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

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.

Inspec keywords: vibration control; compensation; Lyapunov methods; adaptive control; uncertain systems; partial differential equations

Other keywords: vibration suppression; numerical simulations; system uncertainty compensation; adaptive boundary control; inhomogeneous Timoshenko beam equations; boundary output constraints; integral-Barrier Lyapunov function; adaptive IBLF-based boundary control; Timoshenko beam system

Subjects: Differential equations (numerical analysis); Self-adjusting control systems; Vibrations and shock waves (mechanical engineering); Numerical analysis; Stability in control theory; Mechanical variables control

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http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2013.0601
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