Shape matching with smart material structures using piezoceramic actuators

In this paper, we consider the problem of driving a flexible structure from an "unforced" equilibrium position to a given desired shape. Within the context of smart materials. we focus on piezoceramic actuators as controls. Our approach is to base the choice of input voltages on a physical model of the structure, with "good" voltage choices being those whose model-based displacements "closely" match the desired shape. This shape matching problem is posed as a least squares problem in a Hilbert space that represents the displacement component of the state space of the flexible structure model. Here we treat the structure as a distributed parameter system, so that the state space is infinite dimensional. Thus, we must examine questions of existence of solutions and convergence of approximations. To illustrate our techniques. we give some numerical examples.