Stabilization of an Euler–Bernoulli beam with input delay in the boundary control

2012 ◽  
Vol 61 (11) ◽  
pp. 1069-1078 ◽  
Author(s):  
Ying Feng Shang ◽  
Gen Qi Xu
Keyword(s):  
Boundary Control ◽  
Input Delay ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam

Stability analysis of Euler-Bernoulli beam with input delay in the boundary control

2010 ◽  
Vol 14 (1) ◽  
pp. 186-196 ◽  
Author(s):  
Ying Feng Shang ◽  
Gen Qi Xu ◽  
Yun Lan Chen
Keyword(s):  
Stability Analysis ◽  
Boundary Control ◽  
Input Delay ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam

Active vibration control of a nonlinear three-dimensional Euler–Bernoulli beam

2016 ◽  
Vol 23 (19) ◽  
pp. 3196-3215 ◽  
Author(s):  
Wei He ◽  
Chuan Yang ◽  
Juxing Zhu ◽  
Jin-Kun Liu ◽  
Xiuyu He
Keyword(s):  
Differential Equations ◽  
Boundary Control ◽  
Coupling Effect ◽  
Three Dimensional ◽  
Uniform Boundedness ◽  
Transverse Displacement ◽  
Axial Deformation ◽  
Bernoulli Beam ◽  
Parameter Uncertainties ◽  
Euler Bernoulli Beam

In this paper, boundary control is designed to suppress the vibration of a nonlinear three-dimensional Euler–Bernoulli beam. Considering the coupling effect between the axial deformation and the transverse displacement, the dynamics of the beam are modeled as a distributed parameter system described by three partial differential equations (PDEs) and 12 ordinary differential equations (ODEs). Firstly, model-based boundary control is designed based on a mathematical model of the system. Subsequently, adaptive control is proposed when there are parameter uncertainties in the model. The uniform boundedness and uniform ultimate boundedness are proved under the proposed control laws. Finally, numerical simulations illustrate the effectiveness of the results.

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