Stabilization of a given position of an elastic rod

Abstract An elastic rod which can be displaced along a straight line in a plane is considered. The rod is put into motion by an electric motor mounted at one end. A weight is clamped at the other end. The stabilization of the position of the rod by linear feed-back is studied. The control voltage fed to the motor is a linear combination of signals for the displacement of the rod, for the rate of displacement, for its integral, and for the deformations. Delay in the control circuit is taken into account. Domains of asymptotic stability are constructed in the space of feed-back factors. This problem arises, for example, when an elastic manipulator is designed.