Robust control of chaotic vibrations for impacting heat exchanger tubes in crossflow

A robust feedback controller design to suppress flutter-type chaotic vibrations in baffled heat exchanger tubes is presented. The vibrations are the result of the fluid dynamic forces on the tube which behave as a negative damping element. A consequence of these vibrations is that the heat exchanger tubes impact with the baffle plates thereby reducing the service life of the heat exchanger. To eliminate the resulting tube impacts, a feedback control strategy is proposed. The heat exchanger tube and the fluid dynamic forces acting on the tube are modeled with linear delayed differential equations. Due to the presence of the delay, these equations do not have a rational realization. The feedback controller is realized using a frequency domain loop shaping approach which is well suited for systems with transcendental transfer functions. The control effector is a magnetic force transducer that acts on the heat exchanger tube. The design strategy is based upon the premise that stabilizing the linear instability about the undeformed tube position will preclude the formation of the nonlinear chaotic vibrations that arise from impacting. The feedback controller is shown to provide robust stability and performance over a large flow velocity regime.