Stabilisation of Timoshenko beam system with a tip payload under the unknown boundary external disturbances

Abstract

This paper is concerned with the boundary stabilisation of a Timoshenko beam with a tip payload under the boundary external disturbances. Nonlinear feedback control laws are designed to reduce the effects of the external disturbances. Since the controlled system is nonlinear, the well posedness of the nonlinear closed-loop system is investigated using the theory of nonlinear maximal monotone operators and the variational principle. In addition, we show the exponential stability of the nonlinear controlled system using the Lyapunov direct method. In the end, the numerical simulations are displayed to illustrate the effectiveness of the proposed boundary controls.

Stabilization of a Timoshenko Beam With Disturbance Observer‐Based Time Varying Boundary Controls

“…Besides, the local enlarged images located in the lower right corner of Fig. 3 indicate that the control law (18) can obviously attenuate the chattering phenomenon, compared with the SMC law in [33]. This illustrates the advantages of ADRC method.…”

Vibration Control of a Flexible Spacecraft System With Input Backlash

“…In [33], a robust adaptive boundary control for an axially moving string is investigated, by applying a hydraulic actuator at the right boundary of the string. In [34], the stabilization of a Timoshenko beam with a tip payload subjected to boundary external disturbances is considered. The effects of the external disturbances have been eliminated according to design some nonlinear feedback control laws.…”

Boundary vibration control for a flexible Timoshenko robotic manipulator

“…For the practice flexible robotic manipulator, the shear deformation has great influence on the performance of the flexible system and cannot be ignored in the dynamic analysis because of the small span of the link and it is more accurate to regard it as the flexible Timoshenko robotic manipulator. In [36,37], Xu et al studied a Timoshenko cantilever beam and active controllers were designed to stabilise the flexible beam. In [38], a Timoshenko beam with an input constraint was investigated and the boundary control was proposed to reduce the elastic deflection and the shear deformation.…”