Abstract
In this work, a comparative study is developed among different methods for state observers design, analyzing their advantages and drawbacks. Three optimal design methods are considered. First, an observer based on the duality theorem and the Linear Quadratic Regulator (LQR) controller design method. Second, a new optimal observer for noiseless described systems. Third, a Kalman filter. The fuzzy observers are obtained by the linearized Takagi-Sugeno (TS) function at each fuzzy rule, so the optimal observers become suboptimal among the fuzzy interpolation of the rules. Two examples are proposed to evaluate the performance of the observers. The first one is an example of linear discrete system, and the second one is a thermal mixing tank, which is a multivariable, delayed and nonlinear system. The results show that for noiseless described systems, the best and easiest method is the new optimal observer, but the Kalman filter is the best choice for reducing noise.
Keywords
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Luenberger, D.G.: An introduction to observers. IEEE Trans. Autom. Control 16, 596–602 (1971)
Bitmead, R., Gevers, R., Wertz, V.: Adaptive Optimal Control The Thinking Man’s GPC. Prentice Hall, Englewood Cliffs (1990)
Ogata, K.: Modern Control Engineering, 5th edn. Prentice Hall, Upper Saddle River (2009)
Lewis, F.L.: Optimal and Robust Estimation: With an Introduction to Strochastic Control Theory. CRC Press, Boca Raton (2008)
Åström, K.J., Wittenmark, B.: Computer-Controlled Systems: Theory and Design. Courier Corporation, North Chelmsford (2013)
Al-Hadithi, B.M., Jiménez, A., Perez-Oria, J.: New incremental Takagi-Sugeno state model for optimal control of multivariable nonlinear time delay systems. Eng. Appl. Artif. Intell. 45, 259–268 (2015)
Al-Hadithi, B.M., Jiménez, A., Matía, F.: New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems. Optim. Control Appl. Methods 33(5), 552–575 (2012)
Grimble, M.J., Hearns, G.: LQG controllers for state-space systems with pure transport delays: application to hot strip mills. Automatica 34(10), 1169–1184 (1998)
Wold, H.: A Study in the Analysis of Stationary Time Series (Second revised edition, with an Appendix on “Recent Developments in Time Series Analysis” by Peter Whittle). Almqvist and Wiksell Book Co., Uppsala (1954)
Uduehi, D., Ordys, A., Grimble, M.J.: A generalized predictive control benchmark index for MIMO Systems. In: IEEE International Conference on Control Applications, Glasgow, U.K, pp. 18–20 (2002)
Moir, T.J., Grimble, M.J.: Optimal self-tuning filtering, prediction, and smoothing for discrete multivariable processes. IEEE Trans. Autom. Control 29(2), 128–137 (1984)
Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. 1, 116–132 (1985)
Al-Hadithi, B.M., Jiménez, A., Matía, F.: A new approach to fuzzy estimation of Takagi-Sugeno model and its applications to optimal control for nonlinear systems. Appl. Soft Comput. 12(1), 280–290 (2012)
Barbieri, E., Richter, H., Figueroa, F.: Small signal point-to-point tracking of a propellant mixer. In: 2003 Proceedings of the American Control Conference, vol. 4, pp. 2845–2850. IEEE, June 2003
Richter, H.: Modeling, simulation and control automation of rocket test stands. Technical report, NASA Stemis Space Center, Mississippi (2002)
Richler, H., Barbieri, E., Figuero, F.: Nonlinear modeling and control of B propellante mixer. In: American Control Conference, pp. 2814–2839 (2003)
Acknowledgments
This work is funded by the Spanish Ministry of Economy and Competitiveness through the project: COGDRIVE: Cognition inspired navigation for autonomous driving (grant DPI2017-86915-C3-3-R).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Adánez, J.M., Al-Hadithi, B.M., Jiménez, A. (2020). Fuzzy Optimal State Observers for Takagi-Sugeno Fuzzy State Feedback Control. In: Bi, Y., Bhatia, R., Kapoor, S. (eds) Intelligent Systems and Applications. IntelliSys 2019. Advances in Intelligent Systems and Computing, vol 1037. Springer, Cham. https://doi.org/10.1007/978-3-030-29516-5_75
Download citation
DOI: https://doi.org/10.1007/978-3-030-29516-5_75
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-29515-8
Online ISBN: 978-3-030-29516-5
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)