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This paper presents closed-form mathematical models for an acoustic duct with general boundary conditions. These infinite-dimensional models are derived using symbolic computations. A new method to obtain finite dimensional approximations of infinitedimensional models using quartic functions is presented. The theoretical models are compared with the experimental data obtained for the KSU duct. The experimental results of a new robust broadband feedback controller, designed using passivity-based techniques, are presented. The controller design is shown to be robust to the unmodeled dynamics and parametric uncertainty.