Nouceyba Abdelkrim

Diagnosis of Discrete-Time Singularly Perturbed Systems Based on Slow Subsystem

Abstract This paper deals with the diagnosis of discrete-time singularly perturbed systems presenting two time scales property. Parity space method is considered to generate the fault detection residual. The focus is in two directions. First, we discuss the residual illconditioning caused by the singular perturbation parameter. Then, the use of the slow subsystem is considered to make the fault diagnosis easier. It is shown that the designed diagnostic algorithm based on reduced order model is close to the one synthesized using the full order system. The developed approach aims at reducing the computational load and the ill-conditioning for stiff residual generation problem. Two examples of application are used to demonstrate the efficiency of the proposed method.

Actuator fault tolerant control for delayed systems

The actuator fault estimation and a fault tolerant control (FTC) for delayed system are proposed in this paper. The estimation of actuator fault is realized by using the Luen-berger observer, and the fault tolerant control is obtained by adding an additive control law to the nominal one. The nominal control of delayed system is designed by using the Lambert-W function. finally, a simulation example is illustrated in the end of this paper.

Composite control of a delayed singularly perturbed system by using Lambert-W function

The composite state feedback control designed for singularly perturbed system SPS with small time-delay by using Lambert-W function is proposed in this paper. Based on the delayed slow subsystem (SS) and fast subsystems (FS) decomposition, we design a composite sate-feedback control. So the gain of delayed SS will be designed by using Lambert-W function and the gain of FS will be designed on the basis of classical pole placement method, and the two gains will be regrouped in global gain to design the delayed SPS. A numerical example is presented to illustrate the effectiveness of the proposed design approach.

Reconfigurable Control of Two-Time Scale Systems in Presence of Additive Faults

This work presents an adaptive approach for fault tolerant control of singularly perturbed systems, where both actuator and sensor faults are examined in presence of external disturbances. For sensor faults, an adaptive controller is designed based on an output-feedback control scheme. The feedback controller gain is determined in order to stabilize the closed-loop system in the fault free case and vanishing disturbance, while the additive gain is updated using an adaptive law to compensate for the sensor faults and the external disturbances. To correct the actuator faults, a state-feedback control method based on adaptive mechanism is considered. The both proposed controllers depend on the singular perturbation parameter e leading to ill-conditioned problems. A well-posed problem is obtained by simplifying the Lyapunov equations and subsequently the controllers using the singular perturbation method and the reduced subsystems yielding to an e-independent controller. The control scheme, designed based on the Lyapunov stability theory, guarantees asymptotic stability in presence of additive faults and external disturbances provided the singular perturbation parameter is sufficiently small. Finally, a numerical example is presented to demonstrate the effectiveness of the obtained results. DOI: http://dx.doi.org/10.5755/j01.itc.44.4.8532

Output-feedback fault tolerant control for linear time delay systems: Descriptor approach

In this paper we propose a new approach of fault estimation and Fault Tolerant Control (FTC) applied to Linear Time Delay (LTD) systems. To estimate the sensor faults we use the descriptor approach. This method consists in augmenting the state system by considering the faults as an auxiliary state. The used observer can estimate simultaneously both the state of LTD system and sensor faults. The observer gains are then determined according to Linear Matrix Inequalities (LMI) technique. For the step of FTC we construct an output-feedback gain to stabilize the LTD system not only in free-fault case, but also in the fault occurrence. A numerical example is proposed to demonstrate the efficiency of the given design for different form of sensor fault.

Diagnosis of delayed discrete-time singularly perturbed systems based on slow subsystem

This work presents an approach for fault diagnosis of discrete time singularly perturbed systems (SPS) with time-delay, called parity space in order to generate fault detection residual. In fact, to decompose the full system into slow and fast subsystems, we based on singular perturbation method. Then, we can use the reduced residual generated basing on slow subsystem in order to estimate and isolate faults of the global delayed SPS. A numerical example is presented to demonstrate the efficiency of the proposed approach in the case of sensor faults with different values of singular perturbation parameter epsilon.

AN adaptive fault tolerante control in interconnected systems

This work aims at the adaptive fault tolerant control using output feedback. Fault tolerant adaptive control is developed for N-interconnected subsystems with unknown sensors failures. Such sensors failures are characterized by some unknown inputs stuck at some unknown fixed values at unknown time instants. An effective output feedback controller structure is proposed for sensors failures compensation. The FTC scheme has an additive control in the adaptive controller which has an intrinsic robustness in terms of the stability and performance of the estimation sensors failure. This work is an extension of the additive control method presented in [8] to the interconnected subsystems. Numerical and simulation results are provided to demonstrate the effectiveness of the proposed controller.