Speciﬁed motion of piezoelectrically actuated structures T. M. Seigler and A. H. Ghasemi University of Kentucky, Lexington, KY 40506-0503 April 29, 2011 Abstract The problem considered is that of solving for the control input that generates partly speciﬁed motion of a deformable structure with distributed piezoelectric actuation. The motion constraint, called the program constraint, is expressed as a relationship between the motion of selected material points of the structure. The solution is based on a projection method applicable to a class of ﬁnite-dimensional dy- namical systems which includes many common vibration models. For a nonlinear model with a nonlinear program constraint, the proce- dure in general results in a set of diﬀerential algebraic equations. It is shown that for linear models with linear periodic program constraints, the system is reduced to a set of algebraic equations. Application ex- amples are presented for a Euler-Bernoulli beam to demonstrate the usefulness of the procedure. 1