Skip to main content
Log in

A Comparison of Fuzzy and CPWL Approximations in the Continuous-time Nonlinear Model-predictive Control of Time-delayed Wiener-type Systems

  • Published:
Journal of Intelligent and Robotic Systems Aims and scope Submit manuscript

Abstract

This paper deals with a novel method of continuous-time model-predictive control for nonlinear time-delayed systems. The problems relating to time delays are solved by incorporating the Smith-predictor scheme in a control-law derivation. A nonlinear-mapping approximation, employing either continuous piece-wise linear functions or a fuzzy system, is also an integral part of the control scheme, and thus removes the need for output-function invertibility. An illustrative experiment is conducted to compare the control quality in both approaches when tackling a time-delayed Wiener-type system control.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Babuška, R., Verbrüggen, H.B.: An overview of fuzzy modeling for control. Control Eng. Pract. 4(11), 1593–1606 (1996)

    Article  Google Scholar 

  2. Bequette, B.W.: Nonlinear control of chemical processes: a review. Ind. Eng. Chem. Res. 30, 1391–1413 (1991)

    Article  Google Scholar 

  3. Biagiola, S.I., Agamennoni, O.E., Figueroa, J.L.: H control of a Wiener-type system. Int. J. Control 77(6), 572–583 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  4. Chen, W., Ballance, D.J., Gawthrop, P.J.: Optimal control of nonlinear systems: a predictive control approach. Automatica 39, 633–641 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  5. Clarke, D.W., Mohtadi, C., Tuffs, P.S.: Generalized predictive control – Parts 1, Part 2. Automatica 24, 137–160 (1987)

    Article  Google Scholar 

  6. Demircioğlu, H., Gawthrop, P.J.: Continuous-time generalized predictive control. Automatica 27(1), 55–74 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  7. Demircioğlu, H., Gawthrop, P.J.: Multivariable continuous-time generalized predictive control (MCGPC). Automatica 28(4), 697–713 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  8. García, C.E., Prett, D.M., Morari, M.: Model predictive control: theory and practice – a survey. Automatica 25(3), 335–348 (1989)

    Article  MATH  Google Scholar 

  9. Gerkšič, S., Juričić, D., Strmčnik, S., Matko, D.: Wiener model based nonlinear predictive control. Int. J. Syst. Sci. 31(2), 189–202 (2000)

    Article  MATH  Google Scholar 

  10. Henson, M.A.: Nonlinear model predictive control: current status and future directions. Comput. Chem. Eng. 23, 187–202 (1998)

    Article  Google Scholar 

  11. Julián, P., Jordán, M., Desages, A.: Canonical piecewise linear approximation of smooh functions. IEEE Trans. Circuits Syst. 45, 567–571 (1998)

    Article  MATH  Google Scholar 

  12. Lussón Cervantes, A., Agamennoni, O.E., Figueroa, J.L.: A nonlinear model predictive control system based on Wiener piecewise linear models. Process Control 13, 655–666 (2003)

    Article  Google Scholar 

  13. Magni, L., Scattolini, R.: Stabilizing model predictive control of nonlinear continuous time systems. Annu. Rev. Control 28, 1–11 (2004)

    Article  Google Scholar 

  14. Mayne, D.Q., Michalska, H.: Receding horizon control of nonlinear systems. IEEE Trans. Automat. Contr. 35(7), 814–824 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  15. Morari, M., Lee, J.H.: Model predictive control: past, present and future. Comput. Chem. Eng. 23, 667–682 (1999)

    Article  Google Scholar 

  16. Norquay, S.J., Palazoğlu, A., Romagnoli, J.A.: Application of Wiener model predictive control (WMPC) to a pH neutralization experiment. IEEE Trans. Control Syst. Technol. 7(4), 437–445 (1999)

    Article  Google Scholar 

  17. Norquay, S.J., Palazoğlu, A., Romagnoli, J.A.: Application of Wiener model predictive control (WMPC) to an industrial C2-splitter. J. Process Control 9, 461–473 (1999)

    Article  Google Scholar 

  18. Pal, N.R., Bezdek, J.C.: On cluster validity for the fuzzy c-means model. IEEE Trans. Fuzzy Syst. 3(3), 370–379 (1995)

    Article  Google Scholar 

  19. Sentoni, G., Agamennoni, O., Desages, A., Romagnoli, J.: Approximate models for nonlinear process control. AIChE J. 42, 2240–2250 (1996)

    Article  Google Scholar 

  20. Smith, O.J.: Controller to overcome dead time. Instrum. Soc. Am. J. 6(2), 28–33 (1959)

    Google Scholar 

  21. Sung, S.W., Lee, J.: Modeling and control of Wiener-type processes. Chem. Eng. Sci. 59, 1515–1521 (2004)

    Article  Google Scholar 

  22. Škrjanc, I., Matko, D.: Fuzzy predictive functional control in the state space domain. J. Intell. Robot. Syst. 31, 283–297 (2001)

    Article  MATH  Google Scholar 

  23. Škrjanc, I., Blažič, S., Agamennoni, O.: Interval fuzzy modelling applied to Wiener models with uncertainties. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 35(5), 1092–1095 (2005)

    Article  Google Scholar 

  24. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modelling and control. IEEE Trans. Syst. Man. Cybernetics 15, 116–132 (1985)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Simon Oblak.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Oblak, S., Škrjanc, I. A Comparison of Fuzzy and CPWL Approximations in the Continuous-time Nonlinear Model-predictive Control of Time-delayed Wiener-type Systems. J Intell Robot Syst 47, 125–137 (2006). https://doi.org/10.1007/s10846-006-9075-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10846-006-9075-z

Key words

Navigation