Gramian-based actuator placement with spillover reduction for active damping of adaptive structures

Adaptive structures are engineering structures with the ability to modify their response to external loads. This includes active damping of externally induced vibrations. The controller design is usually based on reduced order models that comprise the most important vibration modes of the structure. This can lead to unwanted excitation of the neglected modes, known as control spillover. One means to cope with this problem is by proper placement of the actuators. In this contribution, we present a method for optimal actuator placement for active damping of adaptive structures that explicitly considers spillover effects by optimizing the trade-off between controllability of the considered and neglected modes. The optimization criterion is based on the controllability Gramian. Under certain conditions, the globally optimal solution can be found. The proposed method is applied to a numerical example of a high-rise truss structure.