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Adaptive Fault Tolerant Control of Multi-time-scale Singularly Perturbed Systems

International Journal of Automation and computing 2018年第6期15卷 736-746页

作者： Adel Tellili nouceyba abdelkrim Amina Challouf Mohamed Naceur abdelkrim Research Unit MACS University of Gabes Gabes Tunisia Higher Institute of Industrial Systems at Gabes University of Gabes Gabes Tunisia Higher Institute of Technological Studies at Djerba Djerba Tunisia National School of Engineers of Gabes University of Gabes Gabes Tunisia

This paper studies the fault tolerant control, adaptive approach, for linear time-invariant two-time-scale and three-time-scale singularly perturbed systems in presence of actuator faults and external disturbances. First, the full order system will be controlled using v-dependent control law. The corresponding Lyapunov equation is ill-conditioned due to the presence of slow and fast phenomena. Secondly, a time-scale decomposition of the Lyapunov equation is carried out using singular perturbation method to avoid the numerical stiffness. A composite control law based on local controllers of the slow and fast subsystems is also used to make the control law ε-independent. The designed fault tolerant control guarantees the robust stability of the global closed-loop singularly perturbed system despite loss of effectiveness of actuators. The stability is proved based on the Lyapunov stability theory in the case where the singular perturbation parameter is sufficiently small. A numerical example is provided to illustrate the proposed method.

关键词： Singularly perturbed systems time scale decomposition adaptive fault tolerant control actuator fault Lyapunov equations

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Additive Fault Tolerant Control Applied to Delayed Singularly Perturbed System

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Journal of Software Engineering and Applications 2012年第4期5卷 217-224页

作者： nouceyba abdelkrim Adel Tellili Mohamed Naceur abdelkrim Research Unit Modeling Analysis and Control Systems (MACS) Gabes Tunisia

The additive fault tolerant control (FTC) for delayed system is studied in this work. To design the additive control, two steps are necessary;the first one is the estimation of the sensor fault amplitude using a Luenberger observer with delay, and the second one consists to generate the additive fault tolerant control law and to add it to the nominal control of delayed system. The additive control law must be in function of fault term, then, in the absence of fault the expression of additive control equal to zero. The generation of nominal control law consist to determinate the state feedback gain by using the Lambert W method. Around all these control tools, we propose an extension of the additive FTC to delayed singularly perturbed systems (SPS). So, this extension consists to decompose the delayed SPS in two parts: delayed slow subsystem (delayed SS) and fast subsystem (FS) without time delay. Next, we consider that the delayed SPS is affected at its steady-state, and we apply the principal of FTC to the delayed SS and finally we combine them with the feedback gain control of FS by using the principal of composite control.

关键词： Additive Fault Tolerant Control Composite Control Lambert W Function Order Reduction Sensor Fault Singularly Perturbed System

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