Skip Navigation Links
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email:

Control of a Hydro-electromechanical System Using Fractional-order Controllers: A Comparative Study

Journal of Applied Nonlinear Dynamics 2(4) (2013) 355--371 | DOI:10.5890/JAND.2013.11.004

Roy Abi Zeid Daou; Xavier Moreau; Clovis Francis

$^{1}$ University of Bordeaux 1, laboratory IMS, Department LAPS, 33405 Talence cedex, France

$^{2}$ Lebanese German University, Faculty of Public Health, Biomedical Technologies department, Sahel Alma - P.O. Box: 206, Jounieh, Lebanon

$^{3}$ Lebanese University, Faculty of Engineering I, Tripoli, Lebanon

Download Full Text PDF



This article presents a comparative study of the regulators of a hydro-electromechanical system, composed of two pumps, a uniform tank and a level sensor. Both controllers are fractional orders where the first one is the generalized PID controller and the second one is the CRONE (French acronym: Commande Robuste d’Ordre Non Entier) controller. In a first time, the transfer function of the plant is presented after identification (using the graybox method) and simplification processes. Then, the realization of both regulators is shown where the first controller (generalized PID) is obtained after imposing the regulator model whereas the second one is deduced using the open-loop constraints. At the end, a comparison between the behavior of both controllers is made in the frequency domain around some functional points of the plant as its behavior is nonlinear.


  1. [1]  Dugowson, S. (1994), Les diffrentielles mtaphysiques : histoire et philosophie de la gnralisation de l'ordre de drivation, Thse de Doctorat de l'Universit Paris Nord.
  2. [2]  Cois, O. (2002), Systmes linaires non entiers et identification par modle non entier : application en thermique, Thse de Doctorat de l'Universit Bordeaux 1.
  3. [3]  Lin, J. (2001), Modlisation et identification de systmes d'ordre non entier, Thse de Doctorat, Universit de Poitiers.
  4. [4]  Miller, K.S. and Ross, B., (1993), An Introduction to the Fractional Calculus and Fractional Differential Equations, A Wiley-Interscience Publication, 1993.
  5. [5]  Oldham, K.B. and Spanier, J. (1974), The Fractional Calculus, Academic Press, New-York and London.
  6. [6]  Oustaloup, A. (1995), La dérivation non entière : thoérie, synthèse et applications, Edition Hermès, Paris.
  7. [7]  Samko, S.G., Kilbas A.A., and Marichev, O.I. (1993), Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science Publishers.
  8. [8]  Manabe, S. (1961), The non-integer integral and its application to control systems, ETJ of Japan, 6, 83-87.
  9. [9]  Oustaloup, A. (1975), Etude et réalisation d'un système d'asservissement d'ordre 3/2 de la fréquence d'un laser á colorant continu, Thèse de Docteur-Ingénieur, Universit Bordeaux 1.
  10. [10]  Ziegler, J.G. and Nichols, N. B. (1942), Optimum settings for automatic controllers, Transactions of ASME, 64, 759-768.
  11. [11]  Asröm, K.J. and Hgglund, T. (2000), The future of PID control, IFAC Workshop on Digital Control, Past, Present and Future of PID Control, 19-30, Terressa, Spain.
  12. [12]  Chen, Y.Q., Hu, C.H., and Moore, K. L. (2003), Relay feedback tuning of robust PID controllers with iso-damping property, 42nd IEEE Conference on Decision and Control, Maui, Hawaii, USA.
  13. [13]  Podlubny, I. (1999), Fractional-order systems and PID-controllers, IEEE Transaction on Automatic Control, 44, 208-214.
  14. [14]  Vinagre, B.M., Podlubny, I., Dorcak, L., and Feliu, V. (2000), On fractional PID controllers: a frequency domain approach, IFAC Workshop on Digital Control, Past, Present and Future of PID Control, 53-58, Terressa, Spain.
  15. [15]  Caponetto, R., Fortuna, L., and Porto, D. (2002), Parameter tuning of a non integer order PID controller, Proceedings of 5th International Symposium on Mathematical Theory of Networks and Systems , Notre Dame, Indiana.
  16. [16]  Leu, J.F., Tsay, S.Y., and Hwang, C. (2002), Design of optimal fractional-order PID controllers, Journal of the Chinese Institute of Chemical Engineers, 33, 193-202.
  17. [17]  Monje, C.A., Calderon, A.J., and Vinagre, B.M. (2002), PI vs fractional DI control : first results, Controlo 2002, 5th Portuguese Conference on Automatic Control, 359-364, Aveiro, Portugal.
  18. [18]  Chen, Y.Q., Hu, C.H., Vinagre, B.M., and Monje, C.A. (2004), Robust PID controller tuning rule with iso-damping property, American Control Conference.
  19. [19]  Tulleken, H.J.A.F. (1993), Grey-box modelling and identification using physical knowledge and bayesian techniques, Automatica, 29 (2), 285-308.
  20. [20]  Malti, R., Melchior, P., Lanusse, P., and Oustaloup, A. (2011), Towards an object oriented CRONE toolbox for fractional differential systems, 8th IFAC World Congress, Milano, Italy.