Suppressing chaos in crystal growth process using adaptive phase resonant perturbation

• Published in: Nonlinear dynamics Vol. 108; no. 3; pp. 2655 - 2669
• Main Authors: Zhou, Zi-Xuan, Ren, Hai-Peng, Grebogi, Celso
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.05.2022; Springer Nature B.V
• Subjects: Amplitudes; Automotive Engineering; Classical Mechanics; Control; Control methods; Crystal growth; Crystals; Dynamical Systems; Engineering; Force measurement; Kalman filters; Liapunov exponents; Mechanical Engineering; Original Paper; Perturbation methods; Rotating shafts; Rotation; Vibration; Resonant perturbation; Chaos suppression; Flexible shaft rotating-lifting system; Crystal growth technique; Lyapunov exponent
• DOI: 10.1007/s11071-022-07333-6
• ISSN: 0924-090X

Chaos occurs in the flexible shaft rotating-lifting (FSRL) system of crystal growth process. Chaotic swing does harm to the quality of mono-silicon crystal production. Therefore, it must be suppressed. Previous studies have proposed impulse control method to suppress the chaos in crystal growth process. However, the impulses require sudden and intermittent changes to the rotation speed, which are difficult to implement through the soft rope connection. In this work, a small amplitude resonant perturbation to the rotation speed is being proposed to suppress chaos in the FSRL system. The system state, given by the swing angle between the rotation center on the vertical axis and the soft shaft, is observed by measuring the force on the soft shaft and by using the untraced Kalman filter. The control parameters are selected by calculating the Lyapunov exponent. As compared with the previous impulse control methods, the proposed small amplitude resonant perturbation method engenders a small continuous change instead of the sudden change in the rotation speed. In addition, the proposed method does not alter the average rotation speed, which complies with the crystal growth technique requirement. The effectiveness of the proposed chaos control method is validated by numerical simulations.