In this paper, we present a new approach to multirate predictive control with a multiple reference model in order to control commercial processes with nonlinear models, such as batch dyeing thermal processes. The time delay problem is resolved successfully by using multirate predictive control, and we introduce nonlinear optimization based on an augmented Lagrangien objective function to minimize the multirate predictive control quadratic criterion in the case of the nonlinear plant model. Moreover, the multirate approach improves predictive control robustness. The results of our study are used to simulate nonlinear thermal plant control with very good results. For this reason, our future work will use this method to control a batch dyeing process.
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References
1.
BerkstresserG.BeckK.SmithB.McGregorR.JasperW., Novel Approaches for the Real-Time Prediction of Dye Concentrations in Three Dye Mixture, presented to the AATCC National Technical Conference Meeting, Montreal, Quebec, 1993.
2.
CariniP.MicheliR.ScattoliniR., Multirate Self-Tuning Predictive Control with Application to a Binary Distillation Column, Int. J. System Sci.21, 51–64 (1990).
3.
ClarkeD. W., Application of Generalized Predictive Control to Industrial Processes, IEEE Control Sys. Mag. (4), 49–55 (1988).
4.
ColaneriP.ScattoliniR.SchiavoniN., Regulation of Multirate Sampled-Data Systems, C-TAT7, 429–441 (1991).
5.
ColaneriP.ScattoliniR.SchiavoniN., Stabilization, Regulation and Optimization of Multirate Sampled-Data Systems, in “Control and Dynamic Systems,”LeondesC. T., ed., Academic Press, NY, 1992.
6.
ColaneriP.ScattoliniR.SchiavoniN., Stabilization of Multirate Sampled-Data Systems, Automatica26, 377–380 (1990).
7.
IrwingE.FalinowerC.FonteC., Adaptive Generalized Predictive Control with Multiple Reference Model, in “Proc. 2nd IFAC Workshop on Adaptive Systems in Control and Signal Processing,” Lund, Sweden, 1986.
8.
KevickyL.KumarK. S., Multivariate Self Tuning Regulator with Generalized Cost Function, Int. J. Control.33, 913–921 (1991).
9.
KoncarV.KoubaaM. A.BruniauxP.VasseurC., Predictive Control with Auto-adjustable Parameter, in “Proc. CESA'96 IMACS Multiconference, Symposium on Control Optimization and Supervision,”Lille, France, July 9–12, 1996, pp. 344–349.
10.
KoncarV.KoubaaM. A.BruniauxP.VasseurC., Robust Setting of the Predictive Control Parameters, presented to the 2éme Congrés Maghrébin de Génie Electrique, September 16–17, 1995, Tunis.
11.
KoncarV.KoubaaM. A.VasseurC., Multirate Predictive Control with Multiple Référence Model—Robustness Evaluation in “Proc. 12th International Conference Systems Engineering,” ICSE'95, vol. 1, Wroclaw, Poland, 1995, pp. 444–454.
12.
KoncarV.KoubaaM. A.LegrandX.BruniauxP.VasseurC., Predictive Control with Non Linear Optimization: Application to a Thermal Process, in “Proc. 11th International Conference Systems Engineering, ICSE'96, Las Vegas Nevada, July 9–11, 1996.
13.
KoncarV.VasseurC., Commande Numerique par Suréchantillonnage, Application à la Réalisation d'une Carte d'Axe, ISMM, Lugano, Switzerland, June 1990.
14.
KoncarV.VasseurC., Multirate Predictive Control with Multiple Reference Model, Application on DC Motor, in “Proc. 3rd Int. IEEE Workshop on Advanced Motion Control,” Berkeley, CA, March 1994, pp. 20–23.
15.
KoncarV.VasseurC.BruniauxP.PinchonD., Multirate Predictive Control with Multiple Reference Model Application on Thermic Process, presented to IFAC Conference, System Structure and Control, Nantes, France, July 5–7, 1995.
16.
LenartsonB., Multirate Sampled Data Control of Two Time Scale Systems, IEEE Trans. Auto. Control34, 624–644 (1989).
17.
MinouxM., “Programmation Mathématique, Théorie et Algorithmes,”vol. 1, Ouvrage paru dans la Collection Technique et Scientifique des Télécommunications, Dunod, 1983.
18.
PowellM. J. D., A Method for Non Linear Constraints in Minimization Problems, in “Optimization,”FletcherR., Ed., Academic Press, NY, pp. 283–298.
19.
RachidA., Robustness of Discrete Systems under Structured Uncertainties, Int. J. Control50 (4), 1563–1566 (1989).
20.
ScattoliniR., Multirate Self-Tuning Controller for Multivariable Systems, Int. J. System Sci.23, 1347–1359 (1992).
21.
ScattoliniR.SchiavoniN., A Multirate Model Based Predictive Controller, in “Proc. 33d Conference on Decision Control,” Lake Buena Vista, FL, December 1994, pp. 243–248.
