Robust boundary control approaches to the stabilization of the Euler-Bernoulli beam under external disturbances

作     者：Wang, Yingying Wu, Wei Wang, Zhan Lou, Xuyang Goerges, Daniel 

作者机构：Jiangnan Univ Key Lab Adv Proc Control Light Ind Minist Educ Wuxi 214122 Binhu Peoples R China Jiangnan Univ Sch IoT Engn Wuxi Jiangsu Peoples R China Univ Kaiserslautern Dept Elect & Comp Engn Kaiserslautern Germany 

出 版 物：《JOURNAL OF VIBRATION AND CONTROL》 (振动与控制杂志)

年 卷 期：2023年第29卷第21-22期

页      面：4841-4856页

核心收录：

学科分类：07[理学] 0802[工学-机械工程] 0801[工学-力学（可授工学、理学学位）] 0702[理学-物理学] 

主　　题：Euler-Bernoulli beam robust control distributed parameter system disturbance observer well-posedness 

摘      要：In this paper, the boundary feedback control problem for the Euler-Bernoulli beam with unknown time-varying distributed load and boundary disturbance is investigated. Based on the Lagrangian-Hamiltonian mechanics, the model of the beam is derived as a partial differential equation. To suppress the external disturbance, two disturbance rejection control approaches are adopted in the control design. Firstly, a disturbance observer is designed to estimate the boundary disturbance online. Thus, the effect of the boundary disturbance can be canceled directly in the feedback loop. A time-varying function is applied in the disturbance observer to prevent an excessively large control input. Secondly, a new observer is developed to estimate the upper bound of the disturbance and a sign function is introduced to suppress the influence of the disturbance without demanding the boundedness of the derivative of the boundary disturbance. The well-posedness and the uniform boundedness of the closed-loop system are proved using the operator semigroup theory and the Lyapunov method. Numerical comparisons with existing results are made for demonstrating the advantages of the proposed approaches.