Abstract
This chapter focuses on feedback control of particle size distribution in nanoparticle synthesis and processing. Initially, control methods based on suitable approximations of population balance models are presented to design nonlinear, robust and predictive controllers for particulate systems. The applications of the model-based control methods are then demonstrated through batch and continuous crystallization as well as aerosol synthesis. Finally, the issues of control problem formulation and controller design for high-velocity oxygen-fuel (HVOF) thermal spray coating processing are discussed.
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References
L. Ajdelsztajn, F. Tang, J.M. Schoenung, G.E. Kim, and V. Provenzano. Synthesis and oxidation behavior of nanocrystalline MCrAlY bond coatings. J. Thermal Spray Technol., 14:23–30, 2005.
A. Azarani. Automated high-throughput protein crystallization. In The proteomics protocols handbook, Walker, J. M. (Ed.), pages 955–966. Humana Press, Totowa, New Jersey, 2005.
C.F. Bohren, and D.R. Huffman. Absorption and scattering of light by small particles. Wiley, New York, 1983.
R.D. Braatz, and S. Hasebe. Particle size and shape control in crystallization processes. In AIChE Symposium Series: Proceedings of 6th international conference on chemical process control, Rawlings, J. B. et al. (Eds.), pages 307–327, 2002.
D. Cheng, G. Trapaga, J.W. McKelliget, and E.J. Lavernia. Mathematical modelling of high velocity oxygen fuel thermal spraying of nanocrystalline materials: an overview. Modell. Simul. Mater. Sci. Eng., 11:R1–R31, 2003.
T. Chiu, and P.D. Christofides. Nonlinear control of particulate processes. AIChE J., 45: 1279–1297, 1999.
T. Chiu, and P.D. Christofides. Robust control of particulate processes using uncertain population balances. AIChE J., 46:266–280, 2000.
P.D. Christofides. Model-based control of particulate processes. Kluwer Academic Publishers, Particle Technology Series, Netherlands, 2002.
P.D. Christofides, and T. Chiu. Nonlinear control of particulate processes. In AIChE annual meeting, paper 196a, Los Angeles, CA, 1997.
P.D. Christofides, and P. Daoutidis. Feedback control of hyperbolic PDE systems. AIChE J., 42:3063–3086, 1996.
P.D. Christofides, M. Li, and L. Mädler. Control of particulate processes: Recent results and future challenges. Powder Technol., 175:1–7, 2007.
P. Daoutidis, and M. Henson. Dynamics and control of cell populations. In Proceedings of 6th international conference on chemical process control, pages 308–325, Tucson, AZ, 2001.
J. Dimitratos, G. Elicabe, and C. Georgakis. Control of emulsion polymerization reactors. AIChE J., 40:1993–2021, 1994.
E. Dongmo, M. Wenzelburger, and R. Gadow. Analysis and optimization of the HVOF process by combined experimental and numerical approaches. Surf. Coat. Technol., 202:4470–4478, 2008.
F.J. Doyle, M. Soroush, and C. Cordeiro. Control of product quality in polymerization processes. In AIChE symposium series: Proceedings of 6th international conference on chemical process control, rawlings, J. B. et al. (Eds.), pages 290–306, 2002.
N.H. El-Farra, T. Chiu, and P.D. Christofides. Analysis and control of particulate processes with input constraints. AIChE J., 47:1849–1865, 2001.
N.H. El-Farra, and P.D. Christofides. Integrating robustness, optimality, and constraints in control of nonlinear processes. Chem. Eng. Sci., 56:1–28, 2001.
N.H. El-Farra, and P.D. Christofides. Bounded robust control of constrained multivariable nonlinear processes. Chem. Eng. Sci., 58:3025–3047, 2003.
N.H. El-Farra, and A. Giridhar. Detection and management of actuator faults in controlled particulate processes using population balance models. Chem. Eng. Sci., 63:1185–1204, 2008.
N.H. El-Farra, P. Mhaskar, and P.D. Christofides. Hybrid predictive control of nonlinear systems: Method and applications to chemical processes. Int. J. Robust Nonlinear Control, 14:199–225, 2004.
J.R. Fincke, W.D. Swank, R.L. Bewley, D.C. Haggard, M. Gevelber, and D. Wroblewski. Diagnostics and control in the thermal spray process. Surf. Coat. Technol., 146-147:537–543, 2001.
J.R. Fincke, W.D. Swank, and C.L. Jeffrey. Simultaneous measurement of particle size, velocity and temperature in thermal plasmas. IEEE Trans. Plasma Sci., 18:948–957, 1990.
S.K. Friendlander. Smoke, dust and haze: Fundamentals of aerosol dynamics (2nd Ed.). Oxford University Press, New York, USA, 2000.
A. Gani, P. Mhaskar, and P.D. Christofides. Handling sensor malfunctions in control of particulate processes. Chem. Eng. Sci., 63:1217–1229, 2008.
F. Gelbard, and J.H. Seinfeld. Numerical solution of the dynamic equation for particulate processes. J. Comput. Phys., 28:357–375, 1978.
L. Gil, and M.H. Staia. Influence of HVOF parameters on the corrosion resistance of NiWCrBSi coatings. Thin Solid Films, 420–421:446–454, 2002.
E. Hamalainen, J. Vattulainen, T. Alahautala, R. Hernberg, P. Vuoristo, and T. Mantyla. Imaging diagnostics in thermal spraying. “spraywatch” system. In Thermal spray: Surface engineering via applied research, Proceedings of the international thermal spray conference, pages 79–83, Montreal, QC, Canada, 2000.
T.C. Hanson, and G.S. Settles. Particle temperature and velocity effects on the porosity and oxidation of an HVOF corrosion-control coating. J. Therm. Spray Technol., 12:403–415, 2003.
J.A. Hearley, J.A. Little, and A.J. Sturgeon. The effect of spray parameters on the properties of high velocity oxy-fuel NiAl intermetallic coatings. Surf. Coat. Technol., 123:210–218, 2000.
H.M. Hulburt, and S. Katz. Some problems in particle technology: A statistical mechanical formulation. Chem. Eng. Sci., 19:555–574, 1964.
M. Ivosevic, R.A. Cairncross, and R. Knight. 3D predictions of thermally sprayed polymer splats: Modeling particle acceleration, heating and deformation on impact with a flat substrate. Int. J. Heat Mass Transfer, 49:3285–3297, 2006.
G.R. Jerauld, Y. Vasatis, and M.F. Doherty. Simple conditions for the appearance of sustained oscillations in continuous crystallizers. Chem. Eng. Sci., 38:1675–1681, 1983.
A. Kalani, and P.D. Christofides. Nonlinear control of spatially-inhomogeneous aerosol processes. Chem. Eng. Sci., 54:2669–2678, 1999.
A. Kalani, and P.D. Christofides. Modeling and control of a titania aerosol reactor. Aerosol Sci. Technol., 32:369–391, 2000.
A. Kalani, and P.D. Christofides. Simulation, estimation and control of size distribution in aerosol processes with simultaneous reaction, nucleation, condensation and coagulation. Comput. Chem. Eng., 26:1153–1169, 2002.
O. Knotek, and R. Elsing. Monte carlo simulation of the lamellar structure of thermally sprayed coatings. Surf. Coat. Technol., 32:261–271, 1987.
P.A. Larsen, J.B. Rawlings, and N.J. Ferrier. An algorithm for analyzing noisy, in situ images of high-aspect-ratio crystals to monitor particle size distribution. Chem. Eng. Sci., 61: 5236–5248, 2006.
K. Lee, and T. Matsoukas. Simultaneous coagulation and break-up using constant-n monte carlo. Powder Technol., 110:82–89, 2000.
S.J. Lei, R. Shinnar, and S. Katz. The stability and dynamic behavior of a continuous crystallizer with a fines trap. AIChE J., 17:1459–1470, 1971.
M. Li, and P.D. Christofides. Modeling and analysis of HVOF thermal spray process accounting for powder size distribution. Chem. Eng. Sci., 58:849–857, 2003.
M. Li, and P.D. Christofides. Feedback control of HVOF thremal spray process accounting for powder size distribution. J. Therm. Spray Technol., 13:108–120, 2004.
M. Li, and P.D. Christofides. Multi-scale modeling and analysis of HVOF thermal spray process. y Chem. Eng. Sci., 60:3649–3669, 2005.
M. Li, and P.D. Christofides. Computational study of particle in-flight behavior in the HVOF thermal spray process. Chem. Eng. Sci., 61:6540–6552, 2006.
M. Li, D. Shi, and P.D. Christofides. Diamond jet hybrid HVOF thermal spray: Gas-phase and particle behavior modeling and feedback control design. Ind. Eng. Chem. Res., 43:3632–3652, 2004.
M. Li, D. Shi, and P.D. Christofides. Model-based estimation and control of particle velocity and melting in HVOF thermal spray. Chem. Eng. Sci., 59:5647–5656, 2004.
M. Li, D. Shi, and P.D. Christofides. Modeling and control of HVOF thermal spray processing of WC-Co coatings. Powder Technol., 156:177–194, 2005.
Y. Lin, and E.D. Sontag. A universal formula for stabilization with bounded controls. Syst. Contr. Lett., 16:393–397, 1991.
Y.L. Lin, K. Lee, and T. Matsoukas. Solution of the population balance equation using constant-number Monte Carlo. Chem. Eng. Sci., 57:2241–2252, 2002.
D.L. Ma, D.K. Tafti, and R.D. Braatz. Optimal control and simulation of multidimensional crystallization processes. Comput. Chem. Eng., 26:1103–1116, 2002.
A. Martinez, C. Gonzalez, M. Porras, and J.M. Gutierrez. Nano-sized latex particles obtained by emulsion polymerization using an amphiphilic block copolymer as surfactant. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 270–271:67–71, 2005.
P. Mhaskar, A. Gani, C. McFall, P.D. Christofides, and J.F. Davis. Fault-tolerant control of nonlinear process systems subject to sensor faults. AIChE J., 53:654–668, 2007.
S.M. Miller, and J.B. Rawlings. Model identification and control strategies for batch cooling crystallizers. AIChE J., 40:1312–1327, 1994.
J. Mostaghimi, S. Chandra, R. Ghafouri-Azar, and A. Dolatabadi. Modeling thermal spray coating processes: a powerful tool in design and optimization. Surf. Coat. Technol., 163-164: 1–11, 2003.
D. Ramkrishna. The status of population balances. Rev. Chem. Eng., 3:49–95, 1985.
J.B. Rawlings, S.M. Miller, and W.R. Witkowski. Model identification and control of solution crystallizatin process – a review. Ind. Eng. Chem. Res., 32:1275–1296, 1993.
J.B. Rawlings, C.W. Sink, and S.M. Miller. Control of crystallization processes. In Industrial crystallization - theory and practice, pages 179–207, Butterworth, Boston, 1992.
S. Rohani, and J.R. Bourne. Self-tuning control of crystal size distribution in a cooling batch crystallizer. Chem. Eng. Sci., 12:3457–3466, 1990.
D. Semino, and W.H. Ray. Control of systems described by population balance equations-I. controllability analysis. Chem. Eng. Sci., 50:1805–1824, 1995.
D. Semino, and W.H. Ray. Control of systems described by population balance equations-II. emulsion polymerization with constrained control action. Chem. Eng. Sci., 50:1825–1839, 1995.
D. Shi, N.H. El-Farra, M. Li, P. Mhaskar, and P.D. Christofides. Predictive control of particle size distribution in particulate processes. Chem. Eng. Sci., 61:268–281, 2006.
D. Shi, M. Li, and P.D. Christofides. Diamond jet hybrid HVOF thermal spray: Rule-based modeling of coating microstructure. Ind. Eng. Chem. Res., 43:3653–3665, 2004.
D. Shi, P. Mhaskar, N.H. El-Farra, and P.D. Christofides. Predictive control of crystal size distribution in protein crystallization. Nanotechnology, 16:S562–S574, 2005.
T. Smith, and T. Matsoukas. Constant-number Monte Carlo simulation of population balances. Chem. Eng. Sci., 53:1777–1786, 1998.
W.J. Stark, A. Baiker, and S.E. Pratsinis. Nanoparticle opportunities: pilot-scale flame synthesis of vanadia/titania catalysts. Part. Part. Syst. Charact., 19:306–311, 2002.
W.D. Swank, J.R. Fincke, D.C. Haggard, G. Irons, and R. Bullock. HVOF particle flow field characteristics. In Thermal spray industrial applications, Proceedings of the 7th national thermal spray conference, pages 319–324, Boston, Massachusetts, 1994.
Tecnar Automation. DPV-2000 Reference Manual.
E. Turunen, T. Varis, S.-P. Hannula, A. Vaidya, A. Kulkarni, J. Gutleber, S. Sampath, and H. Herman. On the role of particle state and deposition procedure on mechanical, tribological and dielectric response of high velocity oxy-fuel sprayed alumina coatings. Mat. Sci. Eng. A, 415:1–11, 2006.
P.G. Vekilov, and F. Rosenberger. Dependence of lysozyme growth kinetics on step sources and impurities. J. Cryst. Growth, 158:540–551, 1996.
J. Wilden, J.P. Bergmann, and T. Luhn. Aspects of thermal spray molding of micro components. In Thermal spray: Science, innovation, and application, Proceedings of the 2006 international thermal spray conference, pages 1243–1246, Seattle, WA, 2006.
W. Xie, S. Rohani, and A. Phoenix. Dynamic modeling and operation of a seeded batch cooling crystallizer. Chem. Eng. Comm., 187:229–249, 2001.
D. Zhang, S.J. Harris, and D.G. McCartney. Microstructure formation and corrosion behaviour in HVOF-sprayed Inconel 625 coatings. Mat. Sci. Eng. A, 344:45–56, 2003.
G.P. Zhang, and S. Rohani. On-line optimal control of a seeded batch cooling crystallizer. Chem. Eng. Sci., 58:1887–1896, 2003.
Acknowledgements
Financial support from the NSF (ITR), CTS-0325246, and the Office of Naval Research (2001 Young Investigator Award) is gratefully acknowledged. The authors note that all the figures included in this Chapter are original and have permission to include them in the present chapter.
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Li, M., Christofides, P.D. (2012). Feedback Control of Particle Size Distribution in Nanoparticle Synthesis and Processing. In: Gorman, J., Shapiro, B. (eds) Feedback Control of MEMS to Atoms. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5832-7_2
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