โ Scribed by Shawn E. Burke; James E. Hubbard Jr.; John E. Meyer
No coin nor oath required. For personal study only.
Colocated sensors and actuators offer significant robustness and design benefits in distributed parameter vibration control. The concept of colocation is extended here 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, valid for multidimensional distributed plants. It is also shown that in satisfying these constraints the resulting transducer-augmented plant, if open-loop stable, is minimum phase. These results are demonstrated by a transducer placement study combining distributed piezoelectric actuators with both discrete and distributed sensors. Conditions under which various combinations of discrete and distributed devices are colocated are developed, with examples.
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