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Received March 13, 2021
Accepted March 21, 2021
- This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/bync/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
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A perspective on nonlinear model predictive control
Chemical Engineering Department, Carnegie Mellon University Pittsburgh, PA 15213, USA
biegler@cmu.edu
Korean Journal of Chemical Engineering, July 2021, 38(7), 1317-1332(16), 10.1007/s11814-021-0791-7
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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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References
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Pannocchia G, Rawlings J, Wright S, Systems & Control Letters, 60, 747 (2011).
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Griffith DW, Biegler LT, Patwardhan SC, J. Process Control, 70, 109 (2018)
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Jang H, Lee JH, Biegler LT, Proceedings of DYCOPS-CAB 2016, IFAC Papers Online, 37 (2016).
Puschke J, Mitsos A, J. Process Control, 69, 6 (2018)
Holtorf F, Mitsos A, Biegler LT, J. Process Control, 80, 167 (2019)
Thombre M, Yu Z, Jaschke J, Biegler LT, Comput. Chem. Eng., 148, 107269 (2021)
Houska B, Ferreau HJ, Diehl M, Optimal Control Appl. Methods, 32, 298 (2011)
Andersson J, Gillis J, Horn G, Rawlings JB, Diehl M, Mathematical Programming Computation, 11(1), 1 (2019)
Hedengren JD, Shishavan RA, Powell KM, Edgar TF, Comput. Chem. Eng., 70, 133 (2014)
Dunning I, Huchette J, Lubin M, SIAM Rev., 59, 295 (2017)
Hart W, et al., Pyomo a optimization modeling in python, Springer, New York (2017).
Nicholson BL, Siirola JD, Watson JP, Zavala VM, Biegler LT, Mathematical Programming Computation, 10, 187 (2018).
Pirnay H, Lopez-Negrete R, Biegler LT, Math. Programming Computation, 4, 307 (2012).
Thierry DM, Biegler LT, AIChE J., 65(7), 1 (2019)
Lopez-Negrete R, D'Amato FJ, Biegler LT, Kumar A, Comput. Chem. Eng., 51, 55 (2013)
Leer R, Self-optimizing control structures for active constraint regions of a sequence of distillation columns, Master’s thesis, Norwegian University of Science and Technology (2012).
Yang X, Advanced-multi-step and economically oriented nonlinear model predictive control, Ph.D. thesis, Carnegie Mellon University (2015).
Nie YS, Biegler LT, Villa CM, Wassick JM, AIChE J., 59(7), 2515 (2013)
Biegler LT, Nonlinear programming: Concepts, algorithms, and applications to chemical processes, SIAM, Philadelphia, PA (2010).
Rawlings JB, et al., Model predictive control: Theory, computation and design, Nob Hill Publishing, LLC. (2020).
Pannocchia G, Rawlings J, Wright S, Systems & Control Letters, 60, 747 (2011).
Grune L, Automatica, 49(3), 725 (2013)
Chen H, Allgower F, Automatica, 34, 1205 (1998)
Griffith DW, Biegler LT, Patwardhan SC, J. Process Control, 70, 109 (2018)
Rajhans C, Griffith DW, Patwardhan SC, Biegler LT, Pillai HK, J. Process Control, 83, 30 (2019)
Magni L, Scattolini R, in Assessment and future directions of nonlinear model predictive control, Berlin (2007).
Jazwinski A, Stochastic processess and filtering theory, Dover Publications, Mineola, New York (2007).
Ji L, Rawlings JB, Hu W, Wynn A, Diehl M, IEEE Transactions on Automatic Control, 61(11), 3509 (2016).
Rao CV, Rawlings JBand D. Mayne Q, IEEE transactions on Automatic Control, 48(2), 246 (2003).
Zavala VM, Laird CD, Biegler LT, J. Process Control, 18(9), 876 (2008)
Wynn A, Vukov M, Diehl M, IEEE Transactions on Automatic Control, 59(8), 2215 (2014).
Lopez-Negrete R, et al., Computer Aided Chem. Eng.: 10th Int. Symp. on Process Systems Eng., 27, 1299 (2009).
Lopez-Negrete R, Patwardhan SC, Biegler LT, J. Process Control, 21(6), 909 (2011)
Ascher UM, Petzold LR, Computer methods for ordinary differential equations and differential-algebraic equations, SIAM, Philadelphia (1998).
Conn AR, Scheinberg K, Vicente LN, Introduction to derivative-free optimization, SIAM, Philadelphia, PA, USA (2009).
Nocedal J, Wright S, Numerical optimization, 2nd Ed., SpringerScience+BusinessMedia, LLC, New York (2006).
Betts J, Practical methods for optimal control using nonlinear programming, SIAM, Philadelphia, PA (2001).
Grimm G, Messina M, Tuna S, Teel A, Automatica, 40, 1729 (2004)
Yang X, Griffith DW, Biegler LT, Proc. 5th IFAC Conference on Nonlinear Model Predictive Control, IFAC-PapersOnLine, 48(23), 388 (2015).
Fletcher R, Practical methods of optimization, Wiley, New York (1987).
Robinson SM, Math. Oper. Res., 5, 43 (1980)
Fiacco A, Introduction to sensitivity and stability analysis in nonlinear programming, Academic Press, New York (1983).
Gauvin J, Mathematical Programming, 12(1), 136 (1977)
Janin R, in Sensitivity, stability and parametric analysis, mathematical programming studies, vol. 21, A. Fiacco Ed., Springer Berlin Heidelberg (1984).
Ralph D, Dempe S, Mathematical Programming, 70(1-3), 159 (1995)
Kojima M, in Analysis and computation of fixed points, Academic Press, New York (1980).
Kungurtsev V, Jaschke J, SIAM J. Optimization, 27(1), 538 (2017)
Jaschke J, Yang X, Biegler LT, J. Process Control, 24(8), 1260 (2014)
Forsgren A, Gill P, Wright M, SIAM Rev., 44(4), 525 (2002)
Wachter A, Biegler LT, Mathematical Programming, 106(1), 25 (2006)
Keerthi S, Gilbert E, IEEE Trans. Auto. Cont., 57, 265 (1988)
Jiang Z, Wang Y, Automatica, 37, 857 (2001)
Zavala VM, Anitescu M, SIAM J. Control Optim., 48(8), 5444 (2010)
Diehl M, Bock H, Schloder J, SIAM J. Control Optimization, 43, 1714 (2005)
Kim Y, Thierry DM, Biegler LT, J. Process Control, 96, 82 (2020)
Zavala VM, Biegler LT, Automatica, 45(1), 86 (2009)
Kim Y, Lin KH, Thierry DM, Biegler LT, ADCHEM IFAC Conference to appear (2021).
Nicholson BL, Lopez-Negrete R, Biegler LT, Comp. Chem. Eng., 70, 149 (2014)
Lucia S, Rumschinski P, Krener AJ, Findeisen R, IFAC Papers Online, 48(23), 254 (2015)
Lazar M, Tetteroo M, IFAC Papers Online, 51(20), 141 (2018)
Rajhans C, Patwardhan S, Pillai H, Proc. 12th IEEE Intl. Conf. Control and Automation, 98 (2016).
Angeli D, Amrit R, Rawlings J, IEEE Trans. Auto. Cont., 57(7), 1615 (2012)
Diehl M, Amrit R, Rawlings JB, IEEE Trans. Auto. Cont., 56(3), 703 (2011)
Yu MZ, Biegler LT, 10th IFAC International Symposium on Advanced Control of Chemical Processes (ADCHEM 2018), 103 (2018).
Krishnamoorthy D, Biegler LT, Jaschke J, J. Process Control, 92, 108 (2020)
Griffith DW, Zavala VM, Biegler LT, J. Process Control, 57, 116 (2017)
Srinivasan B, Bonvin D, Visser E, Palanki S, Comput. Chem. Eng., 27(1), 27 (2003)
Diehl M, Bjornberg J, IEEE Transactions on Automatic Control, 49(12), 2253 (2004).
Jung TY, et al., IFAC ADCHEM, IFAC-PapersOnLine, 48(8), 164 (2015).
Lucia S, Finkler T, Engell S, J. Process Control, 23(9), 1306 (2013)
Yu ZJ, Biegler LT, J. Process Control, 84, 192 (2019)
Jang H, Lee JH, Biegler LT, Proceedings of DYCOPS-CAB 2016, IFAC Papers Online, 37 (2016).
Puschke J, Mitsos A, J. Process Control, 69, 6 (2018)
Holtorf F, Mitsos A, Biegler LT, J. Process Control, 80, 167 (2019)
Thombre M, Yu Z, Jaschke J, Biegler LT, Comput. Chem. Eng., 148, 107269 (2021)
Houska B, Ferreau HJ, Diehl M, Optimal Control Appl. Methods, 32, 298 (2011)
Andersson J, Gillis J, Horn G, Rawlings JB, Diehl M, Mathematical Programming Computation, 11(1), 1 (2019)
Hedengren JD, Shishavan RA, Powell KM, Edgar TF, Comput. Chem. Eng., 70, 133 (2014)
Dunning I, Huchette J, Lubin M, SIAM Rev., 59, 295 (2017)
Hart W, et al., Pyomo a optimization modeling in python, Springer, New York (2017).
Nicholson BL, Siirola JD, Watson JP, Zavala VM, Biegler LT, Mathematical Programming Computation, 10, 187 (2018).
Pirnay H, Lopez-Negrete R, Biegler LT, Math. Programming Computation, 4, 307 (2012).
Thierry DM, Biegler LT, AIChE J., 65(7), 1 (2019)
Lopez-Negrete R, D'Amato FJ, Biegler LT, Kumar A, Comput. Chem. Eng., 51, 55 (2013)
Leer R, Self-optimizing control structures for active constraint regions of a sequence of distillation columns, Master’s thesis, Norwegian University of Science and Technology (2012).
Yang X, Advanced-multi-step and economically oriented nonlinear model predictive control, Ph.D. thesis, Carnegie Mellon University (2015).
Nie YS, Biegler LT, Villa CM, Wassick JM, AIChE J., 59(7), 2515 (2013)