Suppression of flow oscillations in a vertical Bridgman crystal growth system

Abstract

We consider the feedback control of flows in a vertical Bridgman crystal growth system. The vertical Bridgman process is used to grow single crystals for a wide array of applications, ranging from lasers to highspeed microelectronics to infrared sensors. We model the Bridgman system using conservation equations for energy and momentum and physically reasonable boundary and initial conditions. The Galerkin finite element method is used to spatially discretize this nonlinear, differential-algebraic equation set. We consider a prototypical Bridgman system experiencing a time-varying disturbance to its furnace temperature profile. A single-input single-output control system is considered for controller design. Proportional, proportional-integral, and input-output linearizing controllers are applied to the vertical Bridgman model to attenuate the flow oscillations. The volume-averaged flow kinetic energy is chosen as the single controlled output. The flows are controlled via rotation of the crucible containing the molten material. Simulation results show that nonlinear control is superior to P and PI control in the suppression of the flow oscillations.