Predictive modeling and robust nonlinear control of a polysilicon reactor system for enhanced solar cell production

Solar-grade silicon production is a critical component in the solar energy sector, with fluidized-bed reactors (FBRs) emerging as a promising alternative offering superior energy efficiency and operational advantages over conventional technologies. However, the operational complexity of FBR systems poses significant challenges to effectively controlling their operation at optimal conditions. This study introduces a predictive modeling framework for silicon production in fluidized bed reactors to characterize both the particle size distribution of the product and powder loss. Two different flow regime modeling approaches are explored to describe the silane pyrolysis reaction and illustrate how the deposition rate affects particle growth and powder loss. A discrete population balance equation is employed to estimate the particle size distribution as a function of the deposition rate. Subsequently, a robust nonlinear model predictive control (RNMPC) approach is utilized to regulate the system at the desired operating conditions, stabilize the product particle size distribution, and minimize powder loss. Detailed open-loop and closed-loop simulation studies demonstrate the successful integration of RNMPC and the proposed predictive modeling approach.