An Active Nonlinear Controller Emulating a Pendulum-Type Auto-parametric Vibration Absorber

Abstract

In this paper, a nonlinear active vibration control method, which is suitable for the vibration mitigation of both linear and nonlinear structures, is proposed. The main idea of this method is to make the controller emulate a pendulum-type auto-parametric vibration absorber, with the purpose of counteracting the different types of nonlinearity in structures. In this way, the difficulty in the passive realization of the pendulum-type vibration absorber due to the physical unsuitable parameters can also be well released. The idea of introducing an exosystem in Byrnes–Isidori regulator is borrowed to design the nonlinear controller. The steps to choose the parameters of the controller are introduced. The validity and robustness of the controller for the vibration mitigation of both linear and nonlinear oscillators are investigated by numerical examples of application. The simulation results show that the proposed nonlinear controller can effectively mitigate the vibration not only of linear oscillators, but also of nonlinear oscillators with third-, quintic- and seventh-order nonlinearities. The good robustness of the proposed nonlinear controller is also demonstrated.