Vibration control for a nonlinear three-dimensional Euler-Bernoulli beam under input magnitude and rate constraints

In this paper, the vibration control problem for the nonlinear three-dimensional Euler-Bernoulli beam with input magnitude and rate constraints is addressed. By using the backstepping method with smooth hyperbolic tangent function, a boundary control scheme is designed to suppress vibration of the nonlinear three-dimensional Euler-Bernoulli beam and to satisfy the input magnitude and rate constraints. It is proved that the proposed control scheme can handle the vibration and input magnitude and rate constraints simultaneously. Finally, numerical simulations illustrate the effectiveness of the proposed control.