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

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 Hamilton’s principle Galerkin projection method, dynamic of piezoelectric actuator constructed in partial differential equations simplified to ordinary design. Then, introducing fast nonsingular terminal sliding mode surface, function based proposed, which means Lyapunov used guarantee finite time stability restriction. Further, deal an updating incorporated on function, proof shows that can ensure disturbance rejection uncertainties compensation simultaneously. Finally, effectiveness laws demonstrated numerical simulations.