Extended kalman filter based nonlinear geometric control of a seeded batch cooling crystallizer

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 (NCC) 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.

[1]  Sohrab Rohani,et al.  A simplified approach to the operation of a batch crystallizer , 1990 .

[2]  J. W. Mullin,et al.  Programmed cooling of batch crystallizers , 1971 .

[3]  Costas Kravaris,et al.  Geometric methods for nonlinear process control. 2. Controller synthesis , 1990 .

[4]  B. Ogunnaike.  Controller design for nonlinear process systems via variable transformations , 1986 .

[5]  R. Kopp,et al.  LINEAR REGRESSION APPLIED TO SYSTEM IDENTIFICATION FOR ADAPTIVE CONTROL SYSTEMS , 1963 .

[6]  G. R. Sullivan,et al.  Generic model control (GMC) , 1988 .

[7]  J. Kantor,et al.  AN EXOTHERMIC CONTINUOUS STIRRED TANK REACTOR IS FEEDBACK EQUIVALENT TO A LINEAR SYSTEM , 1985 .

[8]  Manfred Morari.  SOME COMMENTS ON THE OPTIMAL OPERATION OF BATCH CRYSTALLIZERS , 1980 .

[9]  Jaroslav Nývlt,et al.  Programmed cooling of batch crystallizers , 1988 .

[10]  Manfred Morari,et al.  Design of resilient processing plants—V: The effect of deadtime on dynamic resilience , 1985 .

[11]  Sohrab Rohani,et al.  Self-tuning control of crystal size distribution in a cooling batch crystallizer , 1990 .

[12]  J. Kantor,et al.  Global linearization and control of a mixed-culture bioreactor with competition and external inhibition , 1986 .

[13]  C. Kravaris,et al.  Nonlinear State Feedback Synthesis by Global Input/Output Linearization , 1986, 1986 American Control Conference.

[14]  Sohrab Rohani,et al.  Control of crystal size distribution in a batch cooling crystallizer , 1990 .

[15]  Jeffrey C. Kantor,et al.  LINEAR FEEDBACK EQUIVALENCE AND CONTROL OF AN UNSTABLE BIOLOGICAL REACTOR , 1986 .

[16]  M. B. Ajinkya,et al.  ON THE OPTIMAL OPERATION OF CRYSTALLIZATION PROCESSES , 1974 .

[17]  Allan S. Myerson,et al.  Solvent selection and batch crystallization , 1986 .

[18]  M. R. Chivate,et al.  EFFECT OF SEED CONCENTRATION IN A BATCH DILUTION CRYSTALLIZER , 1979 .

[19]  Å. Rasmuson,et al.  Application of controlled cooling and seeding in batch crystallization , 1992 .

[20]  J. W. Mullin,et al.  Programmed cooling crystallization of potassium sulphate solutions , 1974 .

[21]  M. Aluko.  LINEAR FEEDBACK EQUIVALENCE AND NONLINEAR CONTROL OF A CLASS OF TWO-DIMENSIONAL SYSTEMS , 1988 .

[22]  Fernando V. Díez,et al.  Programmed cooling control of a batch crystallizer , 1995 .

[23]  Henry Cox,et al.  On the estimation of state variables and parameters for noisy dynamic systems , 1964 .

[24]  J. Rawlings,et al.  Model identification and control of solution crystallization processes: a review , 1993 .

[25]  James B. Rawlings,et al.  Model identification and control strategies for batch cooling crystallizers , 1994 .

[26]  C. Kravaris,et al.  Geometric methods for nonlinear process control. 1. Background , 1990 .