Simultaneous placement of actuators and sensors

A placement of actuator and sensors for flexible structures is studied using the H 2 , H∞, and Hankel modal norms. The norm of a flexible structure with multiple actuators and sensors is a root-mean-square sum of norms of structures equipped with single sensor and single actuator. This property allows for the evaluation of the importance of a combination of sensors and actuator, in terms of their participation in the overall structural dynamics. This simple and powerful tool is applicable for structures only, since in a general case, a system norm cannot be decomposed into a combination of single-input-single-output norms, and consequently complex searching techniques need to be used. The algorithm consists of the determination either H 2 , or H∞, or Hankel norms for the rth mode, jth actuator, and kth sensor. Using the norms, the sensor and actuator placement matrices are generated for each considered mode. The matrices are used to evaluate each sensor and actuator combination, and to determine the simultaneous actuator and sensor locations such that the norm of the each mode is maximized. The approach is illustrated with the truss example that includes the physical interpretation of the selection.