Smart structure technology has become a key technology in the design of modern, so-called intelligent, civil, mechanical and aerospace (CMA) systems. One key aspect for a successful design is the communication between structure and controller, for which sensors and actuators are responsible. In continuous CMA systems a crucial point is the distribution of sensors to obtain proper information and the distribution of actuators to influence the behavior of the structure properly. Finding these distributions is the topic of this paper.
A common strategy for the modeling of continuous CMA systems is based on the linearized theory of elasticity; within this paper we consider a three-dimensional linear elastic background body with sources of self-stress. These self-stresses can be produced by smart materials, which exhibit the well known strain induced actuation mechanism; as many of the modern smart materials have both, actuation and sensing properties, we assume the sensing be based on the same mechanism.
We show that a suitable distribution of sensors results into a sensor signal proportional to kinematical entities (e.g. displacement), whereas a suitable distribution of the actuation results in actuators that act like dynamical entities (e.g. force). Our design strategy automatically results into collocated sensor/actuator pairs; this design is highly suitable from a control point of view, because it allows the application of common control strategies in a straightforward manner; e.g. a simple PD-controller ensures stability of the closed loop system.