[go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Fuzzy controllers gains tuning: a constrained nonlinear optimization approach

  • New applications of Artificial Neural Networks in Modeling & Control
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

This paper presents a methodology for tuning the gains of fuzzy proportional-integral controllers where the concept of closed-loop control system performance is explicitly taken into account. The fuzzy controller gains are found by solving a nonlinear constrained optimization problem considering the system’s dynamics described by a nonlinear model and a set of constraints on the controller gains, control actions and outputs. Experimental results collected on a test-bed show the pertinence of using the proposed tuning technique.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Automat Control 19(6):716–723

    Article  MathSciNet  MATH  Google Scholar 

  2. Boubertakh H, Tadjine M, Glorennec PY, Labiod S (2010) Tuning fuzzy pd and pi controllers using reinforcement learning. ISA Trans 49(4):543–551

    Article  Google Scholar 

  3. Chen T, Chen H (1995) Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems. IEEE Trans Neural Netw 6(4):911–917

    Article  Google Scholar 

  4. Chen T, Chen H, wen Liu R (1995) Approximation capability in c(r macr;n) by multilayer feedforward networks and related problems. IEEE Trans Neural Netw 6(1):25–30

    Article  MATH  Google Scholar 

  5. Cybenko G (1989) Approximation by superpositions of a sigmoidal function. Math Control Signals Syst (MCSS) 2:303-314

    Article  MathSciNet  MATH  Google Scholar 

  6. Dong Q, Matsui K, Huang X (2002) Existence and stability of periodic solutions for hopfield neural network equations with periodic input. Nonlinear Anal Theory Methods Appl 49(4):471–479

    Article  MathSciNet  MATH  Google Scholar 

  7. Feng G (2006) A survey on analysis and design of model-based fuzzy control systems. IEEE Trans Fuzzy Syst 14(5):676–697

    Google Scholar 

  8. Hassibi B, Stork D, Wolff G (1993) Optimal brain surgeon and general network pruning. In: IEEE international conference on neural networks, 1993, vol 1. pp 293–299

  9. Herrera F, Lozano M (2009) Fuzzy evolutionary algorithms and genetic fuzzy systems: a positive collaboration between evolutionary algorithms and fuzzy systems. In: Intelligent systems reference library, vol 1. Springer, Berlin

  10. Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2(5):359–366

    Article  Google Scholar 

  11. Lee CC (1990) Fuzzy logic in control systems: fuzzy logic controller. I. IEEE Trans Syst Man Cybern 20:404–418

    Google Scholar 

  12. Leshno M, Lin VY, Pinkus A, Schocken S (1993) Multilayer feedforward networks with a nonpolynomial activation function can approximate any function. Neural Netw 6(6):861–867

    Article  Google Scholar 

  13. Li HX, Gatland HB (1996) Conventional fuzzy control and its enhancement. IEEE Trans Syst Man Cybern Part B Cybern 26(5):791–797

    Google Scholar 

  14. Misir D, Malki HA, Chen GA (1996) A heuristic approach to determine the gains of a fuzzy pid controller. In: Proceedings of the 1996 ACM symposium on applied computing, SAC ’96. ACM, New York, NY, USA, pp 609–613

  15. Murata N, Yoshizawa S, Amari S (1994) Network information criterion-determining the number of hidden units for an artificial neural network model. IEEE Trans Neural Netw 5(6):865–872

    Article  Google Scholar 

  16. Pivonka P (2002) Comparative analysis of fuzzy pi/pd/pid controller based on classical pid controller approach. In: Fuzzy systems, 2002. FUZZ-IEEE ’02. Proceedings of the 2002 IEEE international conference on, vol 1. pp 541–546

  17. Rissanen J (1974) Basis of invariants and canonical forms for linear dynamic systems. Automatica 10(2):175–182

    Article  MathSciNet  MATH  Google Scholar 

  18. Schrijver A (1986) Theory of linear and integer programming. Wiley, New York

    MATH  Google Scholar 

  19. Siegelmann H, Horne B, Giles C (1997) Computational capabilities of recurrent narx neural networks. IEEE Trans Syst Man Cybern Part B Cybern 27(2):208–215

    Article  Google Scholar 

  20. Teoh E, Tan K, Xiang C (2006) Estimating the number of hidden neurons in a feedforward network using the singular value decomposition. IEEE Trans Neural Netw 17(6):1623–1629

    Article  Google Scholar 

  21. Trenn S (2008) Multilayer perceptrons: approximation order and necessary number of hidden units. IEEE Trans Neural Netw 19(5):836-844

    Article  Google Scholar 

  22. Wang HO, Tanaka K, Griffin MF (1996) An approach to fuzzy control of nonlinear systems: stability and design issues. IEEE Trans Fuzzy Syst 4(1):14–23

    Google Scholar 

Download references

Acknowledgments

This work has been supported by iCIS-Intelligent Computing in the Internet of Services, Project CENTRO-07-ST24-FEDER-002003.

Author information

Authors and Affiliations

  1. Departamento de Engenharia Electrotécnica, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Campus de Caparica, 2829-516 Caparica, Portugal

    Paulo Gil & Luis Palma

  2. UNINOVA, Institute for the Development of New Tecnologies, Campus de Caparica, 2829-516, Caparica, Portugal

    Catarina Lucena

  3. Department of Informatics Engineering of the University of Coimbra, CISUC, Centre for Informatics and Systems of the University of Coimbra, Polo II, 3030-290, Coimbra, Portugal

    Paulo Gil & Alberto Cardoso

Authors
  1. Paulo Gil
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Catarina Lucena
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alberto Cardoso
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Luis Palma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paulo Gil.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gil, P., Lucena, C., Cardoso, A. et al. Fuzzy controllers gains tuning: a constrained nonlinear optimization approach. Neural Comput & Applic 23, 617–624 (2013). https://doi.org/10.1007/s00521-013-1415-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-013-1415-x

Keywords

Search

Navigation