Robust Control of Particle Size Distribution in Aerosol Processes
Keywords:
particle size distribution, aerosol process, population balance, nonlinear systems, robust controlAbstract
This paper deals with a comprehensive study on robust control of particle size distribution of fractal agglomerate in aerosol processes with simultaneous chemical reaction, nucleation, condensation and coagulation. Firstly, a general aerosol process is described by population balance and mass and energy balances, which describes the evolution of particle size distribution, continuous phase species and temperature of the aerosol system, respectively. A lognormal moment approximations of the population balance model is then presented. Then, the robust state feedback controller is designed for the aerosol process with some unknown uncertainties, the proposed controller is composed of an nominal control term and a robust control term so that it only ensures the stability of the closed-loop system, but also attenuates the effect of the unknown uncertainties on the system. A high-gain observer is adopted to estimate state variables required in the on-line implementation of the state feedback. Finally, the proposed robust controller is applied to an aerosol process for achieving an aerosol size distribution with desired geometric average particle diameter, the simulation results show the robustness properties of the controller with respect to parametric model uncertainty and unmodeled dynamics.References
J. M. Hidy and J. R. Brock, The Dynamic of Aerocolloidal System, Oxford, Pergamon Press, 1970.
V. M. Voloshuk, and Y. S. Sedunov,Coagulation phenomena in disperse systems, Moscow: Moskovskiy Inghenerno Fizicheskiy Institut, 1975 (in Russia)
V. N. Piskunov, Physical phenomena in disperse systems, Leninggrad: Gidrometeoizdat Publishers, 1991 (in Russia)
M. J. Hounslow, A discretized population balance for continuous systems at steady-state. American Institute of Chemical Engineers Journal, 36, pp. 106-116,1990 http://dx.doi.org/10.1002/aic.690360113
P. J. Hill, and K. M. Ng, New discretization procedure for the breakage equation. American Institute of Chemical Engineers Journal, 41, pp. 1204-1216, 1995 http://dx.doi.org/10.1002/aic.690410516
P. J. Hill, and K. M. Ng, New discretization procedure for the agglomeration equation. American Institute of Chemical Engineers Journal, 42, pp. 727-741, 1996 http://dx.doi.org/10.1002/aic.690420313
N. V. Mantzaris, P. Daoutidis, and F. Srienc, Numerical solution of multivariable cell population balance models. Parts: I, II and III. Computers and Chemical Engineering, 25, pp. 1411-1481, 2001 http://dx.doi.org/10.1016/S0098-1354(01)00709-8
M. Nicmanis, and M. J. Hounslow, Finite-element methods for steady-state population balance equations. American Institute of Chemical Engineers Journal, 44, pp. 2258-2272, 1998 http://dx.doi.org/10.1002/aic.690441015
J. D. Landgrebe, and S. E. Pratsinis, A discrete sectional model for particulate production by gas phase chemical reaction and aerosol coagulation in the free molecular regime. Journal of Colloid Interface Science, 139, pp. 63-86, 1990 http://dx.doi.org/10.1016/0021-9797(90)90445-T
E. Otto, H. Fissan, S. H. Park, and K. W. Lee, The Log-Normal Size Distribution Theory of Brownian Aerosol Coagulation for the Entire Particle Size Range. Part I: Analytical Solution Using the Harmonic Mean Coagulation Kernel, Journal of Aerosol Science, Vol. 30. No. 1 pp. 3-16, 1999
S. H. Park, and K. W. Lee, Analytical Solution to change in size distribution of polydisperse particles in closed chamber due to diffusion and sedimentation, Atmospheric Environment, Vol. 36. pp. 5459-5467, 2002 http://dx.doi.org/10.1016/S1352-2310(02)00673-8
S. H. Park, and K. W. Lee, Change in particle size distribution of fractal agglomerates during Browian coagulation in the free-molecule regime, Journal of Colloid and Intreface Science, Vol. 246. pp. 85-91, 2002 http://dx.doi.org/10.1006/jcis.2001.7946
V. N. Piskunov, and A. I. Golubev, The Generalized Approximation Method for Modelling Coagulation Kinetics ¨C Part I: Justification and Implementation of the Method, Journal of Aerosol Science, Vol. 33, pp. 51-63,2002 http://dx.doi.org/10.1016/S0021-8502(01)00073-8
P. Daoutidis, and P. D. Christofides, Dynamic feedforward/output feedback control of nonlinear processes, Chemical Engineering Science, Vol. 50, pp. 1889-2007, 1995 http://dx.doi.org/10.1016/0009-2509(95)00016-X
A. Kalani, and P. D. Christofides, Nonlinear control of spatially-in homogeneous aerosol processes, Chemical Engineering Science,Vol. 54, pp. 2669-2678, 1999 http://dx.doi.org/10.1016/S0009-2509(98)00315-7
T. J. Crowley, E. S. Meadows, E. Kostoulas, and F. J. Doyle III, Control of Particle Size Distribution Described by a Population Balance Model of Semibatch Emulsion Polymerization, Journal of Process Control, Vol.10, 419-432, 2000. http://dx.doi.org/10.1016/S0959-1524(00)00017-2
D. Semino, andW. H. Ray, Control of systems described by population balance equations-II. Emulsion polymerization with constrained control action, Chemical Engineering Science, Vol.50, pp. 1825-1839, 1995. http://dx.doi.org/10.1016/0009-2509(95)00015-W
T. Chiu, and P. D. Christofides, Nonlinear control of particulate processes, American Institute of chemical Engineers Journal,Vol. 45, pp. 1279-1297, 1999.
N. H. El-Farra, T. Chiu, and P. D. Christofides, Analysis and control of particulate processes with input constraints, American Institute of Chemical Engineering Journal, 47, pp. 1849-1865, 2001. http://dx.doi.org/10.1002/aic.690470815
A. Kalani, and P. D. Christofides, Modeling and control of a titania aerosol reactor, Aerosol Science and Technology, 32, pp. 369-391, 2000. http://dx.doi.org/10.1080/027868200303687
A. Kalani, and P. D. Christofides, Simulation, estimation and control of size distribution in aerosol processes with simultaneoue reaction, nucleation, condensation and coagulation, Computers and Chemical Engineering, 26, pp. 1153-1169, 2002. http://dx.doi.org/10.1016/S0098-1354(02)00032-7
S. K. Friedlander, Smoke, Dust and Haze: Fundamentals of Aerosol Dynamics, New York: Oxford University Press, 2000.
S. E. Pratsinis, Simultaneous nucleation, condensation, and coagulation in aerosol reactors, Journal of Colloid Interface Science, 124, pp. 416-426, 1988. http://dx.doi.org/10.1016/0021-9797(88)90180-4
A. Isidori, Nonlinear control systems: an introduction (Second Edition). Berlin, Heidelberg, Springer-verlag, 1989. http://dx.doi.org/10.1007/978-3-662-02581-9
E. Yaz, Stabilizing compensator design for uncertain nonlinear systems, Systems and Control Letter, 21, pp.11-17, 1993 http://dx.doi.org/10.1016/0167-6911(93)90039-9
Published
Issue
Section
License
ONLINE OPEN ACCES: Acces to full text of each article and each issue are allowed for free in respect of Attribution-NonCommercial 4.0 International (CC BY-NC 4.0.
You are free to:
-Share: copy and redistribute the material in any medium or format;
-Adapt: remix, transform, and build upon the material.
The licensor cannot revoke these freedoms as long as you follow the license terms.
DISCLAIMER: The author(s) of each article appearing in International Journal of Computers Communications & Control is/are solely responsible for the content thereof; the publication of an article shall not constitute or be deemed to constitute any representation by the Editors or Agora University Press that the data presented therein are original, correct or sufficient to support the conclusions reached or that the experiment design or methodology is adequate.