Abstract
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.
Highlights
Several physical processes are on one hand high order and on the other hand are complex what returns their analysis and especially their control, with the aim of certain objectives, very delicate
We consider that the delayed singularly perturbed systems (SPS) is affected at its steady-state, and we apply the principal of fault tolerant control (FTC) to the delayed SS and we combine them with the feedback gain control of fast subsystem (FS) by using the principal of composite control
We will consider that the delayed SPS is affected at its steady-state, so that it is equivalent to consider that the fault affects only the delayed slow subsystem and by consequence we will design only the reduced additive FTC of slow subsystem and the additive control of delayed slow subsystem will be applied to delayed SPS to compensate its sensor fault
Summary
Several physical processes are on one hand high order and on the other hand are complex what returns their analysis and especially their control, with the aim of certain objectives, very delicate Knowing that these systems possess variables evolving in various speeds (temperature, pressure, intensity, voltage...) it turned out interesting to separate their dynamics [1,2,3,4,5,6] with the aim of the implementation of singularly perturbation technique. This one allows, in the case of two time scales, [7] to describe the behavior of global studied process by those of two their subsystem (slow and fast) obtained by a temporal decomposition. This paper is the extension of the additive fault tolerant control designed for the SPS in [13] to the delayed SPS case and it’s the extension of additive FTC in [14, 15] to the delayed systems and specially to the delayed singularly perturbed system
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