Backstepping Control for Vibration Suppression of 2-D Euler-Bernoulli Beam Based on Nonlinear Saturation Compensator

In this article, a boundary control scheme is proposed to suppress 2-D vibration of Euler-Bernoulli beam with output constraints and input saturation. The original partial differential equations (PDEs) model is transformed to a new form containing virtual control. Then a boundary controller is designed via the backstepping method to suppress the coupled vibration. The hyperbolic tangent function and Nussbaum function are employed to deal with the input saturation. A barrier Lyapunov function with time adjusting function is introduced to suppress the structural vibration of Euler-Bernoulli beam with arbitrary initial conditions. The disturbance observer is designed to deal with the unknown boundary disturbance. Finally, the simulation results show the effectiveness of the proposed vibration controller.