Free vibrations control of a cantilever beam using combined time delay feedback

Abstract

A new multi-input single-output delay feedback controller is presented to reduce free vibrations of a cantilever beam. A linear model using the first mode is derived and used to analyze and characterize the damping produced by different delay-feedback controllers as a function of the controller's gains and delay. The stability regions and amount of damping produced by three different single delay feedback and the new combined delayed feedback are investigated. A three-dimensional figure for the new controller showing the stability regions as a function of the controller gains and delay is presented. The characteristic damping of the controller as predicted by the linear model is compared with that calculated using direct long-time integration of a three-mode nonlinear model. Optimal values of the controllers gains and delay are obtained, simulated, and compared. To validate the single mode approximation, numerical simulations are performed using three-mode full nonlinear model. The results obtained using multi-input delay-feedback controllers demonstrate an excellent improvement in mitigating the first-mode vibration.