Suppression of vibration with optimal actuators and sensors placement

It is proposed to place the actuators to maximize the mean value of energy transmitted from or dissipated by the actuators, while the sensor location should maximize the mean square value of system output, which also maximizes the signal-to-noise ratio. By using explicit expressions for controllability and observability grammians as well as modal energies, it is shown that the approaches based on the system responses to transient and persistent disturbances are closely related, and are equivalent for structures which damping is small and the natural frequencies of which are well spaced. The method of actuator and sensor optimal location via grammians was proposed and compared it with results given by the method of matrix norms.