Boundary stabilization for a nonlinear flexible beam under an adaptive fractional-order proportional-integral control

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-09-22 DOI:10.1016/j.cnsns.2025.109352

Cuiying Li , Xin Wang , Yi Cheng , Donal O’Regan

引用次数: 0

Abstract

In this paper, we investigate vibration suppression of a nonlinear flexible beam system. An adaptive fractional-order proportional-integral (FOPI) controller has been applied effectively at the right boundary to suppress the transverse vibration of the system. The well-posedness results of the closed-loop system are carried out by utilizing the Faedo-Galerkin approximation technique. Subsequently, the closed-loop system can be stabilized exponentially by employing the energy perturbation method, where an innovative energy-like functional is constructed. Further, the viability of the controller is shown via a numerical simulation using the finite element method.

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自适应分数阶比例积分控制下非线性柔性梁的边界稳定

本文研究了一类非线性柔性梁系统的振动抑制问题。在右边界处采用自适应分数阶比例积分（FOPI）控制器有效地抑制了系统的横向振动。利用Faedo-Galerkin逼近技术得到了闭环系统的适定性结果。随后，采用能量摄动方法，构造了一个创新的类能泛函，实现了闭环系统的指数稳定。此外，通过采用有限元法的数值模拟显示了控制器的可行性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.