An infinite horizon predictive control algorithm based on multivariable input-output models

• Autorzy: Ławryńczuk M. , Tatjewski P.
• Języki publikacji: EN

Abstrakty

EN

In this paper an infinite horizon predictive control algorithm, for which closed loop stability is guaranteed, is developed in the framework of multivariable linear input-output models. The original infinite dimensional optimisation problem is transformed into a finite dimensional one with a penalty term. In the unconstrained case the stabilising control law, using a numerically reliable SVD decomposition, is derived as an analytical formula, calculated off-line. Considering constraints needs solving on-line a quadratic programming problem. Additionally, it is shown how free and forced responses can be calculated without the necessity of solving a matrix Diophantine equation.

Słowa kluczowe

EN

model predictive control; stability; infinite horizon; singular value decomposition; quadratic programming

PL

sterowanie predykcyjne; horyzont nieskończony; programowanie kwadratowe

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2004
• Tom: Vol. 14, no 2
• Strony: 167--180
• Opis fizyczny: Bibliogr. 28 poz., wykr.

Twórcy

autor

Ławryńczuk M.

• Warsaw University of Technology, Institute of Control and Computation Engineering, ul. Nowowiejska 15/19, 00–665 Warszawa, Poland

autor

Tatjewski P.

• Warsaw University of Technology, Institute of Control and Computation Engineering, ul. Nowowiejska 15/19, 00–665 Warszawa, Poland

Bibliografia

• [1] Bitmead R.R., Gevers M. and Wertz V. (1990): Adaptive Optimal Control—The Thinking Man’s GPC. — Englewood Cliffs: Prentice Hall.
• [2] Camacho E.F. and Bordons C. (1999): Model Predictive Control. — London: Springer.
• [3] Chisci L. and Mosca E. (1994): Stabilizing I-O receding horizon control of CARMA plants.— IEEE Trans. Automat. Contr., Vol. 39, No. 3, pp. 614–618.
• [4] Clarke D.W. and Scattolini R. (1991): Constrained recedinghorizon predictive control. — Proc. IEE, Part D, Vol. 138, No. 4, pp. 347–354.
• [5] Clarke D.W. and Mohtadi C. (1989): Properties of generalized predictive control.— Automatica, Vol. 25, No. 6, pp. 859–875.
• [6] Clarke D.W., Mohtadi C. and Tuffs P.S. (1987a): Generalized predictive control – I. The basic algorithm.— Automatica, Vol. 23, No. 2, pp. 137–148.
• [7] Clarke D.W., Mohtadi C. and Tuffs P.S. (1987b): Generalized predictive control – II. Extensions and interpretations. — Automatica, Vol. 23, No. 2, pp. 149–160.
• [8] Cutler C.R. and Ramaker B.L. (1980): Dynamic matrix control – A computer control algorithm. — Proc. Joint. Automat. Contr. Conf., San Francisco.
• [9] Golub G.H. and Van Loan C.F. (1989): Matrix Computations. — Baltimore: The Johns Hopkins University Press.
• [10] Gutman P. and Hagander P. (1985): A new design of constrained controllers for linear systems. — IEEE Trans. Automat. Contr., Vol. 30, No. 1, pp. 22–33.
• [11] Henson M.A. (1998): Nonlinear model predictive control: current status and future directions. — Comput. Chem. Eng., Vol. 23, No. 2, pp. 187–202.
• [12] Kailath T. (1980): Linear Systems. — Englewood Cliffs: Prentice Hall.
• [13] Kwon W.H. and Byun D.G. (1989): Receding horizon tracking control as a predictive control and its stability properties. — Int. J. Contr., Vol. 50, No. 5, pp. 1807–1824.
• [14] Maciejowski J.M. (2002): Predictive Control with Constraints.— Englewood Cliffs: Prentice Hall.
• [15] Mayne D.Q. (2001): Control of constrained dynamic systems.— Europ. J. Contr., Vol. 7, Nos. 2–3, pp. 87–99.
• [16] Mayne D.Q., Rawlings J.B., Rao C.V. and Scokaert P.O.M. (2000): Constrained model predictive control: Stability and optimality.— Automatica, Vol. 36, No. 6, pp. 789–814.
• [17] Morari M. and Lee J.H. (1999): Model predictive control: past, present and future. — Comput. Chem. Eng., Vol. 23, No. 4/5, pp. 667–682.
• [18] Muske K.R. and Rawlings J.B. (1993): Model predictive control with linear models. — AIChE J., Vol. 39, No. 2, pp. 262–287.
• [19] Ordys W.A., Hangstrup M.E. and Grimble M.J. (2000): Dynamic algorithm for linear quadratic Gaussian predictive control.—Int. J. Appl. Math. Comput. Sci., Vol. 10, No. 2, pp. 227–244.
• [20] Rawlings J.B. and Muske K.R. (1993): The stability of constrained receding horizon control. — IEEE Trans. Automat. Contr., Vol. 38, No. 10, pp. 1512–1516.
• [21] Rouhani R. and Mehra R.K. (1982): Model algoritmic control (MAC); Basic theoretical properties. — Automatica, Vol. 18, No. 4, pp. 401–414.
• [22] Scattolini R. and Bittanti S. (1990): On the choice of the horizon in long-range predictive control – some simple criteria.— Automatica, Vol. 26, No. 5, pp. 915–917.
• [23] Scokaert P.O.M. (1997): Infinite horizon generalized predictive control. — Int. J. Contr., Vol. 66, No. 1, pp. 161–175.
• [24] Scokaert P.O.M. and Clarke D. W. (1994): Stabilising properties of constrained predictive control.—Proc. IEE, Part D, Vol. 141, No. 5, pp. 295–304.
• [25] Sznaier M. and Damborg M.J. (1990): Heuristically enhanced feedback control of constrained discrete-time linear systems. — Automatica, Vol. 26, No. 3, pp. 521–532.
• [26] Tatjewski P. (2002): Advanced Control of Industrial Processes, Structures and Algorithms. — Warszawa: Akademicka Oficyna Wydawnicza Exit (in Polish).
• [27] Zafiriou E. (1990): Robust model predictive control of processes with hard constraints. — Comput. Chem. Eng., Vol. 14, Nos. 4/5, pp. 359–371.
• [28] Zafiriou E. and Marchal A.L. (1991): Stability of SISO quadratic dynamic matrix control with hard output constraints. — AIChE J., Vol. 37, No. 10, pp. 1550–1560.