Adaptive time-varying constraint control for uncertain flexible beam systems

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.