Adaptive boundary control for a class of inhomogeneous Timoshenko beam equations with constraints

• Published in: IET control theory & applications Vol. 8; no. 14; pp. 1285 - 1292
• Main Authors: He, Wei, Zhang, Shuang, Ge, Shuzhi Sam, Liu, Chang
• Format: Journal Article
• Language: English
• Published: Stevenage The Institution of Engineering and Technology 01.09.2014; John Wiley & Sons, Inc
• Subjects: adaptive boundary control; adaptive control; Adaptive control systems; adaptive IBLF‐based boundary control; Boundaries; Boundary control; boundary output constraints; compensation; Dynamical systems; Dynamics; inhomogeneous Timoshenko beam equations; integral‐Barrier Lyapunov function; Lyapunov methods; Mathematical analysis; numerical simulations; partial differential equations; Simplification; system uncertainty compensation; Timoshenko beam system; Timoshenko beams; uncertain systems; vibration control; vibration suppression; adaptive IBLF-based boundary control; numerical simulations; adaptive boundary control; uncertain systems; system uncertainty compensation; adaptive control; integral-Barrier Lyapunov function; Timoshenko beam system; inhomogeneous Timoshenko beam equations; boundary output constraints; vibration suppression; compensation; partial differential equations; vibration control; Lyapunov methods
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2013.0601

In this study, integral-Barrier Lyapunov function (IBLF)-based boundary controls are proposed for a class of inhomogeneous Timoshenko beam equations with boundary output constraints. An IBLF which depends explicitly on time, is employed to prevent the constraint violation. The adaption laws are designed to compensate for the system uncertainties. By using the proposed adaptive IBLF-based boundary control, the vibration of the Timoshenko beam system is suppressed greatly, without any discretisation or simplification of the dynamics in the time and space. The proposed adaptive IBLF-based boundary controls also guarantee that boundary outputs always remain in the constrained space, subject to significantly relaxed feasibility conditions. In the end, numerical simulations are displayed to illustrate the performance of the proposed control.