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首页> 外文期刊>International Journal of Control >Lyapunov approach to the boundary stabilisation of a beam equation with boundary disturbance
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Lyapunov approach to the boundary stabilisation of a beam equation with boundary disturbance

机译：用Lyapunov方法求解带边界扰动的梁方程的边界稳定。

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摘要

In this paper, we are concerned with the boundary output feedback stabilisation of an Euler-Bernoulli beam equation with one free boundary end and control/disturbance on the other end. A variable structure output feedback stabilising control law is designed by the Lyapunov functional approach. It is shown that the resulting closed-loop system without disturbance is associated with a nonlinear semigroup and asymptotically stable except the zero dynamics. In addition, we show that this control law is robust to the external disturbance in the sense that the vibrating energy of the closed-loop system outside of the zero dynamics converges to zero as time goes to infinity in spite of the presence of finite sum of harmonic disturbance on the control end. The existence of the Filippov solution with disturbance is developed by the Galerkin approximation scheme.
机译：在本文中，我们关注一个自由边界端为Euler-Bernoulli束方程的边界输出反馈的镇定，另一端为控制/扰动。利用Lyapunov函数法设计了一种变结构输出反馈稳定控制律。结果表明，所产生的无扰动的闭环系统与非线性半群相关，并且除了零动力学特性外，其渐近稳定。另外，从零动力学之外的闭环系统的振动能量收敛到零的意义上，尽管存在有限的总和，我们证明了该控制律对外部扰动具有鲁棒性。控制端的谐波干扰。通过Galerkin近似方案开发了具有干扰的Filippov解的存在。

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