Abstract

The problem of Fault Detection, Isolation, and Estimation (FDIE) as well as Fault-Tolerant Control (FTC) for a class of nonlinear systems modeled with Euler-Lagrange (EL) equations subjected to simultaneous sensor and actuator faults are considered in this study. To tackle this problem, first state and output linear transformations are introduced to decouple the effects of sensor and actuator faults. These transformations do not depend on the system nonlinearities. An analytical procedure based on two Linear Matrix Inequality (LMI) feasibility conditions is proposed to obtain these transformations.
Once, the effects of faults are decoupled, two Sliding Mode Observers (SMO) are designed to reconstruct each type of fault, separately. Subsequently, the results of fault estimations are fed back to the controller and the effects of faults are compensated for.
In this study, the mathematical stability proof of the coupled controller, observers, and the nonlinear system is provided. Unlike previous methodologies in the literature, no limiting assumptions such as Lipschitz conditions are imposed on the system.
Next, a novel fault tolerant control scheme is proposed in which a single SMO is used to reconstruct sensor faults and provide a compensation term to rectify the effects of faults. However, to deal with actuator faults, a Sliding Mode Controller (SMC) is employed. Using this robust FTC technique, zero tracking error in the presence of uncertainties, measurement noise, disturbances, and faults as well as estimation of the actuator faults are possible. The stability proof for the coupled nonlinear controller, observer and plant is provided by using the properties of Euler-Lagrange equations and sliding mode techniques. Finally, to evaluate the performance of the proposed FDIE and FTC approaches, extensive sets of simulations are performed on a 3 Degrees Of Freedom (DOF) Autonomous Underwater Vehicle (AUV). Simulation studies show the promising results obtained as a result of the presented approaches as compared to those obtained by using the existing methodologies.