A nonlinear dynamic model of a seeded potash alum batch cooling crystallizer is presented. The model of the batch crystallizer is based on the conservation principles of mass, energy and population. In order to maintain constant supersaturation, a nonlinear geometric feedback controller is implemented. It is shown that compared to a natural and a simplified optimal cooling policies, the nonlinear geometric control (NGC) leads to a substantial improvement of the final crystal quality. An extended Kalman filter (EKF) is used as a closed loop observer for this nonlinear system to predict the non-measurable state variables. It is found that the EKF is capable of effectively predicting the first four leading moments of the population density function. The effectiveness of the EKF based nonlinear geometric controller in the presence of plant/model mismatch is also studied. Simulation results show that the EKF based nonlinear geometric controller is reasonably robust in the presence of modeling error.