Skip to main content
SpringerLink
Log in

Multirange Nonlinear Controller Design

  • Chapter
  • First Online:
Computer-aided Nonlinear Control System Design

  • 1787 Accesses

Abstract

In cases that a dual-range linear controller is proved to be inadequate to achieve the objectives of control, one may consider the design of a multirange nonlinear controller. An algorithm for design of multi-range nonlinear controllers for both single-variable and multivariable nonlinear systems is presented. Without loss of generality, nonlinear PID, lead-lag, and \( {H_\infty } \) controllers are considered. Example problems are given to demonstrate the typical results that may be achieved.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    *Source: (Nassirharand 2009a) © Elsevier

  2. 2.

    *Source: (Nassirharand and Mousav Firdeh 2008) © Springer

  3. 3.

    *Source: (Nassirharand and Mousav Firdeh 2008) © Springer

References

  • Atherton, D.P.: Comment on describing function inversion. Electron Lett 6, 779–780 (1970)

    Article  Google Scholar 

  • Besancon-Voda, A., Blaha, P.: Describing function approximation of a two-relay system configuration to Coulomb friction identification. Control Eng Pract 10, 655–668 (2002)

    Article  Google Scholar 

  • Bongard, J.C., Lipson, H.: Nonlinear system identification using coevolution of models and tests. IEEE Trans Evol Comput 9, 361–384 (2005)

    Article  Google Scholar 

  • Colgren, R.D.: Applications of robust control to nonlinear systems. American Institute of Aeronautics and Astronautics, Reston (2004)

    Book  Google Scholar 

  • Dhupia, J.S., Ulsoy, A.G., Katz, R., et al.: Experimental identification of the nonlinear parameters of an industrial translational guide for machine performance evaluation. J Vib Control 14, 645–668 (2008)

    Article  Google Scholar 

  • Ge, H.W., Qian, F., et al.: Identification and control of nonlinear systems by a dissimilation particle swarm optimization-based Elman neural-network. Nonlin Anal: Real World Appl 9, 1345–1360 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  • Gelb, A., Vander Velde, W.E.: Multiple-input describing functions and nonlinear system design. McGraw-Hill, New York (1968)

    MATH  Google Scholar 

  • Haber, R., Keviczky, L.: Nonlinear system identification-input-output modeling approach. Kluwer Acaemic Publishers, Dordrecht (1999)

    Book  MATH  Google Scholar 

  • John, J.: Nonlinear continuous system identification by means of multiple integration II. Acta Polytechnica 41, 64–67 (2001)

    Google Scholar 

  • Kerschen, G., Worden, K., Vakakis, A.F., et al.: Past, present and future of nonlinear system identification in structural dynamics. Mechan Syst Signal Process 20, 505–592 (2006)

    Article  Google Scholar 

  • Kim, M.S., Chung, S.C.: Friction identification of ball-screw driven servomechanisms through the limit cycle analysis. Mechatronics 16, 131–140 (2006)

    Article  Google Scholar 

  • Li, L., Yang, Y., Peng, H.: Fuzzy system identification via chaotic ant swarm. Chaos Solitons Fractiles 41, 401–409 (2010)

    Article  MATH  Google Scholar 

  • Lyashevskiy, S., Chen, Y.: Identification of nonlinear system parameters using describing function approach. Proc Am Control Conf 3, 1944–1945 (1997)

    Google Scholar 

  • Nanka-Bruce, O., Atherton, D.P.: Design of nonlinear controllers for nonlinear plants. Proc IFAC Congr Tallinn 6, 75–80 (1990)

    Google Scholar 

  • Nassirharand, A.: Identification of frequency domain models for nonlinear systems. Adv Eng Softw 10, 195–201 (1988)

    Article  MATH  Google Scholar 

  • Nassirharand, A.: A new software tool for design of linear compensators. Adv Eng Softw 39, 132–136 (2008a)

    Article  Google Scholar 

  • Nassirharand, A.: Controller synthesis procedure for linear unstable plants. Int J Automat Control 2, 137–149 (2008b)

    Article  Google Scholar 

  • Nassirharand, A.: Control system design of multivariable non-linear space robots. Aircr Eng Aerosp Technol 80, 27–34 (2008c)

    Article  Google Scholar 

  • Nassirharand, A.: Matlab software for inversion of describing functions. Adv Eng Softw 40, 600–606 (2009a)

    Article  MATH  Google Scholar 

  • Nassirharand, A.: Computer-aided design of classical linear compensators with application to aerospace. J Syst Eng Electron 20, 1373–1377 (2009b)

    Google Scholar 

  • Nassirharand, A., Karimi, H.: Input/output characterization of highly nonlinear multivariable systems. Adv Eng Softw 33, 825–830 (2002)

    Article  Google Scholar 

  • Nassirharand, A., Karimi, H.: Closed-form solution for design of lead-lag compensators. Int J Elect Eng Educ 41, 172–180 (2004c)

    Google Scholar 

  • Nassirharand, A., Karimi, H.: Nonlinear controller synthesis based on inverse describing function technique in the MATLAB environment. Adv Eng Softw 37, 370–374 (2006)

    Article  Google Scholar 

  • Nassirharand, A., Mousavi Firdeh, S.R.: Design of nonlinear lead and/or lag compensators. Int J Control Automat Syst 6, 394–400 (2008)

    Google Scholar 

  • Nassirharand, A., Mousavi Firdeh, S.R.: Single-range controller design for a cruise missile. Aircr Eng Aerosp Technol: An Int J 81, 283–287 (2009b)

    Article  Google Scholar 

  • Nassirharand, A., Mousavi Firdeh, S.R.: Design of nonlinear H ∞ controllers using describing functions with application to servomechanism. Asian J Control 11, 446–450 (2009c)

    Article  Google Scholar 

  • Nassirharand, A., Karimi, H., Dadfarnia, M.: A new software tool for synthesis of linear PID controllers. Adv Eng Softw 34, 551–557 (2003)

    Article  Google Scholar 

  • Nelder, J.A., Mead, R.: A simplex method for function minimization. J Comput 7, 308–313 (1965)

    Article  MATH  Google Scholar 

  • Ozer, M.B., Ozguven, H.N., Royston, T.J.: Identification of structural non-linearities using describing functions and the Sherman-Morrison method. Mech Syst Signal Process 23, 30–34 (2009)

    Article  Google Scholar 

  • Petrovic I, Baotic M, Perik N (2000) Model structure selection for nonlinear system identification using feedforward neural networks. In: Proceedings of IEEE-INNS-ENNS international joint conference on neural networks, Como, 1:1053

    Google Scholar 

  • Reklaitis, G.V., Ravindran, A., Ragsdell, K.M.: Engineering optimization. Wiley, New York (1983)

    Google Scholar 

  • Shi, J., Sun, H.H.: Nonlinear system identification for cascaded block model: an application to electrode polarization impedance. IEEE Trans Biomed Eng 37, 574–587 (1990)

    Article  Google Scholar 

  • Teh SH (2010) Design of multivariable dual-range linear controllers for nonlinear systems. BEng Thesis, Faculty of Engineering, The University of Nottingham, Semenyih, Selangor

    Google Scholar 

  • Suzuki A, Hedrick JK (1985) Nonlinear controller design by an inverse random-input describing function methods. In: Proceedings of American control conference, Boston, MA, pp 1236–1241

    Google Scholar 

  • Taylor JH (1983) A systematic nonlinear controller design approach based on quasilinear system models. In: Proceedings of American control conference, San Francisco, CA, pp 141–145

    Google Scholar 

  • Taylor JH, Strobel KL (1985) Nonlinear control system design based on quasilinear system models. In: Proceedings of American control conference, Boston, MA, pp 1242–1247

    Google Scholar 

  • Vaerenbergh, S.V., Via, J., Santamaria, I.: Nonlinear system identification using a new sliding-window kernel RLS algorithm. J Commun 2, 1–8 (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Engineering, The University of Nottingham, Malaysia Campus Jalan Broga, 43500, Semenyih, Malaysia

    Amir Nassirharand

Authors
  1. Amir Nassirharand
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag London Limited

About this chapter

Cite this chapter

Nassirharand, A. (2012). Multirange Nonlinear Controller Design. In: Computer-aided Nonlinear Control System Design. Springer, London. https://doi.org/10.1007/978-1-4471-2149-7_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-2149-7_5

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-2148-0

  • Online ISBN: 978-1-4471-2149-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation