Data-driven robust adaptive control based on multi-step error feedback for silicon single crystal diameter control in Czochralski process

Aiming at the limitations of the previous crystal diameter control in the Czochralski silicon single-crystal (Cz-SSC) growth process that relies on the mechanism model and pulling speed regulation, this paper proposes a data-driven robust adaptive control method based on multi-step error feedback. First, the dynamic linearization technique is used to transform the Cz-SSC growth system into an affine form associated with the control input, and the perturbations and uncertainties in the system are attributed to a nonlinear term; subsequently, the extended state observer (ESO) is designed to estimate this nonlinear uncertainty term to achieve effective compensation of the perturbations; and finally, the robust adaptive control law based on multi-step error feedback is constructed. The method only relies on the input and output data of the system without additional model information. Simulation experimental results show that the method can effectively realize accurate and stable control of crystal diameter under different external disturbance conditions.