A simulation algorithm for crystal size distribution dynamics in a continuous crystallizer was developed using the method of lines. Dimensionless crystal sizes, in vector form, were used as state variables. Simulation results using this algorithm satisfied stability criteria for continuous crystallizers, which had been developed previously using different methods. The use of a state space representation of the algorithm permits the use of well-known theoretical and numerical approaches to the modeling of an experimental R-z crystallizer and for design of a proportional controller for a continuous crystallizer system. Boundary conditions defined by the nucleation/growth rate kinetics were separately written as an auxiliary function so that other kinetics can be substituted without any change of the main algorithm. This implies that the algorithm is applicable for any growth-type particulate system. CSD dynamics from an experimental crystallizer were satisfactorily modelled using this algorithm with reasonable parameters: e.g. the recycle ratios of the fines dissolver and the product classifier, crystal sizes at the upper cut size of the dissolver and at the lower cut size of the classifier, initial CSD, and the form of the upset. Algorithms for controller design using pole placement and optimization techniques were applied to develop a proportional matrix controller for an R-z crystallizer. It was evident that pole placement is a better method than optimization to design a controller for this crystallizer system. The system poles are concentrated at a point and it is necessary to assign the controller poles further apart to obtain appropriate control. To summarize controller design using the pole placement method, a schematic flow diagram of a system controller using the minimum order Luenberger observer was illustrated. In this example, only a few population densities need to be measured to drive the controller.
展开▼
