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.K e y w o r d s: nonlinear time-invariant singularly perturbed systems, singular perturbation method, additive fault tolerant control, actuator defect, Lyapunov theory
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.
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