H∞ Strongly Stabilizing Bandpass Controllers for Flexible Systems

In this paper, a MIMO control law for active vibration control for flexible systems is considered. The proposed strategy minimizes an H_∞ index, and results in a stable stabilizing controller with bandpass frequency shape due to the presence of zeros at the origin. The closed-form solution is obtained, thus avoiding numerical calculation of Riccati equations. As a by-product, the H₂ case is also derived, and the explicit equations of the parametrization of both the H_∞ and H₂ controllers are also given. The controller turns out to be well suited for active noise and vibration reduction, even for large order structures. Numerical simulations show the effectiveness of the proposed approach and its robustness.