Adaptive control of flexible structures using a nonlinear vibration absorber

A nonlinear adaptive vibration absorber to control the vibrations of flexible structures is investigated. The absorber is based on the saturation phenomenon associated with dynamical systems possessing quadratic nonlinearities and a two-to-one internal resonance. The technique is implemented by coupling a second-order controller with the structure through a sensor and an actuator. Energy is exchanged between the structure and the controller and, near resonance, the structure's response saturates to a small value. Experimental results are presented for the control of a rectangular plate and a cantilever beam using piezoelectric ceramics and magnetostrictive alloys as actuators. The control technique is implemented using a digital signal processing board and a modeling software. The control strategy is made adaptive by incorporating an efficient frequency-measurement technique. This is validated by successfully testing the control strategy for a nonconventional problem, where nonlinear effects hinder the application of the nonadaptive controller.