Advanced Batch Crystallizer Control

The use of the supersaturation as the measured variable for a control algorithm was first suggested by Han (1969). Rousseau and Howell (1982) used simulations to demonstrate that the substitution of the supersaturation for in Eq. (9.10) could stabilize a cycling crystallizer. While the on-line supersaturation measurement is in general more easily obtained than the determination of properties of the CSD, it is pointed out that the scheme based on supersaturation measurement is more sensitive to measurement noise. 

One of the primary motivations for feedback is to overcome model uncertainty. For the controller to work well in practice, it should be tuned to be robustly stabilizing. That is, the controller should not only stabilize the nominal model, but also all models within some uncertainty region that reflects how well the system has been identified. The areas of robust stability and robust performance are current topics of control research. To date, essentially none of this research has been applied to crystallization. 

There have been relatively few studies of multi-variable controllers for continuous crystallizers. Most studies of MIMO control algorithms are based on linear state-space models of the form 

Nevertheless, as discussed previously, the physical model for a crystallizer is an integro-partial differential equation. A common method for converting the population balance model to a state-space representation is the method of moments however, since the moment equations close only for a MSMPR crystallizer with growth rate no more than linearly dependent on size, the usefulness of this method is limited. The method of lines has also been used to cast the population balance in state-space form (Tsuruoka and Randolph 1987), and as mentioned in Section 9.4.1, the blackbox model used by de Wolf et al. (1989) has a state-space structure. 

Hashemi and Epstein (1982) linearized the set of ordinary differential equations (ODEs) resulting from the application of the method of moments on an MSMPR crystallizer model and used singular value decomposition to define controllability and observability indices. These indices aid in selecting measurements and manipulated and control variables. Myerson et al. (1987) suggested the manipulation of the feed flow rate and the crystallizer temperature according to a nonlinear optimal stochastic control scheme with a nonlinear Kalman filter for state estimation. 

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Nagy, Z.K. Chew, J.W. Fujiwara, M. Braatz, R.D. Advances in the modeling and control of batch crystallizers. Proceedings of the I FAC Symposium on Advanced Control of Chemical Processes, Jan 11-14, 2004 7th International Symposium on Advanced Control of Chemical Processes Hong Kong, 83-90. 

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