Robust control of chaotic vibrations for impacting heat exchanger tubes incrossflow

A robust feedback controller design to suppress flutter-type chaotic vibrat ions in baffled heat exchanger tubes is presented. The vibrations are the r esult of the fluid dynamic forces on the tube which behave as a negative da mping element. A consequence of these vibrations is that the heat exchanger tubes impact with the baffle plates thereby reducing the service life of t he heat exchanger. To eliminate the resulting tube impacts, a feedback cont rol strategy is proposed. The heat exchanger tube and the fluid dynamic for ces acting on the tube are modeled with linear delayed differential equatio ns. Due to the presence of the delay, these equations do not have a rationa l realization. The feedback controller is realized using a frequency domain loop shaping approach which is well suited far systems with transcendental transfer functions. The control effector is a magnetic force transducer th at acts on the heat exchanger tube. The design strategy is based upon the p remise that stabilizing the linear instability about the undeformed tube po sition will preclude the formation of the nonlinear chaotic vibrations that arise from impacting. The feedback controller is shown to provide robust s tability and performance over a large flow velocity regime. (C) 1999 Academ ic Press.