Broad band controller design for remote vibration using a geometric approach

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 or actuators can be located in the region where vibration attenuation is required. However this is either not feasible or prohibitively expensive for many large scale structures or where the system environment is harsh. As a result, optimal control of local vibration may lead to enhancement at remote locations. Controlling remote vibration using only local sensing and actuation is an important concept to resolve this remote vibration control problem. Recently, a geometric methodology that provides an approach for defining the design freedom available for reducing vibrations at both local and remote locations has been proposed by the authors. In an earlier paper, the fundamental results were used to develop design procedures for discrete frequency control; in the current paper, however, the focus is on design procedures for broad band control. A systematic approach is developed that provides an additional design constraint to the geometric methodology to ensure that the resulting compensator provides closed loop stability. The design procedure is illustrated through its application to an active vibration isolation structure.