Use of a Kalman filter to reconstruct particle size distributions from FBRM measurements

Chemical Engineering Science

Volumn 70, Issue , 2012, Pages 99-108

  Mangold, Michael ^a  

^a MAX PLANCK INSTITUTE FOR DYNAMICS OF COMPLEX TECHNICAL SYSTEMS   (Germany)

Author keywords

Crystallisation; FBRM; Kalman filter; Particulate processes; Population balance; Process control

Indexed keywords

CHORD LENGTH DISTRIBUTION; DIRECT INVERSION; FBRM; ILL POSED PROBLEM; MEASUREMENT EQUATIONS; MEASUREMENT PROCEDURES; PARTICULATE PROCESS; POPULATION BALANCES; PROCESS KNOWLEDGE;

CRYSTALLIZATION; KALMAN FILTERS; PARTICLE SIZE ANALYSIS; PROCESS CONTROL; SIZE DISTRIBUTION;

PARTICLE SIZE;

EID: 84855460598     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ces.2011.05.052     Document Type: Article

References (25)

1. Bück A., Peglow M., Tsotsas E., Mangold M., Kienle A. Model-based measurement of particle size distributions in granulation processes - theoretical considerations and results. AIChE J. 2011, 57:929-941.
2. Corriou J.R., Rohani S. Nonlinear control of a batch crystallizer. Chem. Eng. Commun. 2002, 189:1415-1436.
3. Eek R.A., Dijkstra S. Design and experimental validation of a state estimator for a crystallization process. Ind. Eng. Chem. Res. 1995, 34:567-574.
4. Applied Optimal Estimation 1974, The M.I.T. Press. A. Gelb (Ed.).
5. Grover M.A., Barthe S.C., Rousseau R.W. Principal component analysis for estimating population density from chord-length density. AIChE J. 2009, 55:2260-2270.
6. Hermanto M.W., Chiu M., Braatz R. Nonlinear model predictive control for the polymorphic transformation of L-glutamic acid crystals. AIChE J. 2009, 55:2631-2645.
7. Hukkanen E., Braatz R. Measurement of particle size distribution in suspension polymerisation using in situ laser backscattering. Sens. Actuators B 2003, 96:451-459.
8. Kail N., Marquardt W., Briesen H. Estimation of particle size distributions from focused beam reflectance measurements based on an optical model. Chem. Eng. Sci. 2009, 64:984-1000.
9. Kail N., Marquardt W., Briesen H. Process analysis by means of focused beam reflectance measurements. Ind. Eng. Chem. Res. 2009, 48:2936-2946.
10. Kleinert T., Weickgenannt M., Judat B., Hagenmeyer V. Cascaded two-degree-of-freedom control of seeded batch crystallisations based on explicit system inversion. J. Process Control 2010, 20:29-44.
11. Li M., Wilkinson D. Determination of non-spherical particle size distribution from chord length measurements. Chem. Eng. Sci. 2005, 60:3251-3265.
12. Liu W., Clark N.N. Relationships between distributions of chord lengths and distributions of bubble sizes including their statistical parameters. Int. J. Multiphase Flow 1995, 21:1073-1089.
13. Luenberger D. Linear and Nonlinear Programming 1996, Addison-Wesley.
14. Mahoney A.W., Lorenz L., Perlberg A., Seidel-Morgenstern A. Determination of particle size distributions from inline laser backscattering measurements. Chem. Eng. Trans. 2002, 1:197-202.
15. Mangold M., Bück A., Schenkendorf R., Steyer C., Voigt A., Sundmacher K. Two state estimators for the barium sulfate precipitation in a semi-batch reactor. Chem. Eng. Sci. 2009, 64:646-660.
16. Nagy Z.K., Braatz R.D. Robust nonlinear model predictive control of batch processes. AIChE J. 2003, 49:1776-1786.
17. Ramkrishna D. Population Balances: Theory and Applications to Particulate Systems in Engineering 2000, Academic Press.
18. Rawlings J., Miller S., Witkowski W. Model identification and control of solution crystallization processes: a review. Ind. Eng. Chem. Res. 1993, 32:1275-1296.
19. Ruf A., Worlitschek J., Mazzotti M. Modeling and experimental analysis of PSD measurements through FBRM. Part. Part. Syst. Charact. 2000, 17:167-179.
20. Tadayyon A., Rohani S. Determination of particle size distribution by Par-Tec 100: modeling and experimental results. Part. Part. Syst. Charact. 1998, 15:127-135.
21. Tadayyon A., Rohani S. Extended Kalman filter-based nonlinear model predictive control of a continuous KCl-NaCl crystallizer. Can. J. Chem. Eng. 2001, 79:255-262.
22. Worlitschek J., Hocker T., Mazzotti M. Restoration of PSD from chord length distribution data using the method of projections onto convex sets. Part. Part. Syst. Charact. 2005, 22:81-98.
23. Wynn E. Relationship between particle-size and chord-length distributions in focused beam reflectance measurement: stability of direct inversion and weighting. Powder Technol. 2003, 133:125-133.
24. Xie W., Rohani S. Application of extended Kalman filter to a batch cooling crystallizer. Sep. Sci. Technol. 2001, 36:3049-3069.
25. Xie W., Rohani S., Phoenix A. Extended Kalman filter based nonlinear geometric control of a seeded batch cooling crystallizer. Can. J. Chem. Eng. 2002, 80:167-172.