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Fractional Order Differentiation and Robust Control Design pp 63–105Cite as

Fractional Order PID and First Generation CRONE Control System Design

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Part of the book series: Intelligent Systems, Control and Automation: Science and Engineering ((ISCA,volume 77))

Abstract

This chapter presents the design of controllers for Single Input/Single Output (SISO) systems, that is to say only one signal to control only one measured output. The fractional order controller is presented as a generalization of the common PID controller. Then, it is shown how the first generation of the CRONE methodology is able to design robust controllers for a class of gain-like perturbed systems.

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References

  • Cervera J, Baños A (2006) Tuning of fractional PID controllers by using QFT. In: Proceedings of IECON’06 – 32nd annual conference of the IEEE industrial electronics society, Paris

    Google Scholar 

  • Chen YQ, Moore KL, Vinagre B, Podlubny I (2004) Robust PID controller auto tuning with a phase shaper. In: Proceedings of The first IFAC symposium on fractional differentiation and its applications (FDA04), Bordeaux

    Google Scholar 

  • D’Azzo JJ, Houpis CH (1988) Linear control system analysis and design, conventional and modern. McGraw Hill, New York

    Google Scholar 

  • Francis BA, Zames G (1984) On H∞ optimal sensitivity theory for SISO feedback systems. IEEE Trans Autom Control 29:9–16

    Article  MATH  MathSciNet  Google Scholar 

  • Goodwin GC, Graebe SF, Salgado ME (2001) Control system design. Prentice Hall, New Jersey

    Google Scholar 

  • Horowitz IM, Sidi M (1972) Synthesis of feedback systems with large plant ignorance for prescribed time-domain tolerances. Int J Control 16:287–309

    Article  MATH  Google Scholar 

  • Horowitz IM (1991) Survey of quantitative feedback theory (QFT). Int J Control 53:255–291

    Article  MATH  MathSciNet  Google Scholar 

  • Horowitz IM (1993) Quantitative feedback design theory – QFT. QFT Publications, Boulder

    Google Scholar 

  • Kochenburger RJ (1950) A frequency response method for analyzing and synthesizing contactor servomechanisms. Trans AIEE (Am Inst Electr Eng) 69(1):270–284

    Article  Google Scholar 

  • Krylov NM, Bogoliubov N (1943) Introduction to nonlinear mechanics. Princeton University Press, Princeton. ISBN 0691079854

    Google Scholar 

  • Landau ID, Rey D, Karimi A, Voda A, Franco A (1995) A flexible transmission system as a benchmark for digital control. Eur J Control 1(2):77–96

    Article  Google Scholar 

  • Lanusse P (1994) De la commande CRONE de 1ère generation à la commande CRONE de 3ème generation. Ph.D. thesis, Université Bordeaux 1

    Google Scholar 

  • Lanusse P (2010) CRONE control system design, a CRONE toolbox for Matlab. http://www.ims-bordeaux.fr/CRONE/toolbox

  • Lanusse P, Oustaloup A (2005) Anti-windup system for 1st generation crone controller. In: Ubooks (ed) Fractional differentiation and its applications, vol 3, Systems analysis, implementation and simulation, systems identification and control. Ubooks, Neusäss, pp 191–204

    Google Scholar 

  • Lanusse P, Oustaloup A, Sabatier J (2007) Robust design of an anti-windup compensated 3rd generation CRONE controller. In: Sabatier J, Agrawal OP, Tenreiro Machado JA (eds) Advances in fractional calculus: theoretical developments and applications in physics and engineering. Springer, Dordrecht, pp 527–542

    Chapter  Google Scholar 

  • Lanusse P, SabatierJ, Oustaloup A (2010) Design of controllers using damping contours defined from closed loop systems based on fractional complex order integrators. In: ASME/IEEE international conference on mechatronic and embedded systems and applications (MESA10), QingDao

    Google Scholar 

  • Lanusse P, Malti R, Melchior P (2011) CRONE control-system design toolbox for the control engineering community. In: ASME/IEEE international conference on mechatronic and embedded systems and applications, Washington, DC

    Google Scholar 

  • Lanusse P, Oustaloup A, Pommier-Budinger V (2012) Stability of closed-loop fractional-order systems and definition of damping contours for the design of controllers. Int J Bifurcat Chaos 22(4). doi: 10.1142/S0218127412300133

  • Lanusse P, Malti R, Melchior P (2013) Crone control system design toolbox for the control engineering community: tutorial and a case study. Philos Trans Royal Soc A, 371(1990):20120149. doi: 10.1098/rsta.2012.0149

  • Maamri N, Trigeassou JC, Tenoutit M (2010) On fractional PI and PID controllers. In: Proceedings of the FDA 2010 IFAC Workshop, Badajoz

    Google Scholar 

  • Manabe S (1960) The non-integer integral and its application to control systems. ETJ Japan 6(3/4):83–87

    Google Scholar 

  • Manabe S (1961) The non integer integral and its application to control systems. ETJ Japan 6(3–4):83–87

    Google Scholar 

  • Melchior P, Lanusse P, Cois O, Dancla F, Oustaloup A (2002) Crone Toolbox for Matlab: fractional systems toolbox. Tutorial workshop on “fractional calculus applications in automatic control and robotics”. In: 41st IEEE CDC’02, Las Vegas

    Google Scholar 

  • Monje CA, Vinagre B, Chen YQ, Feliu V, Lanusse P, Sabatier J (2004) Proposals for fractional PIλDμ tuning. In: Proceedings of the first IFAC symposium on fractional differentiation and its applications (FDA04), Bordeaux

    Google Scholar 

  • Monje CA, Chen Y, Vinagre BM, Xue D, Feliu-Batlle V (2010) Fractional-order systems and controls: fundamentals and applications. Springer, London\New York

    Book  Google Scholar 

  • Nataraj PSV, Tharewal S (2010) On fractional-order QFT controllers. Trans ASME J Dynamic Syst Meas Control 129:212–218

    Google Scholar 

  • Oustaloup A (1975) Etude et réalisation d’un système d’asservissement d’ordre 3/2 de la fréquence d’un laser à colorant continu. Ph.D. thesis, Université Bordeaux 1, France

    Google Scholar 

  • Oustaloup A (1981) Linear feedback control systems of fractional order between 1 and 2. In: The IEEE international symposium on circuits and systems, Chicago, Illinois

    Google Scholar 

  • Oustaloup A (1983) Systèmes asservis linéaires d’ordre fractionnaire. Ed Masson, Paris

    Google Scholar 

  • Oustaloup A (1991) La commande CRONE. Edition Hermès, Paris

    MATH  Google Scholar 

  • Oustaloup A (1995) La dérivation non entière, théorie, synthèse et applications. Editions Hermès, Paris

    Google Scholar 

  • Oustaloup A, Ballouk A, Lanusse P (1991) Synthesis of a narrow band template based on complex non integer derivation. In: IMACS symposium “modelling and control of technological systems”, Lille

    Google Scholar 

  • Oustaloup A, Lanusse P, Mathieu B (1995) Robust control of SISO plants : the CRONE control. In: ECC’95, Rome

    Google Scholar 

  • Oustaloup A, Sabatier J, Lanusse P (1999) From fractal robustness to the CRONE control. Fractional Calc Appl Anal 2(1):1–30

    Google Scholar 

  • Oustaloup A, Melchior P, Lanusse P, Cois O, Dancla F (2000) The CRONE toolbox for Matlab. In: IEEE international symposium on computer-aided control system design, Anchorage

    Google Scholar 

  • Oustaloup A, Pommier V, Lanusse P (2003) Design of a fractional control using performance contours – application to an electromechanical system. Fractional Calc Appl Anal Int J Theory Appl 6(1):1–24

    MATH  MathSciNet  Google Scholar 

  • Oustaloup A, Lanusse P, Sabatier J, Melchior P (2013) CRONE control : principles, extensions and applications. J Appl Nonlin Dyn 2(3):207–223. doi:10.5890/JAND.2013.08.001

    Article  Google Scholar 

  • Petras I (1999) The fractional-order controllers: methods for their synthesis and application. J Electr Eng 50(9–10):284–288

    Google Scholar 

  • Podlubny I (1999) Fractional-order systems and PIλDμ-controllers. IEEE Trans Autom Control 44(1):208–214

    Article  MATH  MathSciNet  Google Scholar 

  • Pommier-Budinger V, Janat Y, Nelson-Gruel D, Lanusse P, Oustaloup A (2008) Fractional robust control with iso-damping property. In: American control conference 2008, Seattle

    Google Scholar 

  • Popov VM (1962). Absolute stability of nonlinear systems of automatic control, Automation and Remote control, (Russian original in 1961), pp 857–875

    Google Scholar 

  • Tustin A (1958) The design of systems for automatic control of the position of massive object. Proc Inst Electr Eng 105C(1):1–57

    Google Scholar 

  • Valerio D, Sa da Costa J (2012) An introduction to fractional control. IET Editor, Institution of Engineering and Technology

    Google Scholar 

  • Vidyasagar M, Viswanadham N (1982) Algebraic design techniques for realizable stabilisation. IEEE Trans AC 27(5):895–903

    Google Scholar 

  • Wurmthaler C, Hippe P (1991) Systematic compensator design in the presence of input saturation. In: Proceeding of ECC’91, Grenoble

    Google Scholar 

  • Ygorra S, Cazaurang F, Bergeon B (1996) Anti windup control of stable plants with input saturation. In: Proceeding of CESA’96, Lille

    Google Scholar 

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Authors and Affiliations

  1. IMS Laboratory - CNRS UMR 5218 – Bordeaux INP - Bordeaux University Bat A31 – 351 cours de la Libération, 33400, Cedex Talence, France

    P. Lanusse, J. Sabatier & A. Oustaloup

Authors
  1. P. Lanusse
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  2. J. Sabatier
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  3. A. Oustaloup
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Correspondence to P. Lanusse .

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Lanusse, P., Sabatier, J., Oustaloup, A. (2015). Fractional Order PID and First Generation CRONE Control System Design. In: Fractional Order Differentiation and Robust Control Design. Intelligent Systems, Control and Automation: Science and Engineering, vol 77. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9807-5_2

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  • DOI: https://doi.org/10.1007/978-94-017-9807-5_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-017-9806-8

  • Online ISBN: 978-94-017-9807-5

  • eBook Packages: EngineeringEngineering (R0)

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