Dynamics, Stability, and Control of Multivariable Piezoelectric Shunts

This paper is concerned with the dynamics and stability of piezoelectric laminate structures, where several piezoelectric elements are shunted by a multiinput impedance. The problem is shown to be equivalent to a multivariable feedback control problem for a square plant. A parameterization of stabilizing admittance transfer function matrices is given together with a specific class of controllers capable of reducing structural vibrations and guaranteeing closed-loop stability. An efficient method for implementation of a multiport admittance transfer function is introduced and applied experimentally to demonstrate the effectiveness of the proposed methodology.