we consider a control system describing the motion of a flexible-link manipulator with a payload under the action of gravity. The system is actuated by a control torque at the bottom part (hub) of the manipulator. We use Galerkin approximations of an arbitrary order for the Timoshenko beam model in order to take into account any desirable (but finite) number of modal frequencies. Then the observability problem is solved for the output signal as the raising angle and the strain at a fixed point of the manipulator. An explicit procedure for observer design is proposed based on the invariance principle. This result justifies a possibility of implementing a state feedback controller for the stabilization problem