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In this paper, a novel adaptive asymmetrical barrier function-based vibration control law is proposed for the nonlinear flexible cantilever beam system with obstacle restriction, model uncertainties, and distributed disturbances. Firstly, by employing the Hamilton's principle and the Galerkin projection method, the dynamic of the nonlinear flexible cantilever beam with the piezoelectric actuator is constructed in partial differential equations and simplified to nonlinear ordinary differential equations for the control law design. Then, by introducing the fast nonsingular terminal sliding mode surface, a novel asymmetrical barrier function based sliding mode control law is proposed, in which by means of a novel asymmetrical barrier Lyapunov function is used to guarantee the finite time stability with the obstacle restriction. Further, to deal with the model uncertainties, an adaptive updating law is incorporated with the fast nonsingular terminal sliding mode control law based on asymmetrical barrier function, stability proof shows that the proposed control law can ensure the distributed disturbance rejection and the model uncertainties compensation simultaneously. Finally, the effectiveness of the proposed control laws is demonstrated by the numerical simulations.

Asymmetrical Barrier Function-Based Adaptive Vibration Control for Nonlinear Flexible Cantilever Beam With Obstacle Restriction