Colocation: Design Constraints for Distributed and Discrete Transducers

Colocated sensors and actuators offer significant robustness and design benefits in distributed parameter vibration control. The concept of colocation is extended to distributed transducers, and combinations of distributed and discrete transducers, affixed to self-adjoint distributed plants. It is shown that sensors and actuators are colocated only when they have both physically coincident spatial apertures and their “spatial derivative orders” are equal: these constraints are expressed mathematically as an integral equation. In satisfying these constraints the resulting transducer-augmented plant, if open-loop stable, is minimum phase. These results are demonstrated by transducer placement studies.