Adaptive time-varying constraint control for uncertain flexible beam systems

Abstract

In this paper, the vibration control design of the Euler–Bernoulli beam with time-varying constraints is studied when the mass, bending stiffness and tension of the system parameters are known or unknown. For satisfying the time-varying constraints, the controller is designed and the system stability is analysed based on the tangent barrier Lyapunov function (TAN-BLF). Among them, the uncertainty of system parameters is dealt with by the adaptive method. In both cases, the vibration of the Euler–Bernoulli beam can be well restrained without violating the constraint conditions, and all signals in the system are bounded. Finally, the effectiveness of the proposed method is illustrated by a simulation example.

Keywords:

• Euler–Bernoulli beam
• time-varying constraints
• TAN-BLF
• adaptive method

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported in part by the National Natural Science Foundation of China [grant numbers 62025303, 61973147, and 62273171], in part by the LiaoNing Revitalization Talents Program [grant number XLYC2007177], in part by the Doctoral Research Initiation of Foundation of Liaoning Province [grant number 2020-BS-243].