Multimode Control of Flexible Structures Using Saturation

We propose a new strategy for controlling the response of distributed-p arameter systems subjected to multifrequenc y resonant excitations. The technique exploits the saturation phenomenon exhibited by multidegree-of-freedom systems coupled with quadratic nonlinearities and possessing two-to-one autoparametric resonances. The strategy consists of introducing a series of second-order circuits and coupling them with the plant through an actuator and a quadratic feedback control law. Once the plant is forced near its resonances, the responses of the excited modes saturate and the oscillatory energy is channeled into the circuits. We consider the problem of suppressing the oscillations of a flexible cantilever beam where the actuation is provided by piezoceramic patches, and the feedback signal is generated by a strain gauge attached to the beam. We present theoretical and experimental results of the application of the control strategy. First, the equations of motion are developed and analyzed through perturbation techniques. Second, the strategy is tested by regulating the response of a cantilever beam that is subjected to two simultaneous resonant excitations.