Fault Detection Observer Design Research Articles

LMI approach to mixed H_/H ∞ fault detection observer design

To investigate the robust fault detection (RFD) observer design for linear uncertain systems, the H t_ index and H ∞ norm are used to describe this observer design as optimization problems. Conditions for the existence of such a fault detection observer are given in terms of matrix inequalities. The solution is obtained by new iterative linear matrix inequality (ILMI) algorithms. The RFD observer design over finite frequency range in which D f does not have full column rank for a system is also considered. Numerical example demonstrates that the designed fault detection observer has high sensitivity to the fault and strong robustness to the unknown input.

An LMI Approach to Mixed <i>H_/H</i><sub>∞</sub> Robust Fault Detection Observer Design

This paper investigates the problem of the robust fault detection (RFD) observer design for linear uncertain systems with the aid of the H_ index and the H∞ norm, which are used to describe the problem of this observer design as optimization problems. Conditions for the existence of such a fault detection observer are given in terms of matrix inequalities. RFD problem with structured uncertainties in the system matrices is also considered. The solution is obtained by an iterative linear matrix inequality (ILMI) algorithm. Numerical example is employed to demonstrate the effectiveness of the proposed methods.

Design of robust fault detection observer for Takagi-Sugeno models using the descriptor approach

This paper deals with the design of a robust fault detection observer for a Takagi-Sugeno (T- S) fuzzy model affected by sensor and actuator faults and unknown bounded disturbances simulta- neously. An observer based on the technique of descriptor systems is studied. Indeed, by considering faults as auxiliary state variables, both states and faults are estimated simultaneously. In order to guar- antee the best robustness to disturbances and sensitivity to faults, the developed observer combine the H-/H∞ performances. Then, based on Lyapunov method, asymptotic stability conditions are given to design the observer parameters. In order to get convenient and reliable faults estimator in computations, an iterative linear matrix inequality (LMI) algorithm is developed. This algorithm, solved easily using existing numerical tools, allows to minimize influences of disturbances and maximize the ones of faults. Finally, a numerical example is proposed to illustrate the effectiveness of the result.

Optimization of fault detection performance for a class of nonlinear systems

SUMMARYThe problem of observer design for fault detection in a class of nonlinear systems subject to parametric and signal uncertainties is studied. The design procedure includes formalized optimization of observer‐free parameters in terms of trade‐offs for fault detection performance and robustness to external disturbances and model uncertainties. The technique makes use of some monotonicity conditions imposed on the estimation error dynamics. Efficiency of the proposed approach is demonstrated through the oscillatory failure case in aircraft control surface servo‐loops. Copyright © 2011 John Wiley & Sons, Ltd.

Sensor fault detection observer design for nonlinear systems in Takagi–Sugeno’s form

This paper addresses sensor fault detection observer design problems for discrete- and continu- ous-time nonlinear systems in Takagi-Sugeno's (T-S) form. It is desired that the fault detection observer is as sensitive to fault and robust against disturbance as possible. To this end, sufficient conditions for stable T-S fuzzy model-based observer design with H−/H∞ performance are derived in terms of linear matrix inequalities in both cases. An example on the backing-up problem of a truck-trailer is provided to illustrate the effectiveness of the proposed methodol- ogy.

LMI solutions to the mixed ℋ︁−/ℋ︁∞ fault detection observer design for linear parameter‐varying systems

AbstractThis paper addresses the mixed ℋ︁−/ℋ︁∞ fault detection observer design issue for a class of linear parameter‐varying (LPV) systems. Analogous to the definition of the quadratic ℋ︁∞ performance for LPV systems and the ℋ︁− index for linear time invariant (LTI) systems, the quadratic ℋ︁− index and the affine quadratic ℋ︁− index for LPV systems are defined in terms of linear matrix inequalities (LMIs). The first algorithm for designing the mixed ℋ︁−/H∞ observer is proposed, which aims at minimizing the quadratic ℋ︁∞ performance and maximizing the quadratic ℋ︁− index of the observer error dynamic systems. To reduce the conservativeness of this algorithm, the affine quadratic ℋ︁∞ performance and the affine ℋ︁− index for LPV systems are utilized. The robustness conditions and affine ℋ︁− index conditions for the underlying observer optimization issue are formulated as parameter‐dependent LMIs. The Gridding technique and multi‐convexity concept are applied, respectively, for reducing the parameter‐dependent LMIs to finite LMI constraints. Correspondingly, two iterative algorithms are proposed. Furthermore, the threshold design and the estimation of the worst undetectable fault size are investigated. An example is studied to demonstrate the effectiveness of the proposed algorithms. Copyright © 2010 John Wiley & Sons, Ltd.

Robust fault detection observer design for linear uncertain systems

This article addresses the fault detection observer design issue for linear time invariant (LTI) systems with additive or multiplicative uncertainties, which are also subject to unknown disturbances. The observer design is investigated under the ℋ∞/ℋ− index framework using the generalised KYP lemma in the finite-frequency domain. Sufficient conditions for the existence of such a fault detection observer are given in terms of linear matrix inequalities (LMIs). The threshold design issue is discussed and a method for estimating the worst undetectable fault size is proposed. The effectiveness of the proposed algorithms is illustrated by numerical simulation examples.

Design of Robust Fault Detection Observers for Discrete-time Linear Switched Systems

AbstractThis work addresses the design of a robust hybrid observer for discrete-time switched linear systems subject to unknown inputs and modeling errors. The observer herein proposed is synthesized, for the case when the active mode is unknown and in the purpose of robust fault detection. We'll show that a suitable trade-off between the robustness to unknown inputs and sensitivity to faults can be obtained through a H∞ performance index. The latter is optimized using an iterative LMI solution procedure. The efficiency of the proposed approach is illustrated by a numerical example.

Fault detection observer design for networked control system with long time-delays and data packet dropout

Fault detection observer design for networked control system with long time-delays and data packet dropout

Robust Fault Detection Observer and Fault Estimation Filter Design for LTI Systems Based on GKYP Lemma

This paper addresses the robust fault detection observer and fault estimation filter design issues for linear time invariant (LTI) systems with parameter uncertainties in a polytope and the systems are subject to unknown inputs as well. The observer and filter design are investigated in the H∞/H– index framework in the finite frequency interval by using the generalized KYP lemma. The threshold design and the worst undetectable fault size estimation are discussed. A numerical example is given to illustrate the effectiveness of the derived algorithms.

Fault Detection Observer Design in Low Frequency Domain for Linear Time-delay Systems

Fault Detection Observer Design in Low Frequency Domain for Linear Time-delay Systems

Fault Detection Observer Design in Low Frequency Domain for Linear Time-delay Systems

This paper deals with the robust fault detection (FD) problem in low frequency domain for linear time-delay systems. The H ∞ norm and H − index are used to measure the robustness to unknown inputs and the sensitivity to faults, respectively. The main results include derivation of a sufficient condition for the existence of a robust FD observer and its construction based on the linear matrix inequality (LMI) solution parameters. Finally, numerical simulations show the effectiveness of the presented methodology.

Methodology for nonlinear FDI Observer via Nonlinear Transformation : Application to a DC Series Motor

The aim of this paper is to propose a robust observer design for fault detection and isolation (FDI) and to apply this observer scheme to different cases of failures for a DC series motor.

Robust Fault Detection Based-Observer for Linear Switched Systems

Abstract This paper deals with the design of a robust hybrid observer for switched linear systems with unknown inputs and modeling error. The proposed observer is synthesized for the task of robust fault detection and concerns the case when the active mode is unknown. The basic idea of our approach is to formulate the design of the robust fault detection observer as a H∞ model-matching problem. Then, some results of H∞ optimization are exploited and an LMI solution procedure is proposed to synthesize the desired robust observer.

Robust Fault Detection Observer for LTI Systems with Additive Uncertainties

This paper addresses the robust fault detection observer design for LTI systems with model additive uncertainties. The observer design is investigated under the H∞/H_ index framework in the finite frequency domain where the generalized KYP lemma is used. The threshold design and the worst undetectable fault size estimation are also investigated in this paper. Examples are given to illustrate the effectiveness of the proposed methods.

A finite frequency domain approach to fault detection observer design for linear continuous‐time systems

AbstractThis paper deals with the fault detection observer design problem in finite frequency domain for linear time‐invariant continuous‐time systems with bounded disturbances. Two finite frequency performance indexes are introduced to measure the fault sensitivity and the disturbance robustness. Faults are considered in the low frequency domain while disturbances are considered in certain finite frequency domain. With the aid of the Generalized Kalman‐Yakubovich‐Popov lemma, the design methods are presented in terms of solutions to a set of linear matrix inequalities. An example of the VTOL aircraft is studied to illustrate the effectiveness of the proposed method. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Disturbance Attenuation and Fault Detection via Zero-pole Assignment: a Dynamic Observer Approach

In this paper, a zero-pole assignment approach is proposed for disturbance attenuation in dynamic fault detection observer design. The properties of dynamic observers are analysed and it is shown that the poles of a dynamic observer can be shifted and the additional zeros can be assigned arbitrarily. Then, a novel pole-zero assignment approach is proposed and its application to a continuous system is presented. In the simulation, the disturbances are low-frequency signals (< 1 Hz), which is more difficult to be attenuated compared to high-frequency disturbances. The dynamic observer shows the capabilities to attenuate such low-frequency disturbances. The zeros assignment in observer design would be the main contribution of this paper.

An LMI approach to [formula omitted] index and mixed [formula omitted] fault detection observer design

Using the newly developed worst-case fault sensitivity measure, the H - index, and the well-known worst-case robustness measure, the H ∞ norm, this paper addresses the problem of H - index fault detection observer design and multiobjective H - / H ∞ fault detection observer design problems. Necessary and sufficient conditions for the existence of such a fault detection observer are given in terms of matrix inequalities. Both infinite frequency range case [ 0 , ∞ ) and finite frequency range case [ 0 , ω ¯ ) are considered. Iterative linear matrix inequality (ILMI) algorithms are given to obtain the solutions. The effectiveness of the proposed approaches is shown by numerical examples.

Worst-Case Fault Detection Observer Design: Optimization Approach

This paper deals with the fault detection problem for linear systems with unknown inputs. The H∞ norm and H− index are employed to measure the robustness to unknown inputs and the sensitivity to faults, respectively. By using the pole assignment approach, the fault detection problem is transformed to an unconstrained optimization problem. With the aid of a gradient-based optimization approach, an explicit formula for designing the desirable observer gain is derived. Furthermore, the fault sensitivity over a finite frequency range can also be solved by the proposed method. The methodology proposed is verified through numerical simulation studies performed on the fault detection observer design of a vertical takeoff and landing aircraft.

Design of a bilinear fault detection observer for singular bilinear systems

A bilinear fault detection observer is proposed for a class of continuous time singular bilinear systems subject to unknown input disturbance and fault. By singular value decomposition on the original system, a bilinear fault detection observer is proposed for the decomposed system via an algebraic Riccati equation, and the domain of attraction of the state estimation error is estimated. A design procedure is presented to determine the fault detection threshold. A model of flexible joint robot is used to demonstrate the effectiveness of the proposed method.