Anti-disturbance stabilization for a hybrid system of non-uniform elastic string

• Published in: Journal of the Franklin Institute Vol. 358; no. 18; pp. 9653 - 9677
• Main Authors: Wang, Shen, Han, Zhong-Jie, Zhao, Zhi-Xue
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.12.2021; Elsevier Science Ltd
• Subjects: Active control; Closed loop systems; Feedback control; Hybrid systems; Materials elasticity; Numerical analysis; Output feedback; Rejection; Rigid structures; Simulation; Stabilization; State observers; Strings
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2021.10.018

This paper is concerned with the anti-disturbance boundary feedback stabilization for a hybrid system coupling a non-uniform elastic string with a rigid body at one end by the active disturbance rejection control technology. An infinite-dimensional disturbance estimator and a Luenberger state observer are designed to estimate the disturbance and state of the system, respectively, based on which, a boundary output feedback control is further proposed to stabilize the system. The control consists of two parts: one part is for the stabilization of system without external disturbance, and the other part is for the rejection of the disturbance by virtue of the disturbance estimator. The well-posedness and exponential stability of the closed-loop system are proved by employing the semigroup theories and frequency domain method. Besides, all the signals of the closed-loop system are shown to be uniformly bounded. Finally, some numerical simulations are presented to validate the effectiveness of the proposed control strategy.