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Adaptive Differentiators via Second Order Sliding Mode for a Fixed Wing Aircraft

M. Zaouche, A. Beloula, R. Louali1, S. Bouaziz2, M. Hamerlain3

Laboratoire Contrôle et Commande, Ecole Militaire Polytechnique, BP 17 Bordj El Bahri, Alger, 16000, Algeria. E-mail:
University of Paris-Sud , IEF UMR 8622, F-91405 Orsay, France. E-mail:
Center of Development of Advanced Technologies, Alger,16000, Algeria. E-mail:

Computer Modeling in Engineering & Sciences 2015, 104(3), 159-184.


Safety automation of complex mobile systems is a current topic issue in industry and research laboratories, especially in aeronautics. The dynamic models of these systems are nonlinear, Multi-Input Multi-Output (MIMO) and tightly coupled. The nonlinearity resides in the dynamic equations and also in the aerodynamic coefficients’ variability.
This paper is devoted to developing the piloting law based on the combination of the robust differentiator with a dynamic adaptation of the gains and the robust controller via second order sliding mode, by using an aircraft in virtual simulated environments.
To deal with the design of an autopilot controller, we propose an environment framework based on a Software In the Loop (SIL) methodology and we use Microsoft Flight Simulator (FS-2004) as the environment for plane simulation.
The first order sliding mode control may be an appropriate solution to this piloting problem. However, its implementation generates a chattering phenomenon and a singularity problem. To overcome these problems, a new version of the adaptive differentiators for second order sliding modes is proposed and used for piloting.
For the sliding mode algorithm, higher gains values may be used to improve accuracy; however this leads to an amplification of noise in the estimated signals. A good tradeoff between these two criteria (accuracy, robustness to noise ratio) is difficult to achieve. On the one hand, these values must increase the gains in order to derive a signal sweeping of some frequency ranges. On the other hand, low gains values have to be imposed to reduce noise amplification. So, our goal is to develop a differentiation algorithm in order to have a good compromise between error and robustness to noise ratio. To fit this requirement, a new version of differentiators with a higher order sliding modes and a dynamic adaptation of the gains, is proposed: the first order differentiator for the control of longitudinal speed and the second order differentiator for the control of the Euler angles.


Cite This Article

Zaouche, M., Beloula, A., Louali, R., Bouaziz, S., Hamerlain, M. (2015). Adaptive Differentiators via Second Order Sliding Mode for a Fixed Wing Aircraft. CMES-Computer Modeling in Engineering & Sciences, 104(3), 159–184.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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