A geometric design approach to the broadband control of remotely located vibration

Over the past three decades, a wide variety of active control methods have been proposed for controlling problematic vibration. The vast majority of approaches make the implicit assumption that sensors can be located in the region where vibration attenuation is required. However, for many large scale structures or where the system environment is harsh, this is either not feasible or prohibitively expensive. As a result, the optimal control of local vibration may lead to enhancement at remote locations. Motivated by such problems in marine system environments, a geometric methodology that provides an approach for defining the design freedom available for reducing vibration both at local and remote locations has been proposed by the authors in a previous paper. The results are then used to develop design procedures for discrete frequency control. In this paper, design procedures for broadband control are developed. Particularly it is shown that the broadband control problem along with the convex optimization over LMI can be cast into this geometric framework. A numerical example is given with the broadband attenuation of rotor blade vibration to illustrate the design procedure.