Parameter impulse control of chaos in crystal growth process

Abstract

Chaos occurs in the crystal growth process as an irregular swing phenomenon in the flexible shaft rotating-lifting (FSRL) system. Chaos may lead to the failure of mono-silicon crystal production. Therefore, it should be suppressed. Many chaos control methods have been proposed theoretically and some of them have been used in applications. For a practical plant displaying harmful chaos, engineers from a specific area usually face with the challenge to identifying chaos and to suppress it using a proper method. However, despite of the existing methods, chaos control method for the FSRL system is not a trivial task. For example, the seminal chaos control method proposed by Ott-Grebogi-Yorke (OGY method) requires a proper practical adjustable parameter, which cannot be identified for the FSRL system. In this work, an impulsive control method is being proposed to suppress chaos in the system. The merits of the method lie in, first, it manipulates the rotation speed of the motor, which is the only and easily accessible parameter; second, it does not need the state feedback, which is unavailable in the system; third, it is robust against the bounded system parameter uncertainty, as a plant requirement. The control parameter precept is obtained by using the Melnikov method. Simulation results verify the correctness of our theoretical analysis and the effectiveness of the proposed chaos control method.