Active noise control in a one dimensional acoustic duct, in which fluid medium inside the duct has a mean flow velocity, is studied. The acoustic duct model with general boundary conditions is solved in Laplace domain and infinite dimensional system transfer functions are obtained. For controller designs, appropriate microphone, and noise canceling source locations are determined. Low order finite dimensional transfer function approximations of actual system transfer functions are obtained. It is found that, in a selected frequency range, approximations represent actual system in a satisfactory way. By using approximated system transfer functions, finite dimensional, low order, optimal H2 and H controllers are synthesized via linear matrix inequalities method. Closed loop frequency response and time domain simulations show that the controllers successfully suppress unwanted sound, which propagates along the duct.

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