Active impedance control of linear one-dimensional wave equations

Abstract

Active impedance control of linear one-dimensional wave equations is investigated. The proposed control algorithms are based on the concepts of wave propagation and impedance matching. Two control objectives are considered. The first objective is to obtain total reflection, and the second objective is to achieve total absorption (e.g. matched impedance). Both control laws utilize some interesting properties of the wave-type partial differential equation and do not require information about the disturbance and boundary conditions. The resulting controllers, although boundary-independent, contain an infinite number of poles on the imaginary axis and the closed-loop systems are not internally stable. A simple modification is added to the control laws and the stability is analysed. An example of active sound cancellation in ducts with a moving medium is given to demonstrate one of the control algorithms.