Optimal Actuator Placement for Active Vibration Control With Known Disturbances

Two cost functions, based on the disturbance sensitivity grammian, are presented that can be used to find the optimal position of an active vibration control actuator. The disturbance sensitivity grammian is a novel parameter in the field of active vibration control, and by minimizing the "size" of this matrix, one can maximize the effectiveness of the actuator to control the structure in a closed-loop configuration. Two examples—a pinned-pinned beam and an L-shaped membrane—are used to demonstrate the applicability of the criterion. It turns out that the optimal position is very close to where the disturbance acts on the system. The criterion is also not sensitive to the assumed damping included in the model.