CRONE OBSERVER - Definition and Design Methodology

Jocelyn Sabatier, Patrick Lanusse, Mathieu Merveillaut



CRONE control, robust control methodology based on fractional differentiation, is applied to state observer design. State observation can indeed be viewed as a regulation problem given that the goal of a state observer is to cancel the observation errors in spite of measurement noises, disturbances and plant perturbations. This conclusion has been used recently to define a new class of state observers known in the literature as “dynamic observers” or “input-output observer”. It is based on the observation error dynamic feedback. In this paper, this idea is used to define the CRONE observer design methodology. Performance robustness of the obtained observers versus plant perturbations is analysed. As for CRONE control, fractional differentiation in the definition of an equivalent open loop transfer function permits to reduce the number of parameters to be optimised.


  1. Biorci G. and S. Ridella (1970). Ladder RC network with constant RC product - IEEE Trans. Circuit Theory, 17.
  2. Dutta Roy S. C. (1970). On the realization of a constantargument impedance of fractional operation - IEEE Trans. Circuit Theory, 17.
  3. Hartley T. and C. Lorenzo (2005). Conjugated-order Differ Integrals, ASME Conference, Long Beach, California, 2005
  4. Ichise M., Y. Nagayanagi and T. Kojima (1971). An analog simulation of non integer order transfer functions for analysis of electrode processes - J. Electroanal. Chem. Interfacial Electrochem., 33, 253.
  5. Landau I.D., Rey D., Karimi A., Voda A. and Franco A., (1995). A Flexible Transmission System as a Benchmark for Robust Digital Control, European Journal of Control, Vol. 1, pp. 77-96.
  6. Lanusse P., A. Oustaloup and B. Mathieu (2000). Robust control of LTI square MIMO plants using two CRONE control design approaches - IFAC Symposium on Robust Control Design "ROCOND 2000", Prague, Czech Republic, June 21-23.
  7. Luenberger D. G. (1971). An introduction to observers. IEEE transactions on Automatic control, AC-16, 596- 602.
  8. Marquez H. J. (2003). A frequency domain approach to state estimation, Journal of the Franklin Institute, vol. 340, pp 147-157.
  9. Marquez H. J., M. Riaz (2005). Robust state observer design with application to an industrial boiler system, Control Engineering Practice, n° 13, pp 713-728.
  10. Miller K. S. and B. Ross (1993). An introduction to the fractional calculus and fractional differential equations - John Wiley & Sons Inc., New York.
  11. Oldham K. B. (1973). Semiintegral electroanalysis: analog implementation , Anal. Chem., Vol. 45, p 39.
  12. Oldham K. B. and J. Spanier (1974). The fractional calculus, Academic Press, New York.
  13. Oustaloup A. (1975). Etude et réalisation d'un système d'asservissement d'ordre 3/2 de la fréquence d'un laser à colorant continu - PhD Thesis, Bordeaux I University, France.
  14. Oustaloup A., A. Ballouk, P. Melchior, P. Lanusse and A. Elyagoubi (1990). Un nouveau régulateur CRONE fondé sur la dérivation non entiere complexe - GR Automatique CNRS Meeting, Bordeaux, France, March 29-30.
  15. Oustaloup A. (1991). The CRONE control, ECC'91 - Grenoble, France, July 2-5.
  16. Oustaloup A., B. Mathieu and P. Lanusse (1995). The CRONE control of resonant plants: application to a flexible transmission - European Journal of Control, Vol. 1 n°2.
  17. Oustaloup A., F. Levron, F. Nanot and B. Mathieu (2000). Frequency-band complex non integer differentiator: characterization and synthesis, IEEE Transactions on Circuits and Systems, Vol 47, n° 1, pp 25-40.
  18. Pommier V., J. Sabatier, P. Lanusse, A. Oustaloup (2002). CRONE control of a nonlinear Hydraulic Actuator - Control Engineering Practice, Vol. 10, n°4, pp. 391- 402
  19. Sabatier J., Poullain S., Latteux P., Thomas J. L., Oustaloup A. (2004), Robust speed control of a low damped electromechanical system: application to a four mass experimental test bench, International Journal of Nonlinear Dynamics and Chaos in Engineering Systems, Vol. 38, n° 1-4, pp 383-400.
  20. Samko S. G., A. A. Kilbas and O. I. Marichev (1993). Fractional integrals and derivatives - Gordon and Breach Science Publishers.
  21. Suezaki and Takahashi (1966). Phase splitter of symmetric lattice network type and the termination with the impedance 1/ s - Paper of the technical group on network and system theory, IECE, Japan, 1966.

Paper Citation

in Harvard Style

Sabatier J., Lanusse P. and Merveillaut M. (2007). CRONE OBSERVER - Definition and Design Methodology . In Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 3: Fractional Order Systems, (ICINCO 2007) ISBN 978-972-8865-84-9, pages 421-429. DOI: 10.5220/0001637404210429

in Bibtex Style

@conference{fractional order systems07,
author={Jocelyn Sabatier and Patrick Lanusse and Mathieu Merveillaut},
title={CRONE OBSERVER - Definition and Design Methodology},
booktitle={Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 3: Fractional Order Systems, (ICINCO 2007)},

in EndNote Style

JO - Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 3: Fractional Order Systems, (ICINCO 2007)
TI - CRONE OBSERVER - Definition and Design Methodology
SN - 978-972-8865-84-9
AU - Sabatier J.
AU - Lanusse P.
AU - Merveillaut M.
PY - 2007
SP - 421
EP - 429
DO - 10.5220/0001637404210429