Why active Willis metamaterials? A controllability and observability perspectivea)

Recently, active Willis metamaterials (AWM) have been the focus of extensive investigations because of their unique electro-elastic coupling characteristics. However, the treatments of this class of materials have been carried out exclusively, in all the available literature, by approaches that do not rely on solid control theory basis. In this paper, the emphasis is placed on revealing very important control features that are inherent to this class of materials because of their Willis coupling characteristics. These features lie in the enhanced controllability and observability properties of the AWM as compared to non-Willis active materials. Such control properties enable the AWM to possess broad sensing and actuation capabilities that can lend this material to be an effective means for monitoring and controlling the behavior of numerous critical applications, such as acoustic cloaking, particularly when integrated with appropriate robust control strategies. A simple example of a piezoelectric-based AWM is presented to demonstrate its effective control capabilities and distinguish this class of materials from conventional materials. In the selected example, the AWM is structured from two dissimilar masses connected by a piezoelectric spring. Lagrange dynamics formulation is utilized to generate the equations governing the Willis coupling, the piezoelectric coupling, and reveal the inherent control features. With this developed controlled-based structure of the AWM, it is shown that the AWM can simultaneously monitor and control both the strain and velocity whereas the conventional active material, which is formed from two similar masses connected by a piezoelectric spring, can only measure and control the strain alone. It is envisioned that the revealed control metrics for the simple one-dimensional AMW example can serve as means for investigating the potential of AMW's of higher dimensionality.