Adaptive inverse backlash boundary vibration control design for an Euler–Bernoulli beam system

• Published in: Journal of the Franklin Institute Vol. 357; no. 6; pp. 3434 - 3450
• Main Authors: He, Xiuyu, Song, Yuhua, Han, Zhiji, Zhang, Shuang, Jing, Peng, Qi, Suwen
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.04.2020; Elsevier Science Ltd
• Subjects: Adaptive control; Beamforming; Control stability; Control theory; Disturbance observers; Euler-Bernoulli beams; Eulers equations; Nonlinear systems; Nonlinearity; Parameter uncertainty; Simulation; Stability analysis; Vibration; Vibration control
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2019.12.034

In this paper, we address the vibration suppression problem of an Euler–Bernoulli beam structure suffering from the input backlash nonlinearity and the unknown disturbance. Considering the nonlinearity and discontinuity of the backlash with the uncertain parameter, an adaptive inverse backlash dynamics is proposed to handle the nonlinear characteristic and correct the mismatch of the backlash parameter. Further, an adaptive vibration control law is developed to improve the system performance via combining with the proposed inverse backlash dynamics. Meanwhile, a disturbance observer is designed to reject the external boundary disturbance, and we bring a logarithmic barrier function in control design to ensure the end-point displacement of this system be constrained in the desired limitation. At last, we analyze the stability of this flexible system and the effectiveness of the proposed control method with simulation experiments.