Effective dual-mode fuzzy DMC algorithms with on-line quadratic optimization and guaranteed stability

Piotr M. Marusak ; Piotr Tatjewski

International Journal of Applied Mathematics and Computer Science, Tome 19 (2009), p. 127-141 / Harvested from The Polish Digital Mathematics Library

Résumé

Dual-mode fuzzy dynamic matrix control (fuzzy DMC-FDMC) algorithms with guaranteed nominal stability for constrained nonlinear plants are presented. The algorithms join the advantages of fuzzy Takagi-Sugeno modeling and the predictive dual-mode approach in a computationally efficient version. Thus, they can bring an improvement in control quality compared with predictive controllers based on linear models and, at the same time, control performance similar to that obtained using more demanding algorithms with nonlinear optimization. Numerical effectiveness is obtained by using a successive linearization approach resulting in a quadratic programming problem solved on-line at each sampling instant. It is a computationally robust and fast optimization problem, which is important for on-line applications. Stability is achieved by appropriate introduction of dual-mode type stabilization mechanisms, which are simple and easy to implement. The effectiveness of the proposed approach is tested on a control system of a nonlinear plant-a distillation column with basic feedback controllers.

Détail

Publié le : 2009-01-01

Zbl 1169.93358

EUDML-ID : urn:eudml:doc:207914

Bibliographie

[000] Blevins, T., McMillan, G., Wojsznis, W. and Brown, M. (2003). Advanced Control Unleashed, ISA-The Instrumentation, Systems, and Automation Society, Research Triangle Park, NC.

[001] Camacho, E. and Bordons, C. (1999). Model Predictive Control, Springer-Verlag, London. | Zbl 1223.93037

[002] Cao, S., Rees, N. and Feng, G. (1997). Analysis and design for a class of complex control systems. Part I: Fuzzy modelling and identification, Automatica 33(6): 1017-1028. | Zbl 0887.93035

[003] Chen, J., Xi, Y. and Zhang, Z. (1998). A clustering algorithm for fuzzy model identification, Fuzzy Sets and Systems 98(3): 319-329.

[004] Cutler, C. and Ramaker, B. (1980). Dynamic matrix control - A computer control algorithm, Proceedings of the Joint Automatic Control Conference, San Francisco, CA, USA, paper no. WP5-B.

[005] Driankov, D., Hellendoorn, H. and Reinfrank, M. (1993). An Introduction to Fuzzy Control, Springer-Verlag, Berlin. | Zbl 0789.93088

[006] Garcia, C. (1984). Quadratic dynamic matrix control of nonlinear processes: An application to a batch reaction process, Proceedings of the AIChE Annual Meeting, San Francisco, CA, USA, paper no. 82f.

[007] Garcia, C. and Morshedi, A. (1986). Quadratic programming solution of dynamic matrix control (QDMC), Chemical Engineering Communications 46(1-3): 73-87.

[008] Gattu, G. and Zafiriou, E. (1992). Nonlinear quadratic dynamic matrix control with state estimation, Industrial and Engineering Chemistry Research 31(4): 1096-1104.

[009] Lee, J. and Ricker, N. (1994). Extended Kalman filter based nonlinear model predictive control, Industrial and Engineering Chemistry Research 33(6): 1530-1541.

[010] Li, W. and Biegler, L. (1989). Multistep, Newton-type control strategies for constrained, nonlinear processes, Chemical Engineering Research and Design 67(Nov.): 562-577.

[011] Maciejowski, J. (2002). Predictive Control with Constraints, Prentice Hall, Harlow. | Zbl 0978.93002

[012] Marusak, P. (2002). Predictive control of nonlinear plants using dynamic matrix and fuzzy modeling, Ph.D. thesis, Warsaw University of Technology, Warsaw, (in Polish).

[013] Marusak, P. and Tatjewski, P. (2000). Fuzzy dynamic matrix control algorithms for nonlinear plants, Proceedings of the 6-th International Conference on Methods and Models in Automation and Robotics MMAR 2000, Mi˛edzyzdroje, Poland, pp. 749-754.

[014] Marusak, P. and Tatjewski, P. (2001). Stability analysis of nonlinear control systems with fuzzy DMC controllers, Proceedings of the IFAC Workshop on Advanced Fuzzy and Neural Control, AFNC'01, Valencia, Spain, pp. 21-26.

[015] Marusak, P. and Tatjewski, P. (2002). Stability analysis of nonlinear control systems with unconstrained fuzzy predictive controllers, Archives of Control Sciences 12(3): 267-288. | Zbl 1151.93378

[016] Marusak, P. and Tatjewski, P. (2003). Stable, effective fuzzy DMC algorithms with on-line quadratic optimization, Proceedings of the American Control Conference, ACC 2003, Denver, CO, USA, pp. 3513-3518.

[017] Mayne, D., Rawlings, J., Rao, C. and Scokaert, P. (2000). Constrained model predictive control: Stability and optimality, Automatica 36(6): 789-814. | Zbl 0949.93003

[018] Michalska, H. and Mayne, D. (1993). Robust receding horizon control of constrained nonlinear systems, IEEE Transactions on Automatic Control 38(11): 1623-1632. | Zbl 0790.93038

[019] Morari, M. and Lee, J. (1999). Model predictive control: Past, present and future, Computers and Chemical Engineering 23(4): 667-682.

[020] Mutha, R., Cluett, W. and Penlidis, A. (1997). Nonlinear modelbased predictive control of control nonaffine systems, Automatica 33(5): 907-913. | Zbl 0874.93048

[021] Mutha, R., Cluett, W. and Penlidis, A. (1998). Modifying the prediction equation for nonlinear model-based predictive control, Automatica 34(10): 1283-1287. | Zbl 0938.93522

[022] Piegat, A. (2001). Fuzzy Modeling and Control, Physica-Verlag, Berlin. | Zbl 0976.93001

[023] Rossiter, J. (2003). Model-Based Predictive Control, CRC Press, Boca Raton, FL.

[024] Scokaert, P., Mayne, D. and Rawlings, J. (1999). Suboptimal model predictive control (feasibility implies stability), IEEE Transactions on Automatic Control 44(3): 648-654. | Zbl 1056.93619

[025] Setnes, M. and Roubos, H. (2000). GA-fuzzy modeling and classification: Complexity and performance, IEEE Transactions on Fuzzy Systems 8(5): 509-522.

[026] Takagi, T. and Sugeno, M. (1985). Fuzzy identification of systems and its application to modeling and control, IEEE Transactions on Systems, Man and Cybernetics 15(1): 116-132. | Zbl 0576.93021

[027] Tanaka, K. and Sugeno, M. (1992). Stability analysis and design of fuzzy control systems, Fuzzy Sets and Systems 45(2): 135-156. | Zbl 0758.93042

[028] Tatjewski, P. (2007). Advanced Control of Industrial Processes; Structures and Algorithms, Springer-Verlag, London. | Zbl 1134.93037

[029] Yager, R. and Filev, D. (1994). Essentials of Fuzzy Modeling and Control, Wiley, New York, NY.