Supervised Gain-Scheduling Multimodel versus Linear Parameter Varying Internal Model Control of Open-Channel Systems for Large Operating Conditions
Publication: Journal of Irrigation and Drainage Engineering
Volume 136, Issue 8
Abstract
In this paper, two internal model control (IMC) controllers using gain-scheduling techniques are proposed and compared for open-channel systems that allow to deal with large operating conditions. In particular, in one side, a linear parameter varying (LPV) model for an open-flow channel system based on a second-order delay Hayami model is proposed. This model will allow one to design a classic gain-scheduling strategy for the IMC controller. On the other side, the LPV model is discretized in a set of linear time invariant (LTI) models corresponding to different operating points. For each LTI model a LTI IMC controller is designed off-line. Then, a supervised gain-scheduler detects on-line which is the LTI model that represents better the open-flow channel system at the current operating point and decides which is the LTI controller that should be used. Finally, both approaches will be applied to a simulated open canal: the Lunax gallery located at Gascogne, France.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was supported by the Communauté de Travail des Pyrénées referenced as the PREDO project by the Conseil Régional de Midi-Pyrénées and the Generalitat de Catalunya and by the Spanish Ministry of Education under Grant No. UNSPECIFIEDWATMAN DPI2009-13744. Thanks also to our partner the CACG company and its engineering department, located at Tarbes, France.
References
Apkarian, P., Gahinet, P., and Becker, G. (1995). “Self-scheduled h∞ control of linear parameter-varying systems: A design example.” Automatica, 31(9), 1251–1261.
Aström, K. J., and Wittenmark, B. (1997a). Adaptive control, 3rd Ed., Prentice-Hall, Upper Saddle River, N.J.
Aström, K. J., and Wittenmark, B. (1997b). Computer-controlled systems: Theory and design, 3rd Ed., Prentice-Hall, Upper Saddle River, N.J.
Bamieh, B., and Giarré, L. (2002). “Identification of linear parameter varying models.” Int. J. Robust Nonlinear Control, 12, 841–853.
Baume, J., Malaterre, P., Vion, P., and Litrico, X. (1992). SIC user’s guide and theoretical concepts, CEMAGREF, Montpellier, France.
Becker, G., and Packard, A. (1994). “Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback.” Syst. Control Lett., 23, 205–215.
Charbonnaud, P., Rotella, F., and Médar, S. (2001). “Process operating mode monitoring: Switching online the right controller.” IEEE Trans. Syst. Man Cybern., Part C Appl. Rev., 31(1), 77–86.
Cunge, J. A., Holly, F. M., and Verwey, A. (1980). Practical aspects of computational river hydraulics, Pitman Publishing Ltd., London.
Datta, A., and Ochoa, J. (1996). “Adaptive internal model control: Design and stability analysis.” Automatica, 32(2), 261–266.
Deltour, J. -L. (1992). “Application de l’automatique numérique è la régulation des canaux; proposition d’une m’ethodologie d’étude.” Ph.D. thesis, Institut National Polytechnique de Grenoble, Grenoble, France (in French).
Hu, Q., and Rangaiah, G. P. (1999). “Adaptive internal model control of nonlinear processes.” Chem. Eng. Sci., 54(9), 1205–1220.
Korba, P., Babuska, R., Verbruggen, H. B., and Frank, P. M. (2003). “Fuzzy gain scheduling: Controller and observer design based on lyapunov method and convex optimization.” IEEE Trans. Fuzzy Syst., 11(3), 285–298.
Landau, I. D., and Zito, G. (2006). Digital control systems: Design, identification and implementation, Springer, Berlin.
Leith, D. J., and Leithead, W. (2000). “Survey of gain-scheduling analysis and design.” Int. J. Control, 73, 1001–1025.
Leith, D. J., Shorten, R. N., and Leithead, W. E. (2003). “Issues in the design of switched linear control systems: A benchmark study.” Int. J. Adapt. Control Signal Process., 17, 103–118.
Litrico, X. (2002). “Robust IMC flow control of SIMO dam-river open-channel systems.” IEEE Trans. Control Syst. Technol., 10(3), 432–437.
Litrico, X., and Georges, D. (1999). “Robust continuous-time and discrete-time flow control of a dam river system. (i) Modelling.” Appl. Math. Model., 23, 809–827.
Malaterre, P. (1994). “Modelling, analysis and LQR optimal control of an irrigation canal.” Ph.D. thesis, LAAS-CNRS-ENGREF-Cemagref, Montpellier, France (in French).
Miller, W. A., and Cunge, J. (1975). Unsteady flow in open channels, K. Mahmood and V. Yevjevich, eds., Water Resources Pulications, Fort Collins, Colo., 183–257.
Morari, M., and Zafiriou, E. (1989). Robust process control, Prentice-Hall, Englewood Cliffs, N.J.
Normey-Rico, J. E., and Camacho, E. F. (2007). Control of dead-time processes, Springer, Berlin.
Ooi, S. K., Krutzen, M., and Weyer, E. (2003). “On physical and data driven modeling of irrigation channels.” Control Eng. Pract., 13, 461–471.
Rey, J. (1990). Contribution to water transfer modelling and regulation for river-pond systems, ENGREF-USTL-Cemagref, Montpellier, France (in French).
Rugh, W., and Shamma, J. (2000). “Research on gain scheduling.” Automatica, 36, 1401–1425.
Shamma, J. S., and Athans, M. (1991). “Guaranteed properties of gain scheduled control for linear parameter varying plants.” Automatica, 27, 559–564.
Tanaka, K., and Wang, H. O. (2002). Fuzzy control systems design and analysis. A linear matrix inequality approach, Wiley, New York.
Zhuan, X., and Xia, X. (2007). “Models and control methodologies in open water flow dynamics: A survey.” Proc., IEEE AFRICON, IEEE Africon, Windhoek, Namibia, 1–7.
Information & Authors
Information
Published In
Journal of Irrigation and Drainage Engineering
Volume 136 • Issue 8 • August 2010
Pages: 543 - 552
Copyright
© 2010 ASCE.
History
Received: Oct 9, 2008
Accepted: Dec 29, 2009
Published online: Jan 5, 2010
Published in print: Aug 2010
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.