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Second and Third Generation CRONE Control-System Design

  • Chapter
Fractional Order Differentiation and Robust Control Design

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

Abstract

This chapter presents the second generation of the CRONE methodology that extends the field of application of the first generation one. By replacing the real fractional order by a complex order, the third generation of the CRONE methodology is defined for any perturbed SISO system and is finally used to extend the CRONE approach to the design of robust controllers for Multi-Input/Multi-Output (MIMO) systems.

With contributions by D. Nelson Gruel

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References

  • Arkun Y (1987) Dynamic block relative gain and its connection with the performance and stability of decentralized control structures. Int J Control 46(4):1187–1193

    Article  MATH  Google Scholar 

  • Arkun Y, Manousiouthakis B, Putz P (1984) Robust Nyquist array methodology: a new theoretical framework for analysis and design of robust feedback system. Int J Control 40(4):603–629

    Article  MATH  Google Scholar 

  • Åstrom KJ (2000) Model uncertainty and robust control, lecture notes on iterative identification and control design. Lund Institute of Technology, Lund

    Google Scholar 

  • Baños A, Cervera J, Lanusse P, Sabatier J (2011) Bode optimal loop shaping with CRONE compensator. J Vib Control 17:1964–1974. doi:10.1177/1077546310388002

    Article  MATH  MathSciNet  Google Scholar 

  • Barbosa RS, Tenreiro Machado JA, Ferreira IM (2004) Tuning of PID controllers based on Bode’s ideal transfer function. Nonlinear Dyn 38(1):305–321. doi:10.1007/s11071-004-3763-7

    Article  MATH  Google Scholar 

  • Bode HW (1945) Network analysis and feedback amplifier design. Van Nostrand, New York

    Google Scholar 

  • Bristol EH (1966) On a new measure of interactions for multivariable process control. IEEE Trans Autom Control 11:133–134

    Article  Google Scholar 

  • Chang JW, Yu CC (1990) The relative gain for non-square multivariable systems. Chem Eng Sci 45(5):1309–1323

    Article  Google Scholar 

  • Colin G, Lanusse P, Louizimi A, Chamaillard Y, Deng C, Nelson Gruel D (2011) Multi-SISO robust CRONE design for the airpath control of a diesel engine. In: World IFAC congress, Milano

    Google Scholar 

  • Delavari H, Lanusse P, Sabatier J (2013) Fractional order controller design for a flexible link manipulator robot. Asian J Control 15(3):783–795

    Article  MathSciNet  Google Scholar 

  • Feytout B (2013) Mise en place d’un modèle phénoménologique d’une éolienne par simulation numérique et Contribution à l’optimisation de son fonctionnement énergétique et électrique. Ph.D. thesis, Université Bordeaux 1

    Google Scholar 

  • Feytout B, Sabatier J, Lanusse P, Lopes M, Gracia S (2012) Maximizing wind turbine production using revisited CRONE control European Wind Energy Association conference (EWEA 2012), Copenhagen

    Google Scholar 

  • Feytout B, Lanusse P, Sabatier J, Gracia S (2013) Robust CRONE design for a variable ratio planetary gearing in a variable speed wind turbine. Asian J Control 15(3):806–818

    Article  MathSciNet  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 

  • Freudenberg JS, Looze JS (1985) Right half plane poles and zeros and design tradeoffs in feedback systems. IEEE Trans Autom Control 30:555–565

    Article  MATH  MathSciNet  Google Scholar 

  • Garcia Iturricha A, Sabatier J, Oustaloup A (2012) Time-varying z-transform for the analysis of discrete-time linear time periodic. J Dyn Control Syst 9(3):365–392

    Article  MathSciNet  Google Scholar 

  • Graybill FA (1969) Introduction to matrices with applications in statistics, Wadsworth, Belmont

    Google Scholar 

  • Gude JJ, Kahoraho E (2009) Simple tuning rules for fractional PI controllers. In: Emerging technologies & factory automation IEEE conference, Mallorca, Spain

    Google Scholar 

  • Kariwala V, Fraser Forbes J, Meadows ES (2003) Block relative gain: properties and pairing rules. Ind Eng Chem Res 42(20):4564–4574

    Article  Google Scholar 

  • Kristiansson B, Lennartson B (2002) Robust and optimal tuning of PI and PID controllers. IEE Proc 149(1):17–25

    Google Scholar 

  • Lamara A, Colin G, Lanusse P, Chamaillard Y, Charlet A (2012) Decentralized robust control-system for a non-square MIMO system, the air-path of a turbocharged diesel engine. IFAC workshop ECOSM 2012, Rueil Malmaison, France

    Google Scholar 

  • Lamara A, Lanusse P, Colin G, Charlet A, Chamaillard Y (2013) A non-square MIMO fractional robust control for the airpath of a diesel engine. In: European control conference (ECC’13), Zurich

    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 génération à la commande CRONE de 3ème génération. Ph.D. thesis, Université Bordeaux 1

    Google Scholar 

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

  • Lanusse P, Oustaloup A (2005) Control of time-delay systems using robust fractional-order control and robust smith predictor based control. In: ASME International design engineering technical conferences and computers and information in engineering conference, Long Beach

    Google Scholar 

  • Lanusse P, Oustaloup A, Sutter D (1996) Multi-scalar CRONE control of multivariable plants. In: Proceedings of WAC’96-ISIAC Symphosia, Montpellier, France

    Google Scholar 

  • Lanusse P, Oustaloup A, Mathieu B (2000) Robust control of LTI square MIMO plants using two CRONE control design approaches. In: Proceedings of the IFAC ROCOND 2000, Prague

    Google Scholar 

  • Lanusse P, Poinot T, Cois O, Oustaloup A, Trigeassou JC (2004) Restricted-complexity controller with CRONE control-system design and closed-loop tuning. Eur J Control, Hermes Science Publishing 10(3): 242–251

    Google Scholar 

  • Lanusse P, Benlaoukli H, Nelson Gruel D, Oustaloup A (2008) Fractional-order control and interval analysis of SISO systems with time-delayed state. IET Control Theory Appl 2(1):16–23

    Article  MathSciNet  Google Scholar 

  • Lanusse P, Sabatier J, 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, 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 Bifur Chaos 22(4). doi:10.1142/S0218127412300133

  • Lanusse P, Lopes M, Sabatier J, Feytout B (2013) New optimization criteria for the simplification of the design of third generation CRONE controllers. 6th IFAC workshop on “Fractional Differentiation and its Applications” (FDA’13), Grenoble

    Google Scholar 

  • Maciejowski JM (1989) Multivariable feedback design. Addison Wesley, Wokingham

    MATH  Google Scholar 

  • Manousiouthakis V, Savage R, Arkun Y (1986) Synthesis of decentralized process control structures using the concept of block relative gain. AICHE J 32(6):991–1003

    Article  Google Scholar 

  • Mathieu B (1997) De la commande CRONE scalaire à la commande CRONE multivariable. Ph.D. thesis, Université Bordeaux 1

    Google Scholar 

  • Naslin P (1969) Essentials of optimal control. Boston Technical, Boston

    Google Scholar 

  • Nelson Gruel D (2009) Extension de la commande CRONE multivariable aux systèmes non carrés: application à un système d'air de moteurs essence et diesel. Ph.D. thesis, Université Bordeaux 1.

    Google Scholar 

  • Nelson Gruel D, Pommier-Budinger V, Lanusse P, Oustaloup A (2007) Robust control system design for multivariable plants with lightly damped modes. IDETC/CIE, Las Vegas

    Google Scholar 

  • Nelson Gruel D, Lanusse P, Oustaloup A (2008) Decentralized CRONE control of m × n multivariable system with time-delay. 3rd IFAC workshop on “fractional differentiation and its applications”, Ankara

    Google Scholar 

  • Nelson Gruel D, Lanusse P, Oustaloup A (2009) Robust control design for multivariable plants with time-delays. Chem Eng J 146(3):414–427, Elsevier

    Article  Google Scholar 

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

    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, Lanusse P, Mathieu B (1995a) Robust control of SISO plants: the CRONE control; ECC’95, Rome

    Google Scholar 

  • Oustaloup A, Mathieu B, Lanusse P (1995b) The CRONE control of resonant plants: application to a flexible transmission. Eur J Control 1:113–121

    Article  Google Scholar 

  • Oustaloup A, Levron F, Nanot F, Mathieu B (2000) Frequency band complex non integer differentiator: characterization and synthesis. IEEE Trans Circuits Syst 47(1):25–40

    Article  Google Scholar 

  • Oustaloup A, Lanusse P, Levron F (2002) Frequency synthesis of filter using the functions of Viète’s roots. IEEE Trans Autom Control 47(5):837–841

    Article  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  • Pommier-Budinger V (2002) Commande non entière et commande non linéaire robuste d’un banc d’essais hydraulique. Ph.D. thesis, ENSAM Bordeaux

    Google Scholar 

  • Pommier-Budinger V, Sabatier J, Lanusse P, Oustaloup A (2002) CRONE control of a nonlinear hydraulic actuator. Control Eng Pract 10(4):391–402

    Article  Google Scholar 

  • Pommier-Budinger V, Janat Y, Lanusse P, Oustaloup A (2004) CRONE control of the elevation of a helicopter model. 1st IFAC workshop on fractional differentiation and its applications, FDA’04, Bordeaux

    Google Scholar 

  • Pommier-Budinger V, Lanusse P, Janat Y, Oustaloup A (2005) CRONE control of MIMO plants. ECC-CDC 05, Seville

    Google Scholar 

  • Pommier-Budinger V, Janat Y, Lanusse P, Oustaloup A (2006) Fractional robust control of lightly damped systems. 32nd annual conference of the IEEE industrial electronics society (IECON’06), Paris

    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 

  • Poullain S, Latteux P, Thomas JL, Sabatier J, Oustaloup A (2005) Robust speed control of a low damped electromechanical system: application to a four mass experimental test bench. Eur Power Elect Drives J 15(3), 11th European Conference on Power Electronics and Applications, Dresden, Germany

    Google Scholar 

  • Rosenbrock HH (1974) Computer aided system design. Academic, New York

    Google Scholar 

  • Rosenbrock HH, Storey C (1970) Mathematics of dynamical systems. Nelson, London

    MATH  Google Scholar 

  • Sabatier J (1998) La dérivation non entière en modélisation des systèmes à paramètres distribués récursifs et en commande robuste des procédés non stationnaires. Ph.D. thesis, Université Bordeaux 1

    Google Scholar 

  • Sabatier J, Garcia Iturricha A, Oustaloup A (2002a) Analysis and Crone control of time varying systems with asymptotically constant coefficients. IFAC world congress, Barcelona

    Google Scholar 

  • Sabatier J, Garcia Iturricha A, Lanusse P (2002b) CRONE control: principles and extension to time-variant plants with asymptotically constant coefficients. Nonlinear Dyn 29(1–4):363–385, Kluwer Academic Publishers

    Article  MATH  MathSciNet  Google Scholar 

  • Sabatier J, Oustaloup A, Garcia Iturricha A, Levron F (2003) CRONE control of continuous linear time periodic systems: application to a testing bench. ISA Trans 42(3):421–436

    Article  Google Scholar 

  • Sabatier J, Poullain S, Latteux P, Thomas JL, Oustaloup A (2004) Robust speed control of a low damped electromechanical system based on Crone control: application to a four mass experimental test bench. Int J Nonlinear Dyn Chaos Eng Syst (Special Issue on “Fractional Derivatives and Their Applications”, Kluwer Academic Publishers) 38(1–4): 383–400

    Google Scholar 

  • Sabatier J, Garcia Iturricha A, Moze M, Oustaloup A (2008) Application of CRONE control to a sampled time varying system with periodic coefficients. J Dyn Syst Meas Control 130(6):061005

    Article  Google Scholar 

  • Sutter D (1997) La commande CRONE multiscalaire: application à des systèmes mécaniques articulés. Ph.D. thesis, Université Bordeaux 1

    Google Scholar 

  • Vidyasagar M, Viswanadham N (1982) Algebraic design techniques for reliable stabilization. IEEE Trans Autom Control 27(5):1085–1095

    Google Scholar 

  • Zames G (1966) On the input-output stability of time varying feedback systems; Part I: conditions using concepts of loop gain, conicity and positivity. IEEE Trans Autom Control 11:228–238

    Article  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

    2. PRISME Laboratory, Orléans University, EA 4229, F45072, Orléans, France

      D. Nelson Gruel

    Authors
    1. P. Lanusse
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    2. J. Sabatier
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    3. D. Nelson Gruel
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    4. A. Oustaloup
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    Corresponding author

    Correspondence to P. Lanusse .

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    Lanusse, P., Sabatier, J., Nelson Gruel, D., Oustaloup, A. (2015). Second and Third 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_3

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    • DOI: https://doi.org/10.1007/978-94-017-9807-5_3

    • Publisher Name: Springer, Dordrecht

    • Print ISBN: 978-94-017-9806-8

    • Online ISBN: 978-94-017-9807-5

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