Economic model predictive control of nonlinear process systems using empirical models

Alanqar, Anas; Ellis, Matthew; Christofides, Panagiotis D.

doi:10.1002/aic.14683

Title: Economic model predictive control of nonlinear process systems using empirical models

Abstract

Economic model predictive control (EMPC) is a feedback control technique that attempts to tightly integrate economic optimization and feedback control since it is a predictive control scheme that is formulated with an objective function representing the process economics. As its name implies, EMPC requires the availability of a dynamic model to compute its control actions and such a model may be obtained either through application of first principles or through system identification techniques. In industrial practice, it may be difficult in general to obtain an accurate first‐principles model of the process. Motivated by this, in the present work, Lyapunov‐based EMPC (LEMPC) is designed with a linear empirical model that allows for closed‐loop stability guarantees in the context of nonlinear chemical processes. Specifically, when the linear model provides a sufficient degree of accuracy in the region where time varying economically optimal operation is considered, conditions for closed‐loop stability under the LEMPC scheme based on the empirical model are derived. The LEMPC scheme is applied to a chemical process example to demonstrate its closed‐loop stability and performance properties as well as significant computational advantages. © 2014 American Institute of Chemical Engineers AIChE J , 61: 816–830, 2015

Authors:

Alanqar, Anas ^[1]; Ellis, Matthew ^[1]; Christofides, Panagiotis D. ^[2]

Dept. of Chemical and Biomolecular Engineering University of California Los Angeles CA 90095
Dept. of Chemical and Biomolecular Engineering University of California Los Angeles CA 90095, Dept. of Electrical Engineering University of California Los Angeles CA 90095

Publication Date:: Fri Nov 28 00:00:00 EST 2014

Sponsoring Org.:: USDOE

OSTI Identifier:: 1401594

Resource Type:: Publisher's Accepted Manuscript

Journal Name:: AIChE Journal

Additional Journal Information:: Journal Name: AIChE Journal Journal Volume: 61 Journal Issue: 3; Journal ID: ISSN 0001-1541

Publisher:: Wiley Blackwell (John Wiley & Sons)

Country of Publication:: United States

Language:: English

Citation Formats


                    Alanqar, Anas, Ellis, Matthew, and Christofides, Panagiotis D. Economic model predictive control of nonlinear process systems using empirical models.  United States: N. p., 2014. 
Web.  doi:10.1002/aic.14683.

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                    Alanqar, Anas, Ellis, Matthew, & Christofides, Panagiotis D. Economic model predictive control of nonlinear process systems using empirical models.  United States.  https://doi.org/10.1002/aic.14683

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                    Alanqar, Anas, Ellis, Matthew, and Christofides, Panagiotis D. Fri .  
"Economic model predictive control of nonlinear process systems using empirical models".  United States.  https://doi.org/10.1002/aic.14683.

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@article{osti_1401594,

  title        = {Economic model predictive control of nonlinear process systems using empirical models},

  author       = {Alanqar, Anas and Ellis, Matthew and Christofides, Panagiotis D.},

  abstractNote = {Economic model predictive control (EMPC) is a feedback control technique that attempts to tightly integrate economic optimization and feedback control since it is a predictive control scheme that is formulated with an objective function representing the process economics. As its name implies, EMPC requires the availability of a dynamic model to compute its control actions and such a model may be obtained either through application of first principles or through system identification techniques. In industrial practice, it may be difficult in general to obtain an accurate first‐principles model of the process. Motivated by this, in the present work, Lyapunov‐based EMPC (LEMPC) is designed with a linear empirical model that allows for closed‐loop stability guarantees in the context of nonlinear chemical processes. Specifically, when the linear model provides a sufficient degree of accuracy in the region where time varying economically optimal operation is considered, conditions for closed‐loop stability under the LEMPC scheme based on the empirical model are derived. The LEMPC scheme is applied to a chemical process example to demonstrate its closed‐loop stability and performance properties as well as significant computational advantages. © 2014 American Institute of Chemical Engineers AIChE J , 61: 816–830, 2015},

  doi          = {10.1002/aic.14683},

  journal      = {AIChE Journal},

  number       = 3,

  volume       = 61,

  place        = {United States},

  year         = {Fri Nov 28 00:00:00 EST 2014},

  month        = {Fri Nov 28 00:00:00 EST 2014}

}

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Works referenced in this record:

Lyapunov-Based Model Predictive Control of Nonlinear Systems Subject to Data Losses
journal, October 2008

Munoz de la Pena, David; Christofides, Panagiotis D.
IEEE Transactions on Automatic Control, Vol. 53, Issue 9
DOI: 10.1109/TAC.2008.929401

Multiple model LPV approach to nonlinear process identification with EM algorithm
journal, January 2011

Jin, Xing; Huang, Biao; Shook, David S.
Journal of Process Control, Vol. 21, Issue 1
DOI: 10.1016/j.jprocont.2010.11.008

On finite-time and infinite-time cost improvement of economic model predictive control for nonlinear systems
journal, October 2014

Ellis, Matthew; Christofides, Panagiotis D.
Automatica, Vol. 50, Issue 10
DOI: 10.1016/j.automatica.2014.08.011

A tutorial review of economic model predictive control methods
journal, August 2014

Ellis, Matthew; Durand, Helen; Christofides, Panagiotis D.
Journal of Process Control, Vol. 24, Issue 8
DOI: 10.1016/j.jprocont.2014.03.010

Economic model predictive control of nonlinear process systems using Lyapunov techniques
journal, May 2011

Heidarinejad, Mohsen; Liu, Jinfeng; Christofides, Panagiotis D.
AIChE Journal, Vol. 58, Issue 3
DOI: 10.1002/aic.12672

Subspace Algorithms for the Identification of Multivariable Dynamic Errors-in-Variables Models**This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor H. Hjalmarsson under the direction of Editor Torsten Söderström.
journal, October 1997

Chou, C. T.; Verhaegen, Michel
Automatica, Vol. 33, Issue 10
DOI: 10.1016/S0005-1098(97)00092-7

Multiple-model adaptive predictive control of mean arterial pressure and cardiac output
journal, January 1992

Yu, C.; Roy, R. J.; Kaufman, H.
IEEE Transactions on Biomedical Engineering, Vol. 39, Issue 8
DOI: 10.1109/10.148385

Nonlinear System Identification
book, January 2013

Billings, Stephen A.
John Wiley & Sons, Ltd.
DOI: 10.1002/9781118535561

A gap metric based multiple model approach for nonlinear switched systems
journal, October 2012

Hariprasad, K.; Bhartiya, Sharad; Gudi, Ravindra D.
Journal of Process Control, Vol. 22, Issue 9
DOI: 10.1016/j.jprocont.2012.07.005

Stabilization of nonlinear sampled-data systems and economic model predictive control application
conference, June 2014

Ellis, Matthew; Karafyllis, Iasson; Christofides, Panagiotis D.
2014 American Control Conference - ACC 2014
DOI: 10.1109/ACC.2014.6858758

Bounded robust control of constrained multivariable nonlinear processes
journal, July 2003

El-Farra, Nael H.; Christofides, Panagiotis D.
Chemical Engineering Science, Vol. 58, Issue 13
DOI: 10.1016/S0009-2509(03)00126-X

Canonical variate analysis in identification, filtering, and adaptive control
conference, January 1990

Larimore, W. E.
29th IEEE Conference on Decision and Control
DOI: 10.1109/CDC.1990.203665

Algorithms for deterministic balanced subspace identification
journal, May 2005

Markovsky, Ivan; Willems, Jan C.; Rapisarda, Paolo
Automatica, Vol. 41, Issue 5
DOI: 10.1016/j.automatica.2004.10.007

Identification of the deterministic part of MIMO state space models given in innovations form from input-output data
journal, January 1994

Verhaegen, Michel
Automatica, Vol. 30, Issue 1
DOI: 10.1016/0005-1098(94)90229-1

Model predictive control based on Wiener models
journal, January 1998

Norquay, Sandra J.; Palazoglu, Ahmet; Romagnoli, JoséA.
Chemical Engineering Science, Vol. 53, Issue 1
DOI: 10.1016/S0009-2509(97)00195-4

On Average Performance and Stability of Economic Model Predictive Control
journal, July 2012

Angeli, David; Amrit, Rishi; Rawlings, James B.
IEEE Transactions on Automatic Control, Vol. 57, Issue 7
DOI: 10.1109/TAC.2011.2179349

Integrating data-based modeling and nonlinear control tools for batch process control
journal, August 2011

Aumi, Siam; Mhaskar, Prashant
AIChE Journal, Vol. 58, Issue 7
DOI: 10.1002/aic.12720

On the performance of economic model predictive control with self-tuning terminal cost
journal, August 2014

Müller, Matthias A.; Angeli, David; Allgöwer, Frank
Journal of Process Control, Vol. 24, Issue 8
DOI: 10.1016/j.jprocont.2014.05.009

Modelling and identification of non-linear deterministic systems in the delta-domain
journal, November 2007

Anderson, S. R.; Kadirkamanathan, V.
Automatica, Vol. 43, Issue 11
DOI: 10.1016/j.automatica.2007.03.020

Lyapunov stability of economically oriented NMPC for cyclic processes
journal, April 2011

Huang, Rui; Harinath, Eranda; Biegler, Lorenz T.
Journal of Process Control, Vol. 21, Issue 4
DOI: 10.1016/j.jprocont.2011.01.012

Feedback control for optimal process operation
journal, March 2007

Engell, Sebastian
Journal of Process Control, Vol. 17, Issue 3
DOI: 10.1016/j.jprocont.2006.10.011

Subspace state space system identification for industrial processes
journal, April 2000

Favoreel, Wouter; De Moor, Bart; Van Overschee, Peter
Journal of Process Control, Vol. 10, Issue 2-3
DOI: 10.1016/S0959-1524(99)00030-X

Asymptotic stability and transient optimality of economic MPC without terminal conditions
journal, August 2014

Grüne, Lars; Stieler, Marleen
Journal of Process Control, Vol. 24, Issue 8
DOI: 10.1016/j.jprocont.2014.05.003

Contributions to Stability Theory
journal, July 1956

Massera, Jose L.
The Annals of Mathematics, Vol. 64, Issue 1
DOI: 10.2307/1969955

Nolinear model predictive control using Hammerstein models
journal, February 1997

Fruzzetti, K. P.; Palazoğlu, A.; McDonald, K. A.
Journal of Process Control, Vol. 7, Issue 1
DOI: 10.1016/S0959-1524(97)80001-B

System identification—A survey
journal, March 1971

Åström, K. J.; Eykhoff, P.
Automatica, Vol. 7, Issue 2
DOI: 10.1016/0005-1098(71)90059-8

A universal formula for stabilization with bounded controls
journal, June 1991

Lin, Yuandan; Sontag, Eduardo D.
Systems & Control Letters, Vol. 16, Issue 6
DOI: 10.1016/0167-6911(91)90111-Q

N4SID: Subspace algorithms for the identification of combined deterministic-stochastic systems
journal, January 1994

Van Overschee, Peter; De Moor, Bart
Automatica, Vol. 30, Issue 1
DOI: 10.1016/0005-1098(94)90230-5

Subspace-based methods for the identification of linear time-invariant systems
journal, December 1995

Viberg, Mats
Automatica, Vol. 31, Issue 12
DOI: 10.1016/0005-1098(95)00107-5

Model-based predictive control for Hammerstein?Wiener systems
journal, January 2001

Bloemen, H. H. J.; Van Den Boom, T. J. J.; Verbruggen, H. B.
International Journal of Control, Vol. 74, Issue 5
DOI: 10.1080/00207170010014061

A ‘universal’ construction of Artstein's theorem on nonlinear stabilization
journal, August 1989

Sontag, Eduardo D.
Systems & Control Letters, Vol. 13, Issue 2
DOI: 10.1016/0167-6911(89)90028-5

Constructive nonlinear control: a historical perspective
journal, May 2001

Kokotović, Petar; Arcak, Murat
Automatica, Vol. 37, Issue 5, p. 637-662
DOI: 10.1016/S0005-1098(01)00002-4

Selecting nonlinear model structures for computer control
journal, February 2003

Pearson, R. K.
Journal of Process Control, Vol. 13, Issue 1
DOI: 10.1016/S0959-1524(02)00022-7

An overview of subspace identification
journal, September 2006

Qin, S. Joe
Computers & Chemical Engineering, Vol. 30, Issue 10-12
DOI: 10.1016/j.compchemeng.2006.05.045

On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
journal, April 2005

Wächter, Andreas; Biegler, Lorenz T.
Mathematical Programming, Vol. 106, Issue 1
DOI: 10.1007/s10107-004-0559-y

Subspace model identification Part 1. The output-error state-space model identification class of algorithms
journal, November 1992

Verhaegen, Michel; Dewilde, Patrick
International Journal of Control, Vol. 56, Issue 5
DOI: 10.1080/00207179208934363

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Title: Economic model predictive control of nonlinear process systems using empirical models

Abstract

Citation Formats

Lyapunov-Based Model Predictive Control of Nonlinear Systems Subject to Data Losses journal, October 2008

Multiple model LPV approach to nonlinear process identification with EM algorithm journal, January 2011

On finite-time and infinite-time cost improvement of economic model predictive control for nonlinear systems journal, October 2014

A tutorial review of economic model predictive control methods journal, August 2014

Economic model predictive control of nonlinear process systems using Lyapunov techniques journal, May 2011

Multiple-model adaptive predictive control of mean arterial pressure and cardiac output journal, January 1992

Nonlinear System Identification book, January 2013

A gap metric based multiple model approach for nonlinear switched systems journal, October 2012

Stabilization of nonlinear sampled-data systems and economic model predictive control application conference, June 2014

Bounded robust control of constrained multivariable nonlinear processes journal, July 2003

Canonical variate analysis in identification, filtering, and adaptive control conference, January 1990

Algorithms for deterministic balanced subspace identification journal, May 2005

Identification of the deterministic part of MIMO state space models given in innovations form from input-output data journal, January 1994

Model predictive control based on Wiener models journal, January 1998

On Average Performance and Stability of Economic Model Predictive Control journal, July 2012

Integrating data-based modeling and nonlinear control tools for batch process control journal, August 2011

On the performance of economic model predictive control with self-tuning terminal cost journal, August 2014

Modelling and identification of non-linear deterministic systems in the delta-domain journal, November 2007

Lyapunov stability of economically oriented NMPC for cyclic processes journal, April 2011

Feedback control for optimal process operation journal, March 2007

Subspace state space system identification for industrial processes journal, April 2000

Asymptotic stability and transient optimality of economic MPC without terminal conditions journal, August 2014

Contributions to Stability Theory journal, July 1956

Nolinear model predictive control using Hammerstein models journal, February 1997

System identification—A survey journal, March 1971

A universal formula for stabilization with bounded controls journal, June 1991

N4SID: Subspace algorithms for the identification of combined deterministic-stochastic systems journal, January 1994

Subspace-based methods for the identification of linear time-invariant systems journal, December 1995

Model-based predictive control for Hammerstein?Wiener systems journal, January 2001

A ‘universal’ construction of Artstein's theorem on nonlinear stabilization journal, August 1989

Constructive nonlinear control: a historical perspective journal, May 2001

Selecting nonlinear model structures for computer control journal, February 2003

An overview of subspace identification journal, September 2006

On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming journal, April 2005

Subspace model identification Part 1. The output-error state-space model identification class of algorithms journal, November 1992

Lyapunov-Based Model Predictive Control of Nonlinear Systems Subject to Data Losses
journal, October 2008

Multiple model LPV approach to nonlinear process identification with EM algorithm
journal, January 2011

On finite-time and infinite-time cost improvement of economic model predictive control for nonlinear systems
journal, October 2014

A tutorial review of economic model predictive control methods
journal, August 2014

Economic model predictive control of nonlinear process systems using Lyapunov techniques
journal, May 2011

Multiple-model adaptive predictive control of mean arterial pressure and cardiac output
journal, January 1992

Nonlinear System Identification
book, January 2013

A gap metric based multiple model approach for nonlinear switched systems
journal, October 2012

Stabilization of nonlinear sampled-data systems and economic model predictive control application
conference, June 2014

Bounded robust control of constrained multivariable nonlinear processes
journal, July 2003

Canonical variate analysis in identification, filtering, and adaptive control
conference, January 1990

Algorithms for deterministic balanced subspace identification
journal, May 2005

Identification of the deterministic part of MIMO state space models given in innovations form from input-output data
journal, January 1994

Model predictive control based on Wiener models
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On Average Performance and Stability of Economic Model Predictive Control
journal, July 2012

Integrating data-based modeling and nonlinear control tools for batch process control
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On the performance of economic model predictive control with self-tuning terminal cost
journal, August 2014

Modelling and identification of non-linear deterministic systems in the delta-domain
journal, November 2007

Lyapunov stability of economically oriented NMPC for cyclic processes
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journal, March 2007

Subspace state space system identification for industrial processes
journal, April 2000

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Contributions to Stability Theory
journal, July 1956

Nolinear model predictive control using Hammerstein models
journal, February 1997

System identification—A survey
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journal, June 1991

N4SID: Subspace algorithms for the identification of combined deterministic-stochastic systems
journal, January 1994

Subspace-based methods for the identification of linear time-invariant systems
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Model-based predictive control for Hammerstein?Wiener systems
journal, January 2001

A ‘universal’ construction of Artstein's theorem on nonlinear stabilization
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