$\mathcal{H}_{2}$ -Optimal Blending of Inputs and Outputs for Modal Control

For many dynamical systems, it is required to actively control individual modes, especially when these are lightly damped or even unstable. In order to achieve a maximum control performance, these systems are often augmented with a large number of control inputs and measurement outputs. To overcome the challenge of choosing an adequate combination of input and output signals for modal control, an H
₂
-optimal isolation of modes via blending of inputs and outputs is proposed in this brief. Enforcing an explicit mode decoupling, the approach enables controlling individual modes with simple single-input single-output controllers. A numerically efficient algorithm is derived for the joint computation of the interdependent input and output blending vectors. The effectiveness of the proposed approach is demonstrated by increasing the modal damping of an aeroelastic system.