Electromechanical realization of impedance matrices

Abstract

Applications exist at both small and large length scales for which one wishes to design an electromechanical system that reproduces a desired impedance matrix. Such a matrix corresponds to one or more degrees of freedom at several attachment points. The design of MEMS filters for signal processing applications is a small length scale example. At a much larger scale, simplified models of dynamically complex machinery are useful for testing the vibration isolation properties of supporting structures. In the first example, the desired impedance matrix is usually defined mathematically while in the latter, a mobility matrix is obtained by experiment. The realization problem is to obtain an electromechanical system that approximates the desired impedance matrix. Constrained approximation is necessary since the literal realization of idealized filters and complex machinery is often precluded by modal complexity, affecting cost and difficulty of construction, and implementation issues, such as nonideal boundary conditions and the lack of ‘‘sky hooks.’’ A two-stage solution to the realization problem is presented that divides the impedance matrix into passive and active components. In the first stage, a reduced-order passive mechanical model is obtained. This model is then modified to incorporate the active behavior. [Work supported by ONR.]