Balanced actuator and sensor placement for flexible structures

Properties of flexible structures in modal and balanced coordinates are derived. From these properties the root-mean-square law of the Hankel singular values is obtained. It says that the squares of the Hankel singular values of a set of sensors and actuators is approximately a root-mean-square sum of the squares of the Hankel singular values for each individual sensor and actuator. This property allows us to evaluate each actuator and sensor in terms of the joint controllability and observability, and to serve as a tool of the actuator and/or sensor placement methodology.