## “Handling State and Output Constraints in MPC Using Time-dependent Weights”Authors: Morten Hovd and Richard D. Braatz,
Affiliation: NTNU, Department of Engineering Cybernetics and University of Illinois at Urbana-Champaign
Reference: 2004, Vol 25, No 2, pp. 67-84. |

**Keywords:**Model predictive control; constraints; inverse response; penalty functions

**Abstract:**A popular method for handling state and output constraints in a model predictive control (MPC) algorithm is to use ´soft constraints´, in which penalty terms are added directly to the objective function. Improved closed loop performance can be obtained for plants with nontninimum phase zeros by modifying the MPC formulation to include suitably-designed time-dependent weights on the penalty terms associated with the state and output constraints. When the penalty terms are written in terms of the ´worst-ease´ l-infinity norm, incorporating the appropriate time dependence into the weights provides much better closed loop performance. The approach is illustrated using two multivariable plants with nonminimum phase transmission zeros, where the time-dependent weights cause the open loop predictions to coincide with closed loop predictions, which results in a reduction of output constraint violations.

PDF (1677 Kb) DOI: 10.4173/mic.2004.2.1

**DOI forward links to this article:**

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**References:**

[1] ALLWRIGHT, J. C. PAPAVASILIOU, G. C. (1992). On linear programming and robust model predictive control using impulse responses, Systems and Control Letters, 18: 159-164 doi:10.1016/0167-6911(92)90020-S

[2] CAMPO, P. J. MORARI, M. (1986). Infinity-norm formulation of model predictive control problems, Proc of the American Control Conf, pp. 339-343.New York: IEEE Press.

[3] DAVE, P., DOYLE, F. J., III PEKNY, J. F. (1999). Customization strategies for the solution of linear programming problems arising from large scale model predictive control of a paper machine, J of Process Control, 9: 385-396 doi:10.1016/S0959-1524(99)00011-6

[4] DE OLIVEIRA, N. M. C. BIEGLER, L T. (1994). Constraint handling and stability properties of model-predictive control, AlChE J., 40: 1138-1155.

[5] FEATHERSTONE, A.P., VANANTWERP, J. G. BRAATZ, R. D. (2000). Identification and Control of Sheet and Film Processes, London, UK: Springer Verlag.

[6] GARCIA, C. E., PRETT, D.M. MORARI, M. (1989). Model predictive control: Theory and practice-A survey, Automatica, 25: 335-348 doi:10.1016/0005-1098(89)90002-2

[7] HOVD, M. BRAATZ, R. D. (2001). On the use of soft constraints in MPC controllers for plants with inverse response, Proc. of the 61h IFAC Symp. on Dynamics and Control of Process Systems.Kidlington, UK: Elsevier Science, in press.

[8] MORARI, M. ZAFIRIOU, E. (1989). Robust Process Control, Englewood Cliffs, NJ: Prentice-Hall.

[9] PERESSINI, A. L., SULLIVAN, F. E. UHL, J. J., JR (1988). The Mathematics of Nonlinear Programming, New York: Springer-Verlag.

[10] RAWLINGS, J. B. (1999). Tutorial: Model predictive control technology, Proc. of the American Control Conf.Piscataway, New Jersey, pp. 662-676, IEEE Press.

[11] RAWLINGS, J. B. MUSKE, K.R. (1993). The stability of constrained receding horizon control, IEEE Trans. on Automatic Control, 3.10: 1512-1516 doi:10.1109/9.241565

[12] RICKER, N. L., SUBRAHMANIAN, T. SIM, T. (1989). Case studies of model-predictive control in pulp and paper production, Proc. of the IFAC Workshop on Model Based Process Control (T. J. McAvoy, Y. Arkun and& E. Zafiriou, eds.), pp. 13-22 (Oxford, UK: Pergamon Press).

[13] SKOGESTAD, S. POSTLETHWAITE, I. (1996). Multivariable Feedback Control: Analysis and Design, New York: John Wiley and& Sons.

[14] SCOKAERT, P.O.M. RAWLINGS, J. B. (1999). Feasibility issues in linear model predictive control, AIChE J.,45:1649-1659 doi:10.1002/aic.690450805

[15] VANANTWERP, J.G. BRAATZ, R. D. (2000). Fast model predictive control of sheet and film processes, IEEE Trans. on Control Systems ?Technology; 8:408-417.

[16] VANANTWERP, J.G. BRAATZ, R. D. (2000). Model predictive control of large scale processes, J. of Process Control, 10:1-8 doi:10.1016/S0959-1524(99)00050-5

[17] VUTHANDAM, P., GENCELI, H. NIKOLAOU, M. (1994). Analysis and synthesis methods for robust model predictive control, Proc. of the IFAC Symp. on Advanced Control of Chemical Processes, pp. 167-172.Kidlington, UK: Elsevier Science.

[18] ZAFIRIOU, E. MARCHAL, A.L. (1991). Stability of SISO quadratic dynamic matrix control with hard output constraints, AIChE J., 37:1550-1560 doi:10.1002/aic.690371012

[19] ZHENG, A. MORARI, M. (1995). Stability of model predictive control with mixed constraints, IEEE Trans. on Automatic Control, 40:1818-1823 doi:10.1109/9.467664

**BibTeX:**

@article{MIC-2004-2-1,

title={{Handling State and Output Constraints in MPC Using Time-dependent Weights}},

author={Hovd, Morten and Braatz, Richard D.},

journal={Modeling, Identification and Control},

volume={25},

number={2},

pages={67--84},

year={2004},

doi={10.4173/mic.2004.2.1},

publisher={Norwegian Society of Automatic Control}

};