Abstract
Motivated by the special class of nonlinear systems, we introduce a scheduling technique that aims at extending the region of validity of linearization by designing an extra scheduling mechanism. Specifically, we show, how a simplification of a control problem may results in a considerably difficult scheduling procedure. In particular, the scheduling problem in the context of a nonlinear model of four tanks is addressed. The main innovation consists in the use of auxiliary scheduling variables dealing with the problem of limited number of output variables. This allows to construct a linear feedback controller at each operating point. Additionally, an integral control which ensures desired stability and performance requirements is presented. The resulting method has been integrated into the gain scheduled control design of the four tanks system and has shown a great performance through the operating range.
References
Jiang, J.: Optimal gain scheduling controllers for a diesel engine. IEEE Control Syst. Mag. 14(4), 42–48 (1994)
Krhovják, A., Dostál, P., Talaš, S. Rušar, L.: Nonlinear gain scheduled controller for a sphere liquid tank. s.l. In: European Council for Modelling and Simulation (ECMS), pp. 327–332 (2015)
Krhovják, A., Dostál, P., Talaš, S., Rušar, L.: Multivariable gain scheduled control of two funnel liquid tanks in series. In: Strbske Pleso, s.n., pp. 60–65 (2015)
Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice Hall, Upper Saddle River (2002)
Lawrence, D.A., Rugh, W.J.: Gain scheduling dynamic linear controllers for a nonlinear plant. Automatica 31, 381–390 (1995)
Raff, T., Hubber, S., Nagy, Z.K., Allglöwer, F.: Nonlinear Model Predictive Control of a Four Tank System: An Experimental Stability Study, pp. 237–242. IEEE, Munich (2006)
Rugh, W.J.: Analytical framework for gain scheduling. IEEE Control Syst. Mag. 11(1), 79–84 (1991)
Shamma, J.S., Athans, M.: Analysis of gain scheduled control for nonlinear plants. IEEE Trans. Autom. Control 35(8), 898–907 (1990)
Shamma, J.S., Athans, M.: Gain scheduling: potential hazards and possible remedies. IEEE Control Syst. Mag., 101–107 (1991)
Shamma, J.S., Athans, M.: Guaranteed properties of gain scheduled control of linear parameter-varying plants. Automatica 27(4), 559–564 (1991)
Acknowledgments
This article was created with support of the Ministry of Education of the Czech Republic under grant IGA reg. n. IGA/FAI/2016/006.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Krhovják, A., Talaš, S., Rušar, L. (2016). Multivariable Gain Scheduled Control of Four Tanks System: Single Scheduling Variable Approach. In: Silhavy, R., Senkerik, R., Oplatkova, Z.K., Silhavy, P., Prokopova, Z. (eds) Automation Control Theory Perspectives in Intelligent Systems. CSOC 2016. Advances in Intelligent Systems and Computing, vol 466. Springer, Cham. https://doi.org/10.1007/978-3-319-33389-2_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-33389-2_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-33387-8
Online ISBN: 978-3-319-33389-2
eBook Packages: EngineeringEngineering (R0)