Flatness-based Control and Conventional RST Polynomial Control of a Thermal Process


  • Hajer Gharsallaoui í‰cole Nationale d’Ingénieurs de Tunis, LAboratoire de Recherche en Automatique (LA.R.A.) B.P. 37, le Belvédí¨re, 1002 Tunis, Tunisia Laboratoire d’Automatique, Génie Informatique et Signal (LAGIS), í‰cole Centrale de Lille Avenue Paul Langevin BP 48 59651 VILLENEUVE D’ASCQ CEDEX, France
  • Mounir Ayadi
  • Mohamed Benrejeb
  • Pierre Borne


Flatness, RST control, tracking trajectory, robustness, anti-windup


In this paper, a comparison between conventional RST polynomial control by poles placement and RST flatness-based control is proposed. These approaches were developed, in discrete-time formalism by carrying out a generation of a reference starting from a flat output and by then analyzing the tracking error in closedloop. The case of the thermal system, that we applied an output disturbance, was considered by simulation to study the effectiveness of given flatness-based robust controller with the integration of an anti-windup device, in terms of tracking trajectory and disturbance rejection.


M. Fliess, J. Lévine, Ph. Martin and P. Rouchon, Sur les systeme non linéaires différentiellement plats, Compte Rendu de l'Académie des Sciences de Paris, Série I, 315, pp. 619-624, 1992.

M. Ayadi, Contribution ´r la commande des systemes linéaires plats de dimension finie, PhD Thesis, Institut National Polytechnique de Toulouse, 2002.

T. Kailath, Linear systems, Prentice Hall, 1980.

I. Landau, R. Lozano and M. M'Saad, Adaptative control, Springer-Verlag, London, 1998. http://dx.doi.org/10.1007/978-0-85729-343-5

F. Rotella, F J. Carrillo and M. Ayadi, Polynomial controller design based on flatness, Kybernetica Special Issue on System Structure and Control, Vol. 38, n°5, pp. 571-584.

A. Oustaloup, La robustesse. Analyse et synthˇcse de commandes robustes, Hermˇcs, 1994.

M. Fliess and R. Marquez, Towards a module theoretic approach to discrete time linear predictive control, 14th International Symposium on Mathematical Theory of Networks and Systems, MTNS'2004, Perpignan, 2001.

M. M'Saad M. and J. Chebassier, Commande adaptative des systeme, Techniques de l'Ingénieur, Vol. S2, n°S7426, pp. 1-25, Paris, 1999.

P. Borne, G. Dauphin-Tanguy, J. P. Richard, F. Rotella and I. Zambettakis, Commande et optimisation des processus, Edition Technip, Paris, 1990.

S. Médar, Supervision et reconfiguration de la commande des systeme dynamiques en présence de variations dans les conditions de fonctionnement, PhD Thesis, Institut National Polytechnique de Toulouse, 2002.

F. Rotella, F. J. Carrilo and M. Ayadi, Digital flatness-based robust controller applied to a thermal process, IEEE International Conference on Control Application, pp. 936-941, Mexico, 2001. http://dx.doi.org/10.1109/cca.2001.973990

K. J. Aström and B. Wittenlmark, Adaptative Control, Addison Wesley, United States, 1989.

M. Ayadi, N. Langlois, M. Benrejeb and H. Chafouk, Flatness-based robust adaptative polynomial controller for a diesel engine model, Transaction on Systems, Signals & Devices, Vol. 2, n°1, pp. 71-90, 2006.

M. Fliess, J. Lévine, Ph. Martin and P. Rouchon, On Differentially Flat non Linear Systems, IFACSymposium NOLCOS'92, pp. 408-412, Bordeaux ,1992.

R. Marquez, and M. Fliess, Linear Predictive Control Revisited. A Flatness Based Approach, European Control Conference, ECC'99, Karlshrule, 1999.

Ph. Charbonnaud, J. F. Carrilo and S. Médar, Robust control reconfiguration of a thermal process with multiple operating modes,IEEE transaction of control systems technology, Vol. 11, n°4, 2003.

J.Y. Dieulot, I. Thimoumi, F. Colas and R. Béarée, Numerical Aspects and Performances of Trajectory Planning Methods of Flexible Axes, International Journal of Computers, Communications and Control, Vol.I, n°4, pp. 35-44, 2006. http://dx.doi.org/10.15837/ijccc.2006.4.2304

J. Lévine, On the necessary and sufficent conditions for differential flatness, 6th IFAC Symposium on Nonlinear Control Systems, NOLCOS'04, pp. 463-468, Stuttgart, 2004.

H. Sira-Ramirez and S.K. Agrawal, Differentially flat systems, Marcel Dekker, 2004.



Most read articles by the same author(s)

Obs.: This plugin requires at least one statistics/report plugin to be enabled. If your statistics plugins provide more than one metric then please also select a main metric on the admin's site settings page and/or on the journal manager's settings pages.