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.