# Fuzzy feedback linearizing controller and its equivalence with the fuzzy nonlinear internal model control structure

Reda Boukezzoula; Sylvie Galichet; Laurent Foulloy

International Journal of Applied Mathematics and Computer Science (2007)

- Volume: 17, Issue: 2, page 233-248
- ISSN: 1641-876X

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topBoukezzoula, Reda, Galichet, Sylvie, and Foulloy, Laurent. "Fuzzy feedback linearizing controller and its equivalence with the fuzzy nonlinear internal model control structure." International Journal of Applied Mathematics and Computer Science 17.2 (2007): 233-248. <http://eudml.org/doc/207834>.

@article{Boukezzoula2007,

abstract = {This paper examines the inverse control problem of nonlinear systems with stable dynamics using a fuzzy modeling approach. Indeed, based on the ability of fuzzy systems to approximate any nonlinear mapping, the nonlinear system is represented by a Takagi-Sugeno (TS) fuzzy system, which is then inverted for designing a fuzzy controller. As an application of the proposed inverse control methodology, two popular control structures, namely, feedback linearization and Nonlinear Internal Model Control (NIMC) are investigated. Moreover, the paper points out that, under some conditions, both of the control structures are equivalent and naturally implement a Smith predictor in the presence of time delays.},

author = {Boukezzoula, Reda, Galichet, Sylvie, Foulloy, Laurent},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {fuzzy control; internal model control; inverse control; feedback linearization},

language = {eng},

number = {2},

pages = {233-248},

title = {Fuzzy feedback linearizing controller and its equivalence with the fuzzy nonlinear internal model control structure},

url = {http://eudml.org/doc/207834},

volume = {17},

year = {2007},

}

TY - JOUR

AU - Boukezzoula, Reda

AU - Galichet, Sylvie

AU - Foulloy, Laurent

TI - Fuzzy feedback linearizing controller and its equivalence with the fuzzy nonlinear internal model control structure

JO - International Journal of Applied Mathematics and Computer Science

PY - 2007

VL - 17

IS - 2

SP - 233

EP - 248

AB - This paper examines the inverse control problem of nonlinear systems with stable dynamics using a fuzzy modeling approach. Indeed, based on the ability of fuzzy systems to approximate any nonlinear mapping, the nonlinear system is represented by a Takagi-Sugeno (TS) fuzzy system, which is then inverted for designing a fuzzy controller. As an application of the proposed inverse control methodology, two popular control structures, namely, feedback linearization and Nonlinear Internal Model Control (NIMC) are investigated. Moreover, the paper points out that, under some conditions, both of the control structures are equivalent and naturally implement a Smith predictor in the presence of time delays.

LA - eng

KW - fuzzy control; internal model control; inverse control; feedback linearization

UR - http://eudml.org/doc/207834

ER -

## References

top- Babuska R. (1998): Fuzzy Modeling for Control. - Dordrecht: Kluwer Academic Publishers.
- Baoming G., Jingping J., Pengsheng S. and Xiangheng W. (2002): Nonlinear internal-model control for switched reluctance drives. - IEEE Trans. Power Electron., Vol.17, No.3, pp.379-388.
- Baranyi P., Bavelaar I., Babuska R., Koczy L.T., Tli A. and Verbruggen H.B. (1998): A method to invert a linguistic fuzzy model. - Int. J. Systems Sci., Vol.29, No.7, pp.711-721. Zbl1090.93539
- Boukezzoula R., Galichet S. and Foulloy L. (2001): Fuzzy nonlinear adaptive internal model control (FNAIMC). - Europ. J. Contr., Vol.7, No.5, pp.523-540. Zbl1293.93477
- Boukezzoula R., Galichet S. and Foulloy L. (2003): Nonlinear internal model control: Application of inverse model based fuzzy control. - IEEE Trans. Fuzzy Syst., Vol.11, No.6, pp.814-829. Zbl1293.93477
- Boukezzoula R., Galichet S. and Foulloy L. (2004): Observer-based fuzzy adaptive control for a class of nonlinear systems: Real-time implementation for a robot wrist. - IEEE Trans. Contr. Syst. Technol., Vol.12, No.3, pp.340-351.
- Boukezzoula R., Foulloy L. and Galichet S. (2006): Inverse controller design for interval fuzzy systems. - IEEE Trans. Fuzzy Syst., Vol.14, No.1, pp.111-124.
- Cabrera J.B.D and Narendra K.S. (1999): Issues in the application of neural networks for tracking based on inverse control. - IEEE Trans. Automat.Contr., Vol.44, No.11, pp.2007-2027. Zbl0955.93022
- Chen F.C. and Khalil H.K. (1995): Adaptive control of a class of nonlinear discrete-time systems using neural networks. - IEEE Trans. Automat. Contr., Vol.40, No.5, pp.791-801. Zbl0925.93461
- Devanathan R., Rahman F. and Kuanyi Z. (2000): Neural network approach for linearizing control of nonlinear plants. - IEEE Trans. Ind. Electron., Vol.47, No.2, pp.470-477.
- Economou C.G., Morari M. and Palsson B.O. (1986): Internal model control 5. Extention to nonlinear systems. - Ind. Eng. Chem. Proc. Des. Dev.,Vol.25, No.5, pp.403-409.
- Fang W. and Rad A. B. (2000): Fuzzy adaptive internal model control. - IEEE Trans. Ind. Electron., Vol.47, No.1, pp.193-202.
- Foulloy L., Boukezzoula R. and Galichet S. (2006): An educational tool for fuzzy control. - IEEE Trans. Fuzzy Syst., Vol.14, No.2, pp.217-221.
- Galichet S., Boukezzoula R. and Foulloy L. (2004): Explicit analytical formulation and exact inversion of decomposable fuzzy systems with singleton consequents. - Fuzzy Sets Syst., Vol.146, No.3, pp.421-436. Zbl1054.93012
- Hunt K.J. and Sbarbaro D. (1991): Neural Networks for Nonlinear Internal Model Control. - IEE Proc. D, Vol.138, No.5, pp.431-438. Zbl0755.93034
- Jagannathan S. (1998): Adaptive fuzzy logic control of feedback linearizable discrete-time dynamical systems under persistence excation. - Automat.,Vol.34, No.11, pp.1295-1310. Zbl0942.93019
- Jagannathan S. (1999): Discrete-time CMAC NN control of feedback linearizable nonlinear systems under persistence of excation. - IEEE Trans. Neural Netw., Vol.10, No.1, pp.128-137.
- Johansen T.A. and Foss B.A. (1995): Identification of nonlinear system structure and parameters using regime desomposition. - Automat., Vol.31, No.2,pp.321-326. Zbl0825.93114
- Kambhampati C., Mason J. and Warwick K. (2000): A stable one-step-ahead predictive control of non-linear systems. - Automat., Vol.36, No.4, pp.485-495. Zbl0984.93040
- Kang H.J., Kwon C., Lee H. and Park M. (1998): Robust stability analysis and design method for the fuzzy feedback linearization regulator. - IEEE Trans. Fuzzy Syst., Vol.6, No.4, pp.464-472.
- Knospe C.R. and Lindlau J.D. (2000): Feedback linearization of an active bearing with voltage control. - IEEE Trans. Contr. Syst. Technol., Vol.10, No.1,pp.21-31.
- Kwanghee N. (1999): Stabilization of feedback linearizable systems using a radial basis function network. - IEEE Trans. Automat. Contr., Vol.44, No.5,pp.1026-1031. Zbl0956.93011
- Leland R.P. (1998): Feedback linearization control design for systems with fuzzy uncertainty. - IEEE Trans. Fuzzy Syst., Vol.6, No.4, pp.492-503.
- Li H-X and Deng H. (2006): An approximate internal model-based neural control for unknown nonlinear discrete processes. - IEEE Trans. Neural Netw., Vol.17, No.3, pp.659-670.
- Liao H.E. and Chen W.S. (1997): Determination of nonlinear delay elements within NARMA models using dispersion functions. - IEEE Trans. Instrum. Meas., Vol.46, No.4, pp.868-872.
- Lightbody G. and Irwin G.W. (26): Nonlinear control structures based on embedded neural networks. - IEEE Trans. Neural Netw., Vol.8, No.3, pp.553-567.
- Morari M. and Zafiriou E. (1989): Robust Process Control. - Englewood Cliffs, NJ: Prentice-Hall. Zbl0728.93031
- Mizumoto M. (1993): Fuzzy control under product-sum gravy methods and new fuzzy control methods, In: Fuzzy Control Systems (A.Kandel and G.Langholz, Eds.). - Boca Raton, FL: CRC Press, pp.276-294.
- Nahas E.P., Henson M.A. and Seborg D.E. (1992): Nonlinear internal model control strategy for neural networks. - Comput. Chem. Eng., Vol.16, No.12, pp.1039-1057.
- Nakoula Y., Galichet S. and Foulloy L. (1997): A learning method for structure and parameter identification of fuzzy linguistic models, In: Selected Approaches for Fuzzy Model Identification (H.Hellendoorn and D.Driankov, Eds.). - Berlin: Springer Verlag, pp.282-319. Zbl0890.93030
- Narendra K.S. and Mukhopadhyay S. (1997): Adaptive control using neural networks and approximate models. - IEEE Trans. Neural Netw., Vol.8, No.3, pp.475-485.
- Narendra K.S. and Parthasarathy K. (1990): Identification and control of dynamical systems using neural networks. - IEEE Trans. Neural Netw., Vol.1,No.1, pp.4-27.
- Park S. and Han T. (2000): Iterative inversion of fuzzified neural networks. - IEEE Trans. Fuzzy Syst., Vol.8, No.3, pp.266-280.
- Rivals I. and Personnaz L. (2000): Nonlinear internal model control using neural networks: Application to processes with delay and design issues. - IEEE Trans. Neural Netw., Vol.11, No.1, pp.80-90.
- Rovatti R. (1998): Fuzzy piecewise multilinear and piecewise linear systems as universal approximators in Sobolev norms. - IEEE Trans. Fuzzy Syst., Vol.6, No.2, pp.235-249.
- Slotine J.J. and Li W. (1991): Applied Nonlinear Control. - Englewood Cliffs, NJ: Prentice-Hall. Zbl0753.93036
- Sugeno M. (1999): On stability of fuzzy systems expressed by fuzzy rules with singleton consequents. - IEEE Trans. Fuzzy Syst., Vol.7, No.2, pp.201-224.
- Wang L.X. (1993): Stable adaptive fuzzy control of nonlinear systems. - IEEE Trans. Fuzzy Syst., Vol.1, No.2, pp.146-155.
- Wang L.X. (1994): Adaptive Fuzzy Systems and Control. Design and Stability Analysis. - Englewood Cliffs, NJ: Prentice Hall.
- Ying H. and Chen G. (1997): Necessary conditions for some typical fuzzy systems as universal approximators. - Automat., Vol.33, No.7, pp.1333-1338. Zbl0885.93035
- Ying H. (1999): Analytical analysis and feedback linearization tracking control of the general Takagi-Sugeno fuzzy dynamic systems. - IEEE Trans. Syst. Man Cybern., Part C: Applic. Rev., Vol.29, No.1, pp.290-298.
- Zeng X.J. and Singh M.G. (1996a): Desomposition property of fuzzy systems and its applications. - IEEE Trans. Fuzzy Syst., Vol.4, No.2, pp.149-165.
- Zeng X. J. and Singh M.G. (1996b): Approximation accuracy analysis of fuzzy systems as function approximators. - IEEE Trans. Fuzzy Syst., Vol.4, No.1, pp.44-63

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