Adel Tellili, Nouceyba Abdelkrim, Bahaa Jaouadi and Mohamed Naceur Abdelkrim
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.
Adel Tellili, Aymen Elghoul and Mohamed Naceur Abdelkrim
This paper presents the design of an additive fault tolerant control for nonlinear time-invariant singularly perturbed systems against actuator faults based on Lyapunov redesign principle. The overall system is reduced into subsystems with fast and slow dynamic behavior using singular perturbation method. The time scale reduction is carried out when the singular perturbation parameter is set to zero, thus avoiding the numerical stiffness due to the interaction of two different dynamics. The fault tolerant controller is computed in two steps. First, a nominal composite controller is designed using the reduced subsystems. Secondly, an additive part is combined with the basic controller to overcome the fault effect. The derived ε - independent controller guarantees asymptotic stability despite the presence of actuator faults. The Lyapunov stability theory is used to prove the stability provided the singular perturbation parameter is sufficiently small. The theoretical results are simulated using a numerical application.
Aymen Elghoul, Adel Tellili and Mohamed Naceur Abdelkrim
This paper presents the fault tolerant control (FTC) of a flexible joint robot using singular perturbation method in order to compensate for the lost performance due to the occurrence of actuator fault and the uncertainty. This FTC is based on Lyapunov redesign principle. The singular perturbation method is used to reduce the dynamic model of the flexible joint robot in a fast and slow subsystem. The time scale reduction of the flexible joint model is carried out when their joint stiffness is large enough and the singular perturbation parameter is set to zero. The fault-tolerant control structure in this paper is based on two parts. The first term described the composite control for the system without defect and without uncertainty which represents the sum between slow and fast controllers. While the second term of the fault tolerant command describes additive control designed to compensate for the fault effect of the actuator on the uncertain system. The additive approach is based on the Lyapunov theorem, which guarantees asymptotic stability despite the presence of actuator defects and the parametric uncertainty. The theoretical results are applied on a robot manipulator with a single flexible joint.
Radhia Ettouil, Karim Chabir, Dominique Sauter and Mohamed Naceur Abdelkrim
Synergetic control is proposed for heating, ventilating and air-conditioning (HVAC) system control. The synergetic controller is developed using the nonlinear model of the HVAC system. Occupancy information in each zone is required in the design of the controller which offers inherent comfort according to the occupancy in the zone. The stability of the building system using the proposed control is verified through the Lyapunov approach. It is also proved that the synergetic controller is robust to external disturbances. Then, synergetic theories are used to design a reconfigurable control for damper stuck failures in variable air volume (VAV) to recover the nominal performance. Simulations are provided to validate the effectiveness of the proposed controller for a three-zone building.