Abstract
In this paper, we consider the error feedback regulator problem for a 1-D wave equation with velocity recirculation. There are harmonic disturbances in all channels of the system and the reference signal is also a harmonic type. We first introduce an invertible transformation such that the disturbances are only on the left boundary, which is non-collocated with the control. Then we propose an adaptive error-based observer by utilizing the measurable non-collocated tracking error and its derivative. Next, an observer-based error feedback controller is constructed to regulate the tracking error to zero asymptotically and make all internal signals bounded. Finally, the results are illustrated with simulations.
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