Second and Third Generation CRONE Control-System Design

  • P. LanusseEmail author
  • J. Sabatier
  • D. Nelson Gruel
  • A. Oustaloup
Part of the Intelligent Systems, Control and Automation: Science and Engineering book series (ISCA, volume 77)


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.


  1. Arkun Y (1987) Dynamic block relative gain and its connection with the performance and stability of decentralized control structures. Int J Control 46(4):1187–1193CrossRefzbMATHGoogle Scholar
  2. 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):603–629CrossRefzbMATHGoogle Scholar
  3. Åstrom KJ (2000) Model uncertainty and robust control, lecture notes on iterative identification and control design. Lund Institute of Technology, LundGoogle Scholar
  4. 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 CrossRefzbMATHMathSciNetGoogle Scholar
  5. 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 CrossRefzbMATHGoogle Scholar
  6. Bode HW (1945) Network analysis and feedback amplifier design. Van Nostrand, New YorkGoogle Scholar
  7. Bristol EH (1966) On a new measure of interactions for multivariable process control. IEEE Trans Autom Control 11:133–134CrossRefGoogle Scholar
  8. Chang JW, Yu CC (1990) The relative gain for non-square multivariable systems. Chem Eng Sci 45(5):1309–1323CrossRefGoogle Scholar
  9. 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, MilanoGoogle Scholar
  10. Delavari H, Lanusse P, Sabatier J (2013) Fractional order controller design for a flexible link manipulator robot. Asian J Control 15(3):783–795CrossRefMathSciNetGoogle Scholar
  11. 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 1Google Scholar
  12. 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), CopenhagenGoogle Scholar
  13. 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):806–818CrossRefMathSciNetGoogle Scholar
  14. Francis BA, Zames G (1984) On H∞ optimal sensitivity theory for SISO feedback systems. IEEE Trans Autom Control 29:9–16CrossRefzbMATHMathSciNetGoogle Scholar
  15. Freudenberg JS, Looze JS (1985) Right half plane poles and zeros and design tradeoffs in feedback systems. IEEE Trans Autom Control 30:555–565CrossRefzbMATHMathSciNetGoogle Scholar
  16. 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):365–392CrossRefMathSciNetGoogle Scholar
  17. Graybill FA (1969) Introduction to matrices with applications in statistics, Wadsworth, BelmontGoogle Scholar
  18. Gude JJ, Kahoraho E (2009) Simple tuning rules for fractional PI controllers. In: Emerging technologies & factory automation IEEE conference, Mallorca, SpainGoogle Scholar
  19. Kariwala V, Fraser Forbes J, Meadows ES (2003) Block relative gain: properties and pairing rules. Ind Eng Chem Res 42(20):4564–4574CrossRefGoogle Scholar
  20. Kristiansson B, Lennartson B (2002) Robust and optimal tuning of PI and PID controllers. IEE Proc 149(1):17–25Google Scholar
  21. 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, FranceGoogle Scholar
  22. 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), ZurichGoogle Scholar
  23. 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):77–96CrossRefGoogle Scholar
  24. Lanusse P (1994) De la commande CRONE de 1ère génération à la commande CRONE de 3ème génération. Ph.D. thesis, Université Bordeaux 1Google Scholar
  25. Lanusse (2010) CRONE control system design, a CRONE toolbox for Matlab.
  26. 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 BeachGoogle Scholar
  27. Lanusse P, Oustaloup A, Sutter D (1996) Multi-scalar CRONE control of multivariable plants. In: Proceedings of WAC’96-ISIAC Symphosia, Montpellier, FranceGoogle Scholar
  28. 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, PragueGoogle Scholar
  29. 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): 242–251Google Scholar
  30. 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):16–23CrossRefMathSciNetGoogle Scholar
  31. 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), QingDaoGoogle Scholar
  32. 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
  33. 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), GrenobleGoogle Scholar
  34. Maciejowski JM (1989) Multivariable feedback design. Addison Wesley, WokinghamzbMATHGoogle Scholar
  35. Manousiouthakis V, Savage R, Arkun Y (1986) Synthesis of decentralized process control structures using the concept of block relative gain. AICHE J 32(6):991–1003CrossRefGoogle Scholar
  36. Mathieu B (1997) De la commande CRONE scalaire à la commande CRONE multivariable. Ph.D. thesis, Université Bordeaux 1Google Scholar
  37. Naslin P (1969) Essentials of optimal control. Boston Technical, BostonGoogle Scholar
  38. 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
  39. 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 VegasGoogle Scholar
  40. 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”, AnkaraGoogle Scholar
  41. Nelson Gruel D, Lanusse P, Oustaloup A (2009) Robust control design for multivariable plants with time-delays. Chem Eng J 146(3):414–427, ElsevierCrossRefGoogle Scholar
  42. Oustaloup A (1981) Linear feedback control systems of fractional order between 1 and 2. IEEE international symposium on circuits and systems, ChicagoGoogle Scholar
  43. Oustaloup A (1991) La commande CRONE. Edition Hermès, PariszbMATHGoogle Scholar
  44. Oustaloup A (1995) La dérivation non entière, théorie, synthèse et applications. Editions Hermès, ParisGoogle Scholar
  45. Oustaloup A, Lanusse P, Mathieu B (1995a) Robust control of SISO plants: the CRONE control; ECC’95, RomeGoogle Scholar
  46. Oustaloup A, Mathieu B, Lanusse P (1995b) The CRONE control of resonant plants: application to a flexible transmission. Eur J Control 1:113–121CrossRefGoogle Scholar
  47. Oustaloup A, Levron F, Nanot F, Mathieu B (2000) Frequency band complex non integer differentiator: characterization and synthesis. IEEE Trans Circuits Syst 47(1):25–40CrossRefGoogle Scholar
  48. Oustaloup A, Lanusse P, Levron F (2002) Frequency synthesis of filter using the functions of Viète’s roots. IEEE Trans Autom Control 47(5):837–841CrossRefMathSciNetGoogle Scholar
  49. 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):1–24zbMATHMathSciNetGoogle Scholar
  50. Pommier-Budinger V (2002) Commande non entière et commande non linéaire robuste d’un banc d’essais hydraulique. Ph.D. thesis, ENSAM BordeauxGoogle Scholar
  51. Pommier-Budinger V, Sabatier J, Lanusse P, Oustaloup A (2002) CRONE control of a nonlinear hydraulic actuator. Control Eng Pract 10(4):391–402CrossRefGoogle Scholar
  52. 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, BordeauxGoogle Scholar
  53. Pommier-Budinger V, Lanusse P, Janat Y, Oustaloup A (2005) CRONE control of MIMO plants. ECC-CDC 05, SevilleGoogle Scholar
  54. 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), ParisGoogle Scholar
  55. 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, SeattleGoogle Scholar
  56. 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, GermanyGoogle Scholar
  57. Rosenbrock HH (1974) Computer aided system design. Academic, New YorkGoogle Scholar
  58. Rosenbrock HH, Storey C (1970) Mathematics of dynamical systems. Nelson, LondonzbMATHGoogle Scholar
  59. 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 1Google Scholar
  60. Sabatier J, Garcia Iturricha A, Oustaloup A (2002a) Analysis and Crone control of time varying systems with asymptotically constant coefficients. IFAC world congress, BarcelonaGoogle Scholar
  61. 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 PublishersCrossRefzbMATHMathSciNetGoogle Scholar
  62. 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):421–436CrossRefGoogle Scholar
  63. 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): 383–400Google Scholar
  64. 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):061005CrossRefGoogle Scholar
  65. Sutter D (1997) La commande CRONE multiscalaire: application à des systèmes mécaniques articulés. Ph.D. thesis, Université Bordeaux 1Google Scholar
  66. Vidyasagar M, Viswanadham N (1982) Algebraic design techniques for reliable stabilization. IEEE Trans Autom Control 27(5):1085–1095Google Scholar
  67. 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 11:228–238CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • P. Lanusse
    • 1
    Email author
  • J. Sabatier
    • 1
  • D. Nelson Gruel
    • 2
  • A. Oustaloup
    • 1
  1. 1.IMS Laboratory - CNRS UMR 5218 – Bordeaux INP - Bordeaux University Bat A31 – 351 cours de la LibérationCedex TalenceFrance
  2. 2.PRISME LaboratoryOrléans UniversityOrléansFrance

Personalised recommendations