104 Int. J. Automation and Control, Vol. 10, No. 2, 2016
Copyright © 2016 Inderscience Enterprises Ltd.
Adaptive fault tolerant control of singularly perturbed
systems with actuator faults
Adel Tellili*
Research Unit MACS,
Higher National Engineering School at Gabès, Tunisia
and
Higher Institute of Technological Studies at Djerba,
Avenue 7 novembre – 4116 Midoun Djerba, Tunisia
Email: adel_tellili@lycos.com
*Corresponding author
Nouceyba Abdelkrim and Amina Challouf
Research Unit MACS,
Higher National Engineering School at Gabès, Tunisia
and
Higher Institute of Industrial Systems at Gabès,
University of Gabès,
Rue Slaheddine El Ayoubi – 6032 Gabès, Tunisia
Email: nouceyba.naceur@laposte.net
Email: amina_chalouf@yahoo.fr
Mohamed Naceur Abdelkrim
Research Unit MACS,
Higher National Engineering School at Gabès, Tunisia
and
Higher National Engineering School at Gabès,
University of Gabès,
Avenue Omar Ibn El Khattab – Zerig – 6029 Gabès, Tunisia
Email: naceur.abdelkrim@enig.rnu.tn
Abstract: This paper deals with the adaptive fault tolerant control for linear
time-invariant singularly perturbed systems against actuator failures and
external disturbances. By time-scale decomposition using singular perturbation
method, the full-order system is decomposed into slow and fast subsystems. An
ε-dependent fault tolerant controller for the global system is first designed. To
avoid numerical stiffness, a simplification based on singular perturbation
parameter decoupling is secondly carried out using the reduced subsystems and
some manipulations of the Lyapunov equations. The resulting control system is
fault tolerant in that, it provides guaranteed asymptotic stability in presence of
external disturbances when all control components are operational as well as
when actuator failures occur. The stability is guaranteed based on the Lyapunov
stability theory provided the singular perturbation parameter is sufficiently
small. A numerical example is given to illustrate the proposed method, where
the efficiency of the developed approach will be compared with a reliable H
∞
control technique.