Adaptive Control of Flexible Structures Using a Nonlinear Vibration Absorber

A nonlinear adaptive vibration absorber to control the vibrations offlexible structures is investigated. The absorber is based on thesaturation phenomenon associated with dynamical systems possessingquadratic nonlinearities and a two-to-one internal resonance. Thetechnique is implemented by coupling a second-order controller with thestructure through a sensor and an actuator. Energy is exchanged betweenthe structure and the controller and, near resonance, the structure'sresponse saturates to a small value.Experimental results are presented for the control of a rectangularplate and a cantilever beam using piezoelectric ceramics andmagnetostrictive alloys as actuators. The control technique isimplemented using a digital signal processing board and a modelingsoftware. The control strategy is made adaptive by incorporating anefficient frequency-measurement technique. This is validated bysuccessfully testing the control strategy for a nonconventionalproblem, where nonlinear effects hinder the application of thenonadaptive controller.