Three-dimensional vibration suppression for an Euler–Bernoulli beam with asymmetric output constraint

• Published in: Journal of the Franklin Institute Vol. 358; no. 7; pp. 3470 - 3490
• Main Authors: Jing, Zhe, He, Xiuyu, Liu, Zhijie, Zhang, Shuang, Kang, Wen
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.05.2021; Elsevier Science Ltd
• Subjects: Asymmetry; Boundary control; Constraint modelling; Controllers; Euler-Bernoulli beams; Eulers equations; Liapunov functions; Nonlinear systems; Parameter estimation; Parameter uncertainty; Vibration; Vibration analysis; Vibration control
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2021.02.020

A vibration control strategy is addressed for the three-dimensional vibration suppression of an Euler-Bernoulli beam (EBB) subject to asymmetric output constraints in this paper. A special piecewise barrier Lyapunov function candidate is provided to prevent the asymmetric output constraint violation, and a model-based boundary control (MBC) is developed subsequently to ensure the coupled vibration reduction. Moreover, considering the parameter uncertainties, an adaptive law is designed to estimate the uncertain parameter and to update the vibration controller. The main challenge of this work is to consider the asymmetric output constraint in a nonlinear and coupled infinite-dimensional system. Finally, numerical simulations are made to present the system performance under the proposed vibration controllers which maintain the output being restrained in the predefined scope.