Non-collocated Vibration Suppression using Delay-Based Controllers with Multiple Fixed Delays*

Abstract

The problem of non-collocated vibration absorption is targeted utilizing a multiparameter delay-based controller. The combined objective is to achieve closed-loop stability and vibration suppression at a target location, which is different from the position of the absorber. This problem can be translated into an optimization problem of shaping the poles of a closed-loop system with delays subject to zero-location constraints. The solution approach involves remodelling the closed-loop system as a system of delay-differential algebraic equations (DDAEs) which allows to systematically account for delays in the control law, thereby enabling a straightforward technique for computation of controller parameters. Finally, the proposed design method is validated by simulation on a lumped parameter model of a mass-spring-damper system.