Experimental comparison of new adaptive PI controllers based on the ultra-local model parameter identification

  • Hajer Thabet
  • Mounir Ayadi
  • Frédéric Rotella
Regular Papers Control Theory and Applications


This paper is devoted to an experimental comparison between two different methods of ultra-local model control. The concept of the first proposed technique is based on the linear system resolution technique to estimate the ultra-local model parameters. The second proposed method is based on the linear adaptive observer which allows the joint estimation of state and unknown system parameters. The closed-loop control is implemented via an adaptive PID controller. In order to show the efficiency of these two control strategies, experimental validations are carried out on a two-tank system. The experimental results show the effectiveness and robustness of the proposed controllers.


Adaptive PID controller least squares method linear adaptive observer parameter estimation robustness trajectory tracking two-tank system ultra-local model control 


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  1. [1]
    W. S. Levine, The Control Handbook, Cooperation with IEEE Press, New York, 1996.zbMATHGoogle Scholar
  2. [2]
    M. Fliess and C. Join, “Commande sans modèle et commande Ãă modèle restreint,” e-STA, vol. 4, no. 5, pp. 1–23, 2008.Google Scholar
  3. [3]
    M. Fliess and C. Join, “Model-free control and intelligent PID controllers: towards a possible trivialization of nonlinear control?,” Proc. of 15th IFAC Symposium on System Identification, SYSID’2009, Saint-Malo, vol. 15, pp. 1531–1550, 2009.Google Scholar
  4. [4]
    M. Fliess and C. Join, “Model-free control,” International Journal of Control, IJF’2013, vol. 86, no. 12, pp. 2228–2252, 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    M. Fliess, C. Join, and S. Riachy, “Revisiting some practical issues in the implementation of model-free control,” Proc. of 18th IFAC World Congress, Milan, pp. 8589–8594, 2011.Google Scholar
  6. [6]
    F. Lafont, J.F. Balmat, N. Pessel, and M. Fliess, “Modelfree control and fault accomodation for an experimental greenhouse,” Proc. of International Conference on Green Energy and Environmental Engineering (GEEE-2014), Tunisia, 2014.Google Scholar
  7. [7]
    M. Fliess and H. Sira-Ramírez. “An algebraic framework for linear identification,” ESAIM Control Optimization and Calculus of Variations, vol. 9, pp. 151–168, 2003. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    M. Fliess and H. Sira-Ramírez, “Closed-loop parametric identification for continuous-time linear systems via new algebraic techniques,” In H. Garnier & L. Wang (Eds): Identification of Continuous-time Models from Sampled Data, pp. 363–391, 2008.CrossRefGoogle Scholar
  9. [9]
    H. Sira-Ramírez, C. G. Rodríguez, J. C. Romero, and A. L. Juárez, Algebraic Identification and Estimation Methods in Feedback Control Systems, Wiley Series in Dynamics and Control of Electromechanical Systems, 2014.Google Scholar
  10. [10]
    H. Thabet, M. Ayadi, and F. Rotella, “Towards an ultralocal model control of two-tank-system,” International Journal of Dynamics and Control, vol. 4, no. 1, pp. 59–66, 2014.MathSciNetCrossRefGoogle Scholar
  11. [11]
    H. Thabet, M. Ayadi, and F. Rotella, “Ultra-local model control based on an adaptive observer,” Proc. of IEEE Conference on Control Applications (CCA), Antibes, 2014.Google Scholar
  12. [12]
    Q. Zhang, “Adaptive observer for multiple-input-multipleoutput (MIMO) linear time-varying systems,” IEEE Transactions on Automatic Control, vol. 47, pp. 525–529, 2002. [click]CrossRefGoogle Scholar
  13. [13]
    Q. Zhang and A. Clavel, “Adaptive observer with exponential forgetting factor for linear time varying systems,” Proc. of 40th IEEE Conference on Decision and Control (CDC), IEEE Control Systems Society, vol. 4, pp. 3886–3891, 2001.CrossRefGoogle Scholar
  14. [14]
    A. M. Ali and Q. Zhang. “Adaptive observer based fault diagnosis applied to differential-algebraic systems,” In 5th IFAC Symposium on System Structure and Control, Grenoble, 2013.Google Scholar
  15. [15]
    I. D. Landau, Adaptive Control: The Model Reference Approach, Marcel Dekker, New York, 1979.zbMATHGoogle Scholar
  16. [16]
    M. Fliess, J. Lévine, P. Martin, and P. Rouchon, “Flatness and defect of non-linear systems: introductory theory and examples,” International Journal of Control, vol. 61, no. 6, pp. 1327–1361, 1995. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    J. Haggège, M. Ayadi, S. Bouallègue, and M. Benrejeb, “Design of fuzzy flatness-based controller for a DC drive,” Control and Intelligent Systems, vol. 38, pp. 164–172, 2010.CrossRefzbMATHGoogle Scholar
  18. [18]
    F. Rotella, F. J. Carrilo, and M. Ayadi, “Digital flatnessbased robust controller applied to a thermal process,” Proc. of IEEE International Conference on Control Application, Mexico, pp. 936–941, 2001.Google Scholar
  19. [19]
    V. Volterra and J. Pérès, Théorie générale des fonctionnelles, Gauthier-Villars, 1936.zbMATHGoogle Scholar
  20. [20]
    K. J. Aström and T. Hägglund, Advanced PID Controllers, Instrument Society of America, Research Triangle Park, North Carolina, 2nd edition, 2006.Google Scholar
  21. [21]
    A. O’Dwyer, Handbook of PI and PID Controller Tuning Rules, 3rd edition, Imperial College Press, London, 2009.CrossRefzbMATHGoogle Scholar
  22. [22]
    F. Rotella and P. Borne, Théorie et pratique du calcul matriciel, Éditions Technip, Paris, 1995.Google Scholar
  23. [23]
    A. Ben-Israel and T. N.E. Greville, Generalized Inverses: Theory and Applications, John Wiley and Sons, 1974.zbMATHGoogle Scholar
  24. [24]
    A.H. Jazwinski, “Stochastic Processes and Filtering Theory,” in Mathematics in Science and Engineering, Academic, New York, vol. 64, 1970.Google Scholar
  25. [25]
    Q. Zhang, Adaptive observer for MIMO linear time varying systems, Technical Report 1379, IRISA,, 2001.Google Scholar
  26. [26]
    B. D. Anderson, R. R. Bitmead, C. R. J. Johnson, P. V. Kokotovic, R. L. Kosut, I. M. Mareels, L. Praly, and B. D. Riedle, Stability of Adaptive Systems: Passivity and Averaging Analysis, series in Signal Processing, Optimization, and Control, Cambridge, MIT Press, MA, 1986.zbMATHGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Hajer Thabet
    • 1
  • Mounir Ayadi
    • 1
  • Frédéric Rotella
    • 2
  1. 1.Laboratoire de Recherche en AutomatiqueUniversité de Tunis El Manar, Ecole Nationale d’Ingénieurs de TunisTunisTunisia
  2. 2.Laboratoire de Génie de ProductionEcole Nationale d’Ingénieurs de TarbesTarbes CEDEXFrance

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