Bi-directional impulse chaos control in crystal growth

Mono-silicon crystals, free of defects, are essential for the integrated circuit industry. Chaotic swing in the flexible shaft rotating-lifting (FSRL) system of the mono-silicon crystal puller causes harm to the quality of the crystal and must be suppressed in the crystal growth procedure. From the control system viewpoint, the constraints of the FSRL system can be summarized as not having measurable state variables for state feedback control, and only one parameter is available to be manipulated, namely, the rotation speed. From the application side, an additional constraint is that the control should affect the crystallization physical growth process as little as possible. These constraints make the chaos suppression in the FSRL system a challenging task. In this work, the analytical periodic solution of the swing in the FSRL system is derived using perturbation analysis. A bi-directional impulse control method is then proposed for suppressing chaos. This control method does not alter the average rotation speed. It is thus optimum regarding the crystallization process as compared with the single direction impulse control. The effectiveness and the robustness of the proposed chaos control method to parameter uncertainties are validated by the simulations.