Optimal placement of actuators and sensors for floor vibration control

Lightweight floor systems are susceptible to excessive levels of vibration caused by occupant activities such as walking, dancing, and aerobics. Ongoing research utilizes active control to reduce vibration. Placement of multiple actuators and sensors for effective vibration control of flexible systems such as floors is a challenging task. The method proposed in this paper simultaneously determines optimal placements for multiple actuators, sensors, and appropriate output feedback gains of the controller. Instead of carrying out the controller design in the analog domain and then applying a transformation to arrive at a digital implementation, the proposed algorithm provides a digital controller directly. This allows lower sampling rates to be used at the implementation stage. To obtain faster settling times in the presence of external disturbances, a performance index that penalizes system states exponentially is utilized. The nonlinearities associated with actuator saturation due to force/stroke limitations is considered explicitly in the optimization. The proposed algorithm uses an interpolation scheme in case only partial knowledge of the mode shape is available. Hence it is applicable to a wider class of 2D structures that do not possess closed-form expressions for modal shapes and for which one has to resort to finite-element or experimental modal analysis.