This work presents the Czochralski growth dynamics as time-varying delay based model, applied to the growth of La3Ga5.5Ta0.5O14 (LGT) piezoelectric crystals. The growth of high-quality large-diameter oxides by Czochralski technique requires the theoretical understanding and optimization of all relevant process parameters, growth conditions, and melts chemistry. Presently, proportional-integral- derivative (PID) type controllers are widely accepted for constant-diameter crystal growth by Czochralski. Such control systems, however, do not account for aspects such as the transportation delay of the heat from crucible wall to the crystal solidification front, heat radiated from the crucible wall above the melt surface, and varying melt level. During crystal growth, these time delays play a dominant role, and pose a significant challenge to the control design. In this study, a time varying linear delay model was applied to the identification of nonlinearities of the growth dynamics. Initial results reveled the benefits of this model with actual growth results. These results were used to develop a long-range model predictive control system design. Two different control techniques using long range prediction are studied for the comparative study. Development and testing of the new control system on real time growth system are discussed in detail. The results are promising and suggest future work in this direction. Other discussion about the problems during the crystal growth, optimization of crystal growth parameters are also studied along with the control system design.