Stabilization analysis of Euler-Bernoulli beam equation with locally distributed disturbance

• Published in: Journal of Hebei University of Science and Technology Vol. 38; no. 6; pp. 536 - 541
• Main Authors: Pengcheng HAN, Danhong LIU
• Format: Journal Article
• Language: Chinese
• Published: Hebei University of Science and Technology 01.12.2017
• Subjects: asymptotic stabilization; Euler-Bernoulli beam equation; local feedback control; locally distributed disturbance; theory of stability; well-posedness
• ISSN: 1008-1542
• DOI: 10.7535/hbkd.2017yx06005

In order to enrich the system stability theory of the control theories, taking Euler-Bernoulli beam equation as the research subject, the stability of Euler-Bernoulli beam equation with locally distributed disturbance is studied. A feedback controller based on output is designed to reduce the effects of the disturbances. The well-posedness of the nonlinear closed-loop system is investigated by the theory of maximal monotone operator, namely the existence and uniqueness of solutions for the closed-loop system. An appropriate state space is established, an appropriate inner product is defined, and a non-linear operator satisfying this state space is defined. Then, the system is transformed into the form of evolution equation. Based on this, the existence and uniqueness of solutions for the closed-loop system are proved. The asymptotic stability of the system is studied by constructing an appropriate Lyapunov function, which proves the asymptotic stability of the closed-loop system. The result shows that designi