MODEL IDENTIFICATION AND CONTROL STRATEGIES FOR BATCH COOLING CRYSTALLIZERS

The open-loop optimal control strategy to regulate the crystal-size distribution of batch cooling crystallizers handles input, output, and final-time constraints, and is applicable to crystallization with size-dependent growth rate, growth dispersion, and fines dissolution. The objective function can be formulated to consider solid-liquid separation in subsequent processing steps. A model-based con trol algorithm requires a model that accurately predicts system behavior. Uncertainty bounds on model parameter estimates are not reported in most crystallization model identification studies. This obscures the fact that resulting models are often based on experiments that do not provide sufficient information and are therefore unreliable. A method for assessing parameter uncertainty and its use in experimental design are presented. Measurements of solute concentration in the continuous phase and the transmittance of light through a slurry sample allow reliable parameter estimation. Uncertainty in the parameter estimates is decreased by data from experiments that achieve a wide range of supersaturation. The sensitivity of the control policy to parameter uncertainty, which connects the model identification and control problems, is assessed. The model identification and control strategies were experimentally verified on a bench-scale KNO3-H2O system. Compared to natural cooling, increases in the weight mean size of up to 48% were achieved through implementation of optimal cooling policies.