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This work focuses on control of a batch protein crystallization process that produces tetragonal hen egg-white (HEW) lysozyme crystals. First, a population balance model, which incorporates experimentally-determined nucleation and growth rates, is used to simulate the evolution of the entire crystal size distribution (CSD). Then, a reduced-order model, which describes the evolution of the dominant moments of the CSD and of the solute concentration and crystallizer temperature, is derived and used for controller design. A predictive controller is designed to achieve the objective of maximizing the volume-averaged crystal size while respecting constraints on the manipulated input variable and the process state variables including constraints on the shape of the CSD. Simulation results demonstrate that the proposed predictive controller is able to increase the volume-averaged crystal size by 30% and 8.5% compared to constant temperature control (CTC) and constant supersaturation control (CSC) strategies, respectively, while reducing the number of fine crystals produced. The robustness of the proposed control method with respect to: (a) plant-model mismatch, and (b) open-loop operation, is also successfully demonstrated.