Robust control of flexible structures with stable bandpass controllers

In this paper, a control law for the active vibration control of mechanical 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 control authority is thus effective in a chosen band of frequency, resulting in a selective broadband control action, as opposed to narrow-band (tonal) vibration reduction. Moreover, the explicit closed-form solution of the controller is also obtained, thus avoiding numerical calculation of the solution of the Riccati equations, which can be ill-conditioned in the case of very high-order, poorly damped flexible systems. The parametrization of all the H∞ controllers is also given and a family of controllers with the above properties is deduced. The H2 case is also obtained as a byproduct. The controller is based on a colocated actuators/sensors pair strategy and numerical simulations are presented, showing the robustness of the proposed approach even for systems with zero damping. Finally, experimental results on a skin panel of a Boeing 717 aircraft also prove the effectiveness of the proposed approach in practical complex applications, with global vibration reduction performances.