Optimal Control Of Beam Structures By Shape Memory Wires

Abstract

The paper studies the optimal control of shape memory wires. These wires can be used as actuators in smart structures in order to alter the structural shape according to changing environmental conditions. As a first step, a very simple smart structure is analyzed, viz. the combination of an elastic beam with a shape memory wire. An extension of the dynamic Muller-Achenbach model, accounting for the possibility of electric heating, is used for the description of the shape memory behavior. This together with the beam bending equation leads to a coupled system of nonlinear ODEs. The resulting optimal control problem is solved by a direct method, thus determining the heating function for the wire that is necessary to produce a desired beam shape. Finally, an accelerated version is presented, which might be the basis for future real-time control applications.