Controllability and observability measures of structural vibration and acoustic radiation

This paper studies the controllability and observability measures of structural vibration and acoustic radia- tion and proposes a measure of modal observability based on acoustic pressure outputs and measures of controllability and observability of acoustic radiation by combining the measures of modal controllability and observability of vibration modes with corresponding modal acoustic radiation efficiencies. A plate with control force inputs and vibrational response outputs and acoustic pressure outputs is involved to show the modal controllability and observability measures of vibration modes and measures of controllability and observability of structural vibration and acoustic radiation. Observability measures based on vibrational response outputs and acoustic pressure outputs are compared and the emphasis is on the measures based on the acoustic pressure outputs. Finally the application and usefulness of the controllability and observability measures to active control of structural vibration and acoustic radiation are illustrated and compared. It shows that the controllability and observability measures provide useful guidance for active control design especially in optimal actuator and sensor placement.