Modeling and control of particulate processes and application to poly-silicon production

Abstract

The population balance is used to develop a model and control system strategies for poly-silicon production in a fluidized bed reactor (FBR). An energy function is developed to study the stability property of particle growth. An analytical expression for the stationary distribution function is derived and compared with simulation and experimental results. The distribution is stable if the seed particles are sufficiently large. A novel discretization scheme solves the population balance equations. We demonstrate the equivalence of the continuous and discretized population balance. An equivalent stability condition for the discretized population balance is derived using Tellegen's theorem. Finally we design an inventory control system to control the particle size distribution. The zero-dynamics, i.e. the dynamics of particle phase, are asymptotically stable if the seed particles are sufficiently large.