Fault detection, isolation and estimation for Takagi–Sugeno nonlinear systems

International audience

A data-driven fault isolation and estimation approach for unknown linear systems

Fault detection, isolation and estimation problems for linear systems with partial disturbance decoupling are studied in this article. By using singular value decomposition technique and geometric approach, the detailed design and implementation of partial disturbance decoupling are presented. On this basis, observers are designed, whose most important character is that each observer is affected by only one particular fault. By using Laplace transform, fault estimation strategy is addressed. A simulation example is presented to show the validity and effectiveness of the proposed approach.

In this paper, we consider the fault Detection and isolation (FDI) problem for faulty linear parameter-varying (LPV) systems subject to disturbances and propose a observer-based solution by using multiobjective optimization techniques. To simply the design process, a general faulty LPV system will be constructed from standard LPV description by converting actuator/system component faults into sensor faults at first. Then a bank of LPV FDI filters will be designed to identify each fault. Each FDI filter could generate a residual signal to track individual fault with minimum error and suppressing the effects of disturbances and other fault signals. The design of FDI filters will be formulated as multiobjective optimization problems in terms of linear matrix inequalities (LMIs) and can be solved efficiently. Two numerical examples are also presented to demonstrate the proposed fault detection and isolation approach on both LPV and LTI systems.

Sensor fault detection and isolation filter for polytopic LPV systems: A winding machine application

In this paper, the problems of fault detection and estimation for nonlinear dynamic systems are considered by using fault detection observer and adaptive fault diagnosis observer. Based on Lyapunov stability theory and linear matrix inequality (LMI) techniques, a new sufficient condition in terms of LMIs for the proposed problem is derived. At the same time, we get the adaptive fault estimation algorithm. The LMI condition can be easily solved by MATLAB LMI toolbox. Finally, a flexible joint robotic example is given to illustrate the efficiency of the proposed approach.

A two-stage extended kalman filter method for fault estimation of satellite attitude control systems

In this paper the problem of fault diagnosis in an aircraft jet engine is investigated by using an intelligent-based methodology. The proposed fault detection and isolation (FDI) scheme is based on the multiple model approach and utilizes autoassociative neural networks (AANNs). This methodology consists of a bank of AANNs and provides a novel integrated solution to the problem of both sensor and component fault detection and isolation even though possibly both engine and sensor faults may occur concurrently. Moreover, the proposed algorithm can be used for sensor data validation and correction as the first step for health monitoring of jet engines. We have also presented a comparison between our proposed approach and another commonly used neural network scheme known as dynamic neural networks to demonstrate the advantages and capabilities of our approach. Various simulations are carried out to demonstrate the performance capabilities of our proposed fault detection and isolation scheme.

An approach for nonlinear unknown input observer (NUIO) design is proposed for a class of nonlinear systems representable by a Takagi—Sugeno (TS) fuzzy system. The proposed NUIO design for TS fuzzy systems is carried out for two cases: (1) the premise variables do not depend on the unmeasured state variables; and (2) the premise variables depend on the unmeasured state variables. Sufficient conditions for the existence of NUIOs are derived, and a linear matrix inequality (LMI)-based design strategy is presented for NUIO design purposes. The proposed NUIO design approach is then applied to solve actuator fault detection and isolation problems for nonlinear systems described by TS fuzzy systems. To this end, a system structure with two groups of inputs where one group of inputs is treated as unknown inputs is developed. Based on the system structure, a bank of NUIOs are then designed using the developed NUIO design approach in order to investigate the following fault diagnosis problems. (1) How can the NUIOs be used for detecting faults? (2) Under what conditions is it possible to isolate single and/or multiple faults? (3) What is the maximum number of faults that can be isolated simultaneously? (4) How can multiple fault isolation be achieved? In this article we present a NUIO-based fault-detection scheme for problem (1), give sufficient conditions for problem (2), determine the maximum number of faults that can be isolated for problem (3), and propose a fault-diagnosis scheme using a bank of NUIOs to solve problem (4). As an illustrative example, Lorenz’s chaotic system with multi-inputs is chosen to show the effect of the designed NUIOs and the proposed fault detection and isolation scheme. Simulation results show that accurate state estimation is achieved and actuator faults can be detected and isolated successfully.

ABSTRACTQuick and timely fault detection is of great importance in control systems reliability. Undetected faulty sensors could result in irreparable damages. Although fault detection and isolation (FDI) methods in control systems have received much attention in the last decade, these techniques have not been applied for some classes of nonlinear systems yet. This paper deals with the issues of sensor fault detection and isolation for a class of Lipschitz uncertain nonlinear system. By introducing a coordinate transformation matrix for states and output, the original system is first divided into two subsystems. The first subsystem is affected by uncertainty and disturbance. The second subsystem just has sensor faults. The nonlinear term is separated to linear and pure nonlinear parts. For fault detection, two sliding mode observers (SMO) are designed for the two subsystems. The stability condition is obtained based on the Lyapunov approach. The necessary matrices and parameters are obtained by solving the linear matrix inequality (LMI) problem. Furthermore, two sliding mode observers are designed for fault isolation. Finally, the effectiveness of the proposed approach is illustrated by simulation examples.

Robust fault detection for uncertain switched systems

This paper addresses the Fault Detection and Isolation (FDI) of the problem of multiple non-concurrent faults on actuator and sensor of quadrotors, which is described by a nonlinear model. To the best of authors' knowledge, this paper provides, for the first time, a solution to the FDI problem for quadrotors affected by both actuator and sensor faults. The literature proposes FDI schemes dedicated only to actuators or only to sensors, indeed. The Non Linear Geometric Approach is based on the mathematical model of the system and allows to determine detection filters sensitive to a selected set of fault and structurally decoupled from the other faults (out of the selected set) thus providing the base for the fault isolation. Several simulation trials have been performed and the analysis of the results proves that the developed diagnostic system represents an effective solution to the problem of multiple actuator and sensor fault detection and isolation for quadrotors.

This chapter considers fault detection and isolation (FDI) for nonlinear systems with uncertainties using particular sliding mode observers for which the parameters can be obtained using LMI techniques. A sliding mode observder-based approach is presented to estimate system faults using bounds on the uncertainty, and as a special case, a fault reconstruction scheme is available where the reconstructed signal can approximate the fault signal to any accuracy. Sensor FDI for nonlinear systems is considered where a nonlinear diffeomorphism is introduced to exploit the system structure and a simple filter is presented to ‘transform’ the sensor fault into a pseudo-actuator fault scenario. Both fault estimation and reconstruction are considered. Case studies on a robotic arm and a mass–spring system are given to demonstrate the effectiveness of the proposed schemes.

Robust fast adaptive fault estimation for systems with time-varying interval delay

This paper deals with the problem of fault estimation for linear and nonlinear systems. An adaptive proportional integral observer is designed to estimate both the system state and sensor and actuator faults which can affect the system. The model of the system is first augmented in such a manner that the original sensor faults appear as actuator faults in this new model. The faults are then considered as unknown inputs and are estimated using a classical proportional-integral observer. The proposed method is first developed for linear systems and is then extended to nonlinear ones that can be represented by a Takagi-Sugeno model. In the two cases, examples of low dimensions illustrate the effectiveness of the proposed method.