Adaptive error feedback regulator problem for a 1-D wave equation with velocity recirculation

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.

Automated summary

This paper investigates the error feedback regulator problem for a 1-D wave equation with velocity recirculation. By introducing an invertible transformation and an adaptive error-based observer, an observer-based error feedback controller is constructed to regulate the tracking error to zero asymptotically and ensure bounded internal signals.