Abstract
Model predictive control (MPC) is widely accepted as a generic multivariable controller with constraint handling. More recently, MPC has been extended to nonlinear model predictive control (NMPC) in order to realize high-performance control of highly nonlinear processes. In particular, NMPC allows incorporation of detailed process models (validated by off-line analysis) and also integrates with on-line optimization strategies consistent with higherlevel tasks, such as scheduling and planning. NMPC for tracking and so-called “economic” stage costs has been developed, and fundamental stability and robustness properties of NMPC have been analyzed. This perspective provides an overview of NMPC concepts and approaches, as well as the underlying optimization strategies that support the solution strategies. In addition, three challenging process case studies are presented to demonstrate the effectiveness of NMPC.
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L. T. Biegler and V. M. Zavala, Comput. Chem. Eng., 33, 575 (2009).
L. T. Biegler, Nonlinear programming. Concepts, algorithms, and applications to chemical processes, SIAM, Philadelphia, PA (2010).
J. B. Rawlings, D. Q. Mayne and M. M. Diehl, Model predictive control. Theory, computation and design, Nob Hill Publishing, LLC. (2020).
G. Pannocchia, J. Rawlings and S. Wright, Systems & Control Letters, 60, 747 (2011).
L. Grüne, Automatica, 49, 725 (2013).
H. Chen and F. Allgöwer, Automatica, 34, 1205 (1998).
D. W. Griffith, L. T. Biegler and S. C. Patwardhan, J. Process Control, 70, 109 (2018).
C. Rajhans, D. W. Griffith, S. C. Patwardhan, L. T. Biegler and H. K. Pillai, J. Process Control, 83, 30 (2019).
L. Magni and R. Scattolini, in Assessment and future directions of nonlinear model predictive control, R. Findeisen, F. Allgöwer, L. Biegler Eds., Springer, Berlin (2007).
A. Jazwinski, Stochastic processess and filtering theory, Dover Publications, Mineola, New York (2007).
L. Ji, J. B. Rawlings, W. Hu, A. Wynn and M. Diehl, IEEE Transactions on Automatic Control, 61(11), 3509 (2016).
C. V. Rao, J. B. Rawlings and D. Q. Mayne, IEEE transactions on Automatic Control, 48(2), 246 (2003).
V. Zavala, C. Laird and L. Biegler, J. Process Control, 18, 876 (2008).
A. Wynn, M. Vukov and M. Diehl, IEEE Transactions on Automatic Control, 59(8), 2215 (2014).
R. López-Negrete, S. C. Patwardhan and L. T. Biegler, in Computer Aided Chem. Eng.: 10th Int. Symp. on Process Systems Eng., 27, 1299 (2009).
R. López-Negrete, S. C. Patwardhan and L. T. Biegler, J. Process Control, 21(6), 909 (2011).
U. M. Ascher and L. R. Petzold, Computer methods for ordinary differential equations and differential-algebraic equations, SIAM, Philadelphia (1998).
A. R. Conn, K. Scheinberg and L. N. Vicente, Introduction to derivative-free optimization, SIAM, Philadelphia, PA, USA (2009).
J. Nocedal and S. Wright, Numerical optimization, 2nd Ed., SpringerScience+BusinessMedia, LLC, New York (2006).
J. Betts, Practical methods for optimal control using nonlinear programming, SIAM, Philadelphia, PA (2001).
G. Grimm, M. Messina, S. Tuna and A. Teel, Automatica, 40, 1729 (2004).
X. Yang, D. W. Griffith and L. T. Biegler, Proc. 5th IFAC Conference on Nonlinear Model Predictive Control, IFAC-PapersOnLine, 48(23), 388 (2015).
R. Fletcher, Practical methods of optimization, Wiley, New York (1987).
S. M. Robinson, Math. Oper. Res., 5, 43 (1980).
A. Fiacco, Introduction to sensitivity and stability analysis in nonlinear programming, Academic Press, New York (1983).
J. Gauvin, Mathematical Programming, 12(1), 136 (1977).
R. Janin, in Sensitivity, stability and parametric analysis, mathematical programming studies, vol. 21, A. Fiacco Ed., Springer Berlin Heidelberg (1984).
D. Ralph and S. Dempe, Mathematical Programming, 70(1–3), 159 (1995).
M. Kojima, in Analysis and computation of fixed points, S. M. Robinson Ed., Academic Press, New York (1980).
V. Kungurtsev and J. Jäschke, SIAM J. Optimization, 27(1), 538 (2017).
J. Jäschke, X. Yang and L. T. Biegler, J. Process Control, 24, 1260 (2014).
A. Forsgren, P. Gill and M. Wright, SIAM Rev., 44(4), 525 (2002).
A. Wächter and L. T. Biegler, Mathematical Programming, 106(1), 25 (2006).
S. Keerthi and E. Gilbert, IEEE Trans. Auto. Cont., 57, 265 (1988).
Z. Jiang and Y. Wang, Automatica, 37, 857 (2001).
V. Zavala and M. Anitescu, SIAM J. Control Optim., 48, 5444 (2010).
M. Diehl, H. Bock and J. Schlöder, SIAM J. Control Optimization, 43, 1714 (2005).
Y. Kim, D. M. Thierry and L. T. Biegler, J. Process Control, 96, 82 (2020).
V. M. Zavala and L. T. Biegler, Automatica, 45, 86 (2009).
Y. Kim, K. H. Lin, D. M. Thierry and L. T. Biegler, ADCHEM IFAC Conference to appear (2021).
B. L. Nicholson, R. Lopez-Negrete and L. T. Biegler, Comp. Chem. Eng., 70, 149 (2014).
S. Lucia, P. Rumschinski, A. J. Krener and R. Findeisen, IFAC Papers Online, 48(23), 254 (2015).
M. Lazar and M. Tetteroo, IFAC Papers Online, 51(20), 141 (2018).
C. Rajhans, S. Patwardhan and H. Pillai, Proc. 12th IEEE Intl. Conf. Control and Automation, 98 (2016).
D. Angeli, R. Amrit and J. Rawlings, IEEE Trans. Auto. Cont., 57(7), 1615 (2012).
M. Diehl, R. Amrit and J. B. Rawlings, IEEE Trans. Auto. Cont., 56(3), 703 (2011).
M. Z. Yu and L. T. Biegler, 10th IFAC International Symposium on Advanced Control of Chemical Processes (ADCHEM 2018), 103 (2018).
D. Krishnamoorthy, L. T. Biegler and J. Jaeschke, J. Process Control, 92, 108 (2020).
D. W. Griffith, V. M. Zavala and L. T. Biegler, J. Process Control, 57, 116 (2017).
B. Srinivasan, D. Bonvin, E. Visser and S. Palanki, Comput. Chem. Eng., 27(1), 27 (2003).
M. Diehl and J. Bjornberg, IEEE Transactions on Automatic Control, 49(12), 2253 (2004).
T. Y. Jung, Y. Nie, J. H. Lee and L. T. Biegler, Proceedings 9th International Symposium on Advanced Control of Chemical Processes, IFAC ADCHEM, IFAC-PapersOnLine, 48(8), 164 (2015).
S. Lucia, T. Finkler and S. Engell, J. Process Control, 23(9), 1306 (2013).
Z. Yu and L. T. Biegler, J. Process Control, 84, 192 (2019).
H. Jang, J. H. Lee and L. T. Biegler, Proceedings of DYCOPS-CAB 2016, IFAC Papers Online, 37 (2016).
J. Puschke and A. Mitsos, J. Process Control, 69, 6 (2018).
F. Holtorf, A. Mitsos and L. T. Biegler, J. Process Control, 80, 167 (2019).
M. Thombre, Z. Yu, J. Jäschke and L. T. Biegler, Comput. Chem. Eng., 148, 107269 (2021).
B. Houska, H. J. Ferreau and M. Diehl, Optimal Control Appl. Methods, 32, 298 (2011).
J. Andersson, J. Gillis, G. Horn, J. B. Rawlings and M. Diehl, Mathematical Programming Computation, 11(1), 1 (2019).
J. D. Hedengren, R. A. Shishavan, K. M. Powell and T. F. Edgar, Comput. Chem. Eng., 70, 133 (2014).
I. Dunning, J. Huchette and M. Lubin, SIAM Rev., 59(2), 295 (2017).
W. Hart, C. Laird, J. P. Watson, D. Woodruff, G. Hackebeil, B. Nicholson and J. Siirola, Pyomo â optimization modeling in python, Springer, New York (2017).
B. L. Nicholson, J. D. Siirola, J. P. Watson, V. M. Zavala and L. T. Biegler, Mathematical Programming Computation, 10, 187 (2018).
H. Pirnay, R. López-Negrete and L. T. Biegler, Math. Programming Computation, 4, 307 (2012).
D. M. Thierry and L. T. Biegler, AIChE J., 65(7), 1 (2019).
R. Lopez-Negrete, F. J. DâAmato, L. T. Biegler and A. Kumar, Comput. Chem. Eng., 51, 55 (2013).
R. Leer, Self-optimizing control structures for active constraint regions of a sequence of distillation columns, Master’s thesis, Norwegian University of Science and Technology (2012).
X. Yang, Advanced-multi-step and economically oriented nonlinear model predictive control, Ph.D. thesis, Carnegie Mellon University (2015).
Y. Nie, L. T. Biegler, C. M. Villa and J. Wassick, AIChE J., 59(7), 2515 (2013).
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Lorenz T. (Larry) Biegler is the Covestro University Professor of Chemical Engineering at Carnegie Mellon University. His research interests lie in computer aided process engineering (CAPE) and include flowsheet optimization, optimization of systems of differential and algebraic equations, reactor network synthesis, nonlinear process control and real-time optimization. Contributions in these areas include analysis and development of nonlinear programming algorithms, optimization software design and application to real-world chemical processes and energy systems.
He is an author on over 500 archival publications and two textbooks, has edited 11 technical books and given numerous invited presentations at national and international conferences. His awards include the Lewis Award, Walker Award and Computers in Chemical Engineering Award, given by AIChE; the Lectureship Award, Curtis McGraw Research Award and CACHE Computing Award, given by ASEE; the INFORMS Computing Prize, and an honorary doctorate in engineering sciences from the Technical University of Berlin. He is a Fellow of AIChE, IFAC and SIAM, and a member of the National Academy of Engineering.
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Biegler, L.T. A perspective on nonlinear model predictive control. Korean J. Chem. Eng. 38, 1317–1332 (2021). https://doi.org/10.1007/s11814-021-0791-7
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DOI: https://doi.org/10.1007/s11814-021-0791-7