“State Space Realization of Model Predictive Controllers Without Active Constraints”

Authors: Sigurd Skogestad and Audun Faanes,
Affiliation: Statoil and NTNU, Department of Chemical Engineering
Reference: 2003, Vol 24, No 4, pp. 231-244.

Keywords: MPC, reference tracking, state estimation, state space controller realization

Abstract: To enable the use of traditional tools for analysis of multivariable controllers such as model predictive control (MPC), we develop a state space formulation for the resulting controller for MPC without constraints or assuming that the constraints are not active. Such a derivation was not found in the literature. The formulation includes a state estimator. The MPC algorithm used is a receding horizon controller with infinite horizon based on a state space process model. When no constraints are active, we obtain a state feedback controller, which is modified to achieve either output tracking, or a combination of input and output tracking. When the states are not available, they need to be estimated from the measurements. It is often recommended to achieve integral action in a MPC by estimating input disturbances and include their effect in the model. We show that to obtain offset free steady state the number of estimated disturbances must equal the number of measurements. The estimator is included in the controller equation, and we obtain a formulation of the overall controller with the set-points and measurements as inputs, and the manipulated variables as outputs. One application of the state space formulation is in combination with the process model to obtain a closed loop model. This can for example be used to check the steady-state solution and see whether integral action is obtained or not.

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DOI forward links to this article:
[1] Audun Faanes and Sigurd Skogestad (2005), doi:10.1016/j.jprocont.2004.07.001
[2] A.W. Hermansson and S. Syafiie (2019), doi:10.1016/j.isatra.2019.01.037
[3] Kazuhiro MIMURA, Tetsuo SHIOTSUKI and Shigeyasu KAWAJI (2010), doi:10.9746/jcmsi.3.237
[1] ÅKESSON HAGANDER, P. (2003). Integral Action - a Disturbance Observer Approach, European Control Conference, ECCO3, Sept. 1-4, 2003, Cambridge, UK.
[2] ÅSTRÖM. K. J. (1970). Introduction to Stochastic Control Theory, Mathematics in Science and Engineering. Academic Press. New York San Francisco London.
[3] BADGWELL, T. A. QIN, S. J. (2002). Industrial model predictive control - an updated overview, Process Control Consortium, University of.California.UCSB, 8-9 March, 2002.
[4] BEMPORAD, A., MORARI M., DUA, V. PISTIKOPOULUS, E. N. (1999). The explicit linear quadratic regulator for constrained systems, Technical Report AUT99-16. ETH, Zurich.
[5] BEMPORAD, A., MORARI, M., DUA, V. PISTIKOPOULUS, E. N. (2002). The explicit linear quadratic regulator for constrained systems, Automatica 38. 3-20 doi:10.1016/S0005-1098(01)00174-1
[6] FAANES, A. (2003). Controllability Analysis for Process and Control System Design, PhD thesis. Department of Chemical Engineering, Norwegian University of Science and Technology.
[7] FAANES, A. SKOGESTAD, S. (2003). Control design for serial processes, Submitted to J. Proc. Control.
[8] FAANES, A. SKOGESTAD, S. (2003). Offset free tracking with IVIPC under uncertainty: Experimental verification, Submitted to I Proc. Control.
[9] HALVORSEN, I. (1998). Private communication, .
[10] LEE, J. H., MORARI, M. GARCIA, C. E. (1994). State-space interpretation of model predictive control, Automatica 30(4). 707-717 doi:10.1016/0005-1098(94)90159-7
[11] LUNDSTRÖM, P., LEE, J. H., MORARI, M. SKOGESTAD, S. (1995). Limitations of dynamic matrix control, Comp. Chem. Engng. 19(4), 409-421 doi:10.1016/0098-1354(94)00063-T
[12] MACIEJOWSKI J.M. (2002). Predictive Control with Contraints, Prentice Hall. Harlow, England.
[13] MUSKE, K. R. RAWLINGS, Ji B. (1993). Model predictive control with linear models, AIChE Journal 3.2. 262-287 doi:10.1002/aic.690390208
[14] MUSKE, K. R. BADGWELL, T. A. (2002). Disturbance modeling for offset-free linear model predictive control, I Proc. Cont. 12, 617-632.
[15] PANNOCCHIA, G. RAWLINGS, J. 13. (2003). Disturbance Models for Offset-Free Model-Predictive Control, AlChE Journal. 4.2, 426-437.
[16] PHILLIPS, C. L. HARBOR, R. D. (1991). Feedback Control Systems, Prentice-Hall International, Inc., London.
[17] QIN, S. J. az BADGWELL, T. A. (1996). An overview of industrial model predictive control technology, Presented at Chemical Process Control-V, Jan 7-12, 1996, Tahoe, CA. Proceedings AlChE Symposium Series 316 93, 232 - 256.
[18] RAWLINGS, J. B. (1999). Private communication, European Control Conference, ECC´99, Karlsruhe, September 2, 1999.

  title={{State Space Realization of Model Predictive Controllers Without Active Constraints}},
  author={Skogestad, Sigurd and Faanes, Audun},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}