Vibration Control of a Flexible Beam With Output Constraint

• Published in: IEEE transactions on industrial electronics (1982) Vol. 62; no. 8; pp. 5023 - 5030
• Main Authors: He, Wei, Ge, Shuzhi Sam
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptation models; Barriers; Boundaries; Boundary conditions; Boundary Control; Design engineering; Distributed Parameter System; Euler-Bernoulli Beam; Euler-Bernoulli beams; Flexible Structure; Lyapunov functions; Lyapunov methods; Mathematical model; Mathematical models; Noise; Output Constraint; Payloads; Vibration; Vibration Control; Vibrations; output constraint; Boundary control; flexible structure; Euler–Bernoulli beam; distributed parameter system; vibration control
• ISSN: 0278-0046; 1557-9948
• DOI: 10.1109/TIE.2015.2400427

In this paper, we present the vibration control design for a Euler-Bernoulli beam with the boundary output constraint. To prevent the constraint violation, a novel barrier Lyapunov function is employed for the control design and stability analysis. This paper represents an important step in extending the barrier Lyapunov function theory to distributed parameter systems. Model-based barrier control is proposed to suppress the vibration of a flexible Euler-Bernoulli beam under the boundary output constraint. Then, adaptive control is designed to handle the system parametric uncertainties. The vibration suppression is well achieved without violation of the constraint. Numerical simulations are provided to illustrate the performance of the control system.