A review on static and dynamic shape control of structures by piezoelectric actuation

A literature review is presented for shape control of structures, where special emphasis is laid upon smart structures with piezoelectric control actuation. In shape control one intends to specify the spatial distribution, or the shape, of an actuating control agency, such that the displacement field of a structure distorted from its original shape eventually vanishes, or such that the structure follows some desired field of trajectories. The disturbances that distort the shape of structures may be transient, or they may be slowly varying in time. While the problem of (quasi-) static shape control refers to the latter situation, one speaks about dynamic shape control in the former case. In the present review, some structural aspects are emphasized that contribute to the complexity of shape control. Particularly, we discuss the necessity of a distributed actuation, and we refer to the inverse character of the shape control problem. We shortly mention the requirements posed by the latter two aspects upon methods of automatic control for smart structures. Since an analogy exists between piezoelectric actuation and thermal actuation, some references are cited concerning the latter topic. In order to stimulate interdisciplinary work, a short account is further presented with respect to the similar strategies of shape control by shape memory alloys and shape control by distributed pre-stress.