Simultaneous fault detection, isolation and tracking design using a single observer-based module

Abstract

Fault diagnosis (FD) has received much attention for complex modern automatic systems such as car, aircraft, rockets, unmanned vehicles, and so on since 1970s. In the FD research field, the diagnostic systems are often designed separately from the control algorithms, although it is highly desirable that both the control and diagnostic modules are integrated into one system module. Hence, the problem of simultaneous fault detection and control (SFDC) has attracted a lot of attention in the last two decades, both in research and application domains. The simultaneous design unifies the control and detection units into a single unit which results in less complexity as compared with the case of separate design; so, it is a reasonable approach. However, the current literature in the field of SFDC suffers from the following limitations and drawbacks. First, most of the literature that considers the problem of SFDC, can achieve the control objective of "regulation" but none of them consider the problem of "tracking" in SFDC design. Therefore, considering the problem of tracking in SFDC design methodology is of great significance and importance. Second, although most of the current references in the field of SFDC can achieve acceptable fault detection, they cannot achieve fault isolation. Hence, although there are certain published works in the field of SFDC, none of them is capable of detecting and isolating simultaneous faults in the system as well as tracking the specified reference input. In this paper, the problem of simultaneous fault detection, isolation and tracking (SFDIT) design for linear continuous-time systems is considered. An H_infty/H_index formulation of the SFDIT problem using a dynamic observer detector and state feedback controller is developed. Indeed, a single module based on dynamic observer is designed which produces two signals, namely the residual and the control signals. The SFDIT module is designed such that the effects of disturbances and reference inputs on the residual signals are minimized (for accomplishing fault detection) subject to the constraint that the transfer matrix function from the faults to the residuals is equal to a pre assigned diagonal transfer matrix (for accomplishing fault isolation), while the effects of disturbances, reference inputs and faults on the specified control output are minimized (for accomplishing fault-tolerant control and tracking problems). Sufficient conditions for solvability of the problem are obtained in terms of linear matrix inequality (LMI) feasibility conditions. On the other hand, it is shown that by applying our methodology, the computational complexity from the view point of the number and size of required observers is significantly reduced in comparison with all of the existing methodologies. Moreover, using this approach the system can not only detect and isolate the occurred faults but also able to track the specified reference input. The proposed method can also handle isolation of simultaneous faults in the system. Simulation results for an autonomous unmanned underwater vehicle (AUV) illustrate the effectiveness of our proposed design methodology.