Vibration suppression of an Euler–Bernoulli beam by backstepping iterative learning control

• Published in: IET control theory & applications Vol. 13; no. 16; pp. 2630 - 2637
• Main Authors: Liu, Yu, Zhan, Wenkang, Gao, Huanli, Liu, Haiming
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 05.11.2019
• Subjects: backstepping term; beams (structures); B‐BILC scheme; closed loop systems; closed‐loop system state; control nonlinearities; control system synthesis; Euler–Bernoulli beam system; hybrid backstepping‐boundary iterative learning control; iterative learning control; iterative term; Lyapunov methods; Lyapunov synthesis method; Lyapunov theory; nonlinear control systems; PD‐BILC; Proportion–Derivative‐BILC; Research Article; unknown boundary disturbance; unknown external disturbance; vibration control; vibration problem; vibration suppression; vibrations; backstepping term; PD-BILC; unknown external disturbance; hybrid backstepping-boundary iterative learning control; beams (structures); control system synthesis; Lyapunov theory; Euler–Bernoulli beam system; Lyapunov synthesis method; B-BILC scheme; closed loop systems; iterative learning control; nonlinear control systems; control nonlinearities; iterative term; vibration problem; unknown boundary disturbance; vibration suppression; Proportion–Derivative-BILC; vibrations; vibration control; Lyapunov methods; closed-loop system state
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2019.0011

This study puts forward a hybrid backstepping-boundary iterative learning control (B-BILC) to tackle vibration problem for an Euler–Bernoulli beam system subjected to an unknown external disturbance. Based on Lyapunov's synthesis method, a backstepping term and an iterative term are designed to reduce the vibration and attenuate the effects of the unknown boundary disturbance under the consideration of model property. With the proposed B-BILC scheme, the uniform boundedness of the closed-loop system state and the convergence of the system output are proved via Lyapunov theory. Simulations are provided to show the effectiveness of the proposed scheme and demonstrate that B-BILC yields better performance compared to the Proportion–Derivative-BILC (PD-BILC).