×

zbMATH — the first resource for mathematics

Model predictive control: Theory and practice - a survey. (English) Zbl 0685.93029
Summary: We refer to Model Predictive Control (MPC) as that family of controllers in which there is a direct use of an explicit and separately identifiable model. Control design methods based on the MPC concept have found wide acceptance in industrial applications and have been studied by academia. The reason for such popularity is the ability of MPC designs to yield high performance control systems capable of operating without expert intervention for long periods of time.
In this paper the issues of importance that any control system should address are stated. MPC techniques are then reviewed in the light of these issues in order to point out their advantages in design and implementation. A number of design techniques emanating from MPC, namely Dynamic Matrix Control, Model Algorithmic Control, Inferential Control and Internal Model Control, are put in perspective with respect to each other and the relation to more traditional methods like Linear Quadratic Control is examined.
The flexible constraint handling capabilities of MPC are shown to be a significant advantage in the context of the overall operating objectives of the process industries and the 1-, 2-, and \(\infty\)-norm formulations of the performance objective are discussed. The application of MPC to non-linear systems is examined and it is shown that its main attractions carry over. Finally, it is explained that though MPC is not inherently more or less robust than classical feedback, it can be adjusted more easily for robustness.

MSC:
93B40 Computational methods in systems theory (MSC2010)
93B50 Synthesis problems
62M20 Inference from stochastic processes and prediction
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Arkun, Y., Design of steady-state optimizing control structures for chemical processes, ()
[2] Arkun, Y.; Hollett, J.; Canney, W.M.; Morari, M., Experimental study of internal model control, Ind. engng chem. process des. dev., 25, 102-108, (1986)
[3] Athans, M.; Falb, P.L., ()
[4] Bristol, E.H., After DDC. idiomatic control, Chem. engng prog., 76, 11, 84-89, (1980)
[5] Brosilow, C.B., The structure and design of Smith predictors from the viewpoint of inferential control, () · Zbl 0575.93029
[6] Brosilow, C.B.; Zhao, G.Q.; Rao, K.C., A linear programming approach to constrained multivariable control, (), 667-674
[7] Brosilow, C.B.; Zhao, G.Q., A linear programming approach to constrained multivariable process control, Adv. control dyn. syst., 24, (1986) · Zbl 0649.93034
[8] Bryson, A.E.; Denham, W.F.; Dreyfus, S.E., Optimal programming problems with inequality constraints—I. necessary conditions for extremal solutions, Aiaa j., 1, 2544-2550, (1963) · Zbl 0142.35902
[9] Bryson, A.E.; Ho, Y., (), Wiley, New York
[10] Caldwell, J.M.; Martin, G.D., On-line analyzer predictive control, ()
[11] Campo, P.J.; Morari, M., ∞-norm formulation of model predictive control problems, (), 339-343
[12] Chang, S.S.L., ()
[13] Chang, T.S.; Seborg, D.E., A linear programming approach to multivariable feedback control with inequality constraints, Int. J. control, 37, 583-597, (1983) · Zbl 0502.93043
[14] Clarke, D.W.; Mohtadi, C., Properties of generalized predictive control, (), 63-74 · Zbl 0699.93028
[15] Clarke, D.W.; Mohtadi, C.; Tuffs, P.S., Generalized predictive control—I. the basic algorithm, Automatica, 23, 137-148, (1987) · Zbl 0621.93032
[16] Clarke, D.W.; Mohtadi, C.; Tuffs, P.S., Generalized predictive control—II. extensions and interpretations, Automatica, 23, 149-160, (1987) · Zbl 0621.93033
[17] Cutler, C.R.; Ramaker, B.L., Dynamic matrix control—a computer control algorithm, (), also
[18] Cutler, C.R.; Hawkins, R.B., Constrained multivariable control of a hydrocracker reactor, (), 1014-1020
[19] DeKeyser, R.M.C.; van Cauwenberghe, A.R., Typical application possibilities for self-tuning predictive control, (), 1552-1557
[20] DeKeyser, R.M.C.; van Cauwenberghe, A.R., Extended prediction self-adaptive control, (), 1255-1260
[21] DeKeyser, R.M.C.; VandeVelde, Ph.G.A.; Dumoriter, F.A.G., A comparative study of self-adaptive long-range predictive control methods, (), 1317-1322
[22] Denham, W.F.; Bryson, A.E., Programming problems with inequality constraints—II. solution by the steepest ascent, Aiaa j., 2, 25-26, (1964)
[23] Economou, C.G.; Morari, M., Newton control laws for nonlinear controller design, (), 1361-1366
[24] Economou, C.G., An operator theory approach to nonlinear controller design, ()
[25] Economou, C.G.; Morari, M.; Palsson, B., Internal model control—5. extension to nonlinear systems, Ind. engng chem. process des. dev., 25, 403-411, (1986)
[26] Enns, D., Model reduction for control system design, ()
[27] Frank, P.M., (), (1974)
[28] Gantmacher, F.R., ()
[29] García, C.E., Studies in optimizing and regulatory control of chemical processing systems, ()
[30] García, C.E.; Morari, M., Internal model control—1. A unifying review and some new results, Ind. engng chem. process des. dev., 21, 308-323, (1982)
[31] García, C.E., Quadratic dynamic matrix control of nonlinear processes. an application to a batch reaction process, ()
[32] García, C.E.; Morshedi, A.M., Quadratic programming solution of dynamic matrix control (QDMC), (), Chem. engng commun., 46, 73-87, (1986), also
[33] García, C.E.; Morari, M., Internal model control—2. design procedure for multivariable systems, Ind. engng chem. process des. dev., 24, 472-484, (1985)
[34] García, C.E.; Morari, M., Internal model control—3. multivariable control law computation and tuning guidelines, Ind. engng chem. process des. dev., 24, 484-494, (1985)
[35] García, C.E.; Prett, D.M., Advances in industrial model—predictive control, (), 249-294
[36] Giloi, W., Zur theorie und verwirklichung einer regelung für laufzeitstreken nach dem prinzip der ergänzenden Rückführung, Ph.D. thesis, (1959), TH Stuttgart
[37] Grosdidier, P. (1987). Setpoint, Inc., Houston, Personal communication.
[38] Gutman, P.O., Controllers for bilinear and constrained linear systems, ()
[39] Hirschorn, R.M., Invertibility of multivariable nonlinear control systems, IEEE trans. aut. control, 24, 855-865, (1979) · Zbl 0427.93020
[40] Horowitz, I.M., ()
[41] Kwakernaak, H.; Sivan, R., ()
[42] Lee, E.B.; Markus, L., ()
[43] Levien, K.L., Studies in the design and control of coupled distillation columns, ()
[44] Levien, K.L.; Morari, M., Internal model control of coupled distillation columns, A.I.ch.E. jl, 33, 83, (1987)
[45] Marqués, D., On-line optimization of large scale dynamic systems, ()
[46] Marqués, D.; Morari, M., Model predictive control of gas pipeline networks, (), 349-354
[47] Martin, G.D.; Caldwell, J.M.; Ayral, T.E., Predictive control applications for the petroleum refining industry, ()
[48] Matsko, T.N., Internal model control for chemical recovery, Chem. engng prog., 81, 12, 46-51, (1985)
[49] Mehra, R.K.; Rouhani, R., Theoretical considerations on model algorithmic control for nonminimum phase systems, ()
[50] Mehra, R.K.; Rouhani, R.; Eterno, J.; Richalet, J.; Rault, A., Model algorithmic control: review and recent development, (), 287-310
[51] Morari, M.; Stephanopoulos, G., Minimizing unobservability in inferential control schemes, Int. J. control, 31, 367-377, (1980) · Zbl 0428.93008
[52] Morari, M.; Doyle, J.C., A unifying framework for control system design under uncertainty and its implications for chemical process control, (), 5-52
[53] Morari, M.; Scali, C., A comparison of internal model control and linear quadratic optimal control for SISO systems, Ind. engng chem. res., (1989), (submitted)
[54] Morari, M.; Zafiriou, E., ()
[55] Morshedi, A.M.; Cutler, C.R.; Skrovanek, T.A., Optimal solution of dynamic matrix control with linear programming techniques (LDMC), (), 199-208
[56] Newton, G.C.; Gould, L.A.; Kaiser, J.F., ()
[57] Parrish, J.R.; Brosilow, C.B., Inferential control applications, Automatica, 21, 527-538, (1985) · Zbl 0575.93029
[58] Peterka, V., Predictor-based self-tuning control, Automatica, 20, 39-50, (1984) · Zbl 0539.93054
[59] Prett, D.M.; Gillette, R.D.; Prett, D.M.; Gillette, R.D., Optimization and constrained multivariable control of a catalytic cracking unit, (), also
[60] Prett, D.M.; García, C.E., ()
[61] Propoi, A.I., Use of LP methods for synthesizing sampled-data automatic systems, Automn remote control, 24, 837, (1963)
[62] Reid, J.G.; Mehra, R.K.; Kirkwood, E., Robustness properties of output predictive dead-beat control: SISO case, ()
[63] Richalet, J.A.; Rault, A.; Testud, J.L.; Papon, J., Model predictive heuristic control: applications to an industrial process, Automatica, 14, 413-428, (1978)
[64] Ricker, N.L., The use of quadratic programming for constrained internal model control, Ind. engng chem. process des. dev., 24, 925-936, (1985)
[65] Skogestad, S.; Morari, M., Control of ill-conditioned plants: high purity distillation, () · Zbl 0669.93055
[66] Smith, O.J.M., Closer control of loops with dead time, Chem. engng prog., 53, 5, 217-219, (1957)
[67] Vidyasagar, M., ()
[68] Ydstie, B.E., Extended horizon adaptive control, () · Zbl 0572.93070
[69] Youla, D.C.; Bongiorno, J.J.; Jabr, H.A., Modern Wiener-Hopf design of optimal controllers—I. the single-input-output case, IEEE trans. aut. control, AC-21, 3-13, (1976) · Zbl 0323.93047
[70] Youla, D.C.; Jabr, H.A.; Bongiorno, J.J., Modern Wiener-Hopf design of optimal controllers—II. the multivariable case, IEEE trans. aut. control, AC-21, 319-338, (1976) · Zbl 0339.93035
[71] Zadeh, L.A.; Whalen, B.H., On optimal control and linear programming, IRE trans. aut. control, 7, 4, 45, (1962)
[72] Zafiriou, E.; Morari, M., Digital controllers for SISO systems, A review and a new algorithm, Int. J. control, 42, 855-876, (1985) · Zbl 0577.93044
[73] Zafiriou, E.; Morari, M., Robust digital controller design for multivariable systems, () · Zbl 0642.93025
[74] Zafiriou, E.; Morari, M., Design of the IMC filter by using the structured singular value approach, (), 1-6
[75] Zafiriou, E.; Morari, M., Design of robust controllers and sampling time selection for SISO systems, Int. J. control, 44, 711-735, (1986) · Zbl 0602.93048
[76] Zafiriou, E.; Morari, M., Digital controller design for multivariable systems with structural closed-loop performance specifications, Int. J. control, 46, 2087-2111, (1987) · Zbl 0642.93025
[77] Zames, G., Feedback and optimal sensitivity: model reference transformations, multiplicative seminorms, and approximate inverses, IEEE trans. aut. control, AC-26, 301-320, (1981) · Zbl 0474.93025
[78] Zirwas, H.C., Die ergänzende Rückführung als mittel zur schnellen regelung von regelstrecken mit laufzeit, Ph.D. thesis, (1958), TH Stuttgart
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.