Active Control of Flow-Induced Vibrations via Feedback Decoupling

This paper deals with the flutter instability characteristics of a cantilever pipe conveying fluid flow, and explores the applicability of an active nodal vibration control for suppressing the associated structural vibration. The Euler-Bernoulli theory is used to represent pipe bending. The finite element method is used to discretize the governing equation. The control law is based on full state feedback and pole assignment, and requires as many actuators as the number of nodal degrees-of-freedom. Considering that this is not practical, a reduced order model with less number of elements is used to design the controller, and the resulting control input is applied to the “full” or the “truth” model. In this case, since the feedback simplification will not be complete, some performance degradation is to be expected. It is however demonstrated that the proposed control strategy can ensure closed loop stability for a wide range of flow velocity even if the critical flow velocity is exceeded. The effectiveness of the proposed method, in damping out the pipe vibrations, is also demonstrated clearly by comparing its results with those obtained by a direct velocity feedback control which is equivalent to add an external viscous damper to the pipe. The proposed control is essentially a model-based controller, and hence suffers from modeling errors and uncertainties in model parameters. Therefore, the robustness of the control is also investigated. It is shown that the proposed controller significantly reduces sensitivity of the uncontrolled system to flow conditions. It works effectively to suppress the vibrations of a fluid conveying cantilever pipe due to any disturbance.