Extending wave-based control to non-uniform systems: Conditions for vibration suppression

Although wave-based control was originally designed for uniform lumped systems, it has often been successfully applied to non-uniform systems. In this context, many claims have been published in the past, promising stability and accuracy of control of non-uniform systems by wave-based control. Despite the wide support of the claims through simulation and application results, there is no exact mathematical proof of either stability or accuracy. This paper revisits and refines the claim of wave-based control functionality for non-uniform systems. Sufficient conditions for the stability and accuracy of the control are derived and proved by a rigorous procedure. The main result of this paper is that through sufficiently fast actuator dynamics, it is possible to suppress all frequency modes of even a non-uniform system by precise wave-based control.