An Active Nonlinear Controller Emulating a Pendulum-Type Auto-parametric Vibration Absorber
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ORIGINAL PAPER
An Active Nonlinear Controller Emulating a Pendulum‑Type Auto‑parametric Vibration Absorber Zhui Tian1,2 · Jun Jiang1 Received: 30 March 2019 / Revised: 29 April 2019 / Accepted: 2 May 2019 © Krishtel eMaging Solutions Private Limited 2019
Abstract Purpose 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 pendulumtype 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. Methods 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. Results 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. Keywords Vibration control · Linear and nonlinear oscillators · Pendulum-type auto-parametric vibration absorber · Nonlinear vibration controller
Introduction Nonlinearities in dynamical systems are the source of a wealth of interesting phenomena. With continual interest in expanding the performance envelope of engineering systems, nonlinear components are increasingly utilized in real-world applications. A recent trend in the technical literatures is to exploit nonlinear dynamical phenomena instead of avoiding them. For instance, it demonstrated a new mechanism for tunable rectification that uses bifurcations and chaos [1]. And a new strategy for engineering low-frequency noise oscillators was provided through capitalizing on the intrinsic nonlinear phenomena of micromechanical * Jun Jiang [email protected] 1
State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an 710049, China
Active Structures Laboratory, Université Libre de Bruxelles (ULB), 50, Av. F. D. Roosevelt, CP 165/42 Brussels, Belgium
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resonators [2]. Nonlinearity is also more and more utilized for vibration mitigation. On the one hand, the applications of nonlinear vibration absorbers to eliminate undesirable vibration of linear structures have been examined by numerous researchers [3, 4]. Recent developments in passive nonlinear vibration absorbers include the nonlinear energy sink (NES) [5, 6] and the auto-parametric vibration absorber (AVA) [7]. On the other hand, mitigating the resonant vibrations of nonlinear structures is be
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