scispace - formally typeset
Search or ask a question
Journal ArticleDOI

Brief paper: Nonlinear robust fault reconstruction and estimation using a sliding mode observer

01 Sep 2007-Automatica (Pergamon Press, Inc.)-Vol. 43, Iss: 9, pp 1605-1614
TL;DR: This paper considers fault detection and estimation issues for a class of nonlinear systems with uncertainty, using an equivalent output error injection approach, and a particular design of sliding mode observer is presented for which the parameters can be obtained using LMI techniques.
About: This article is published in Automatica.The article was published on 2007-09-01. It has received 509 citations till now. The article focuses on the topics: Fault detection and isolation & Fault (power engineering).
Citations
More filters
Journal ArticleDOI
TL;DR: This paper presents a fault detection and isolation (FDI) scheme for a class of Lipschitz nonlinear systems with nonlinear and unstructured modeling uncertainty that significantly extends previous results by considering a more general class of system nonlinearities which are modeled as functions of the system input and partially measurable state variables.

327 citations


Cites background or methods from "Brief paper: Nonlinear robust fault..."

  • ...The known nominal system model in (3) is similar to the model used in Yan and Edwards (2007)....

    [...]

  • ...…considered for Lipschitz nonlinear systems in the fault diagnosis literature (e.g., Chen and Saif (2007), Vijayaraghavan et al. (2007), Yan and Edwards (2007)), which, to achieve robustness, additionally assumes that certain rank conditions are satisfied by the distribution matrix of the…...

    [...]

  • ...For instance, Vijayaraghavan, Rajamani, and Bokor (2007) addressed the sensor fault diagnosis problem by assuming the absence of modeling uncertainty, and in Chen and Saif (2007), Yan and Edwards (2007) sliding mode 0005-1098/$ – see front matter© 2009 Elsevier Ltd....

    [...]

  • ...By choosing x1 = q1, x2 = q̇1, x3 = q2, x4 = q̇2, and assuming that the motor position, motor velocity, and the sum of link position and link velocity are measured (see, e.g. Yan and Edwards (2007)), a state space model of the system can be obtained....

    [...]

  • ...…2004; Garciá & Frank, 1997; Hammouri, Kinnaert, & El Yaagoubi, 1999; Krishnaswami & Rizzoni, 1997; Mhaskar, McFall, Gani, Christofides, & Davis, 2008; De Persis & Isidori, 2001; Wang, Huang, & Daley, 1997; Yan & Edwards, 2007; Zhang, Polycarpou, & Parisini, 2002, and the references cited therein)....

    [...]

Journal ArticleDOI
TL;DR: This paper investigates the problem of fault estimation and fault-tolerant control against sensor failures for a class of nonlinear Ito stochastic systems with simultaneous input and output disturbances using a new descriptor sliding mode approach.

293 citations

Journal ArticleDOI
TL;DR: Two types of observer approaches are presented to solve the state and fault estimation problem for linear continuous-time switched systems with simultaneous disturbances, sensor and actuator faults, and both developed observer approaches avoid the sliding surface switching problem of traditional sliding mode observers in application to switched systems.

234 citations

Journal ArticleDOI
TL;DR: The purpose of the addressed problem is to design a time-varying fault estimator such that, in the presence of channel fading and randomly occurring faults, the influence from the exogenous disturbances onto the estimation errors is attenuated at the given level quantified by a H∞-norm in the mean square sense.
Abstract: This technical note is concerned with the finite-horizon ${\cal H}_{\infty}$ fault estimation problem for a class of nonlinear stochastic time-varying systems with both randomly occurring faults and fading channels. The system model (dynamical plant) is subject to Lipschitz-like nonlinearities and the faults occur in a random way governed by a set of Bernoulli distributed white sequences. The system measurements are transmitted through fading channels described by a modified stochastic Rice fading model. The purpose of the addressed problem is to design a time-varying fault estimator such that, in the presence of channel fading and randomly occurring faults, the influence from the exogenous disturbances onto the estimation errors is attenuated at the given level quantified by a ${\cal H}_{\infty}$ -norm in the mean square sense. By utilizing the stochastic analysis techniques, sufficient conditions are established to ensure that the dynamic system under consideration satisfies the prespecified performance constraint on the fault estimation, and then a recursive linear matrix inequality approach is employed to design the desired fault estimator gains. Simulation results demonstrate the effectiveness of the developed fault estimation design scheme.

158 citations


Additional excerpts

  • ..., [4], [6], [9], [14], [17] and the references therein....

    [...]

Journal ArticleDOI
TL;DR: An observer-based fault reconstruction method for PEM fuel cells using an adaptive-gain second-order sliding mode (SOSM) observer for observing the system states, where the adaptive law estimates the uncertain parameters.
Abstract: This paper presents an observer-based fault reconstruction method for PEM fuel cells. This method extends the results of a class of nonlinear uncertain systems with Lipschitz nonlinearities. An adaptive-gain second-order sliding mode (SOSM) observer is developed for observing the system states, where the adaptive law estimates the uncertain parameters. The inherent equivalent output error injection feature of SOSM algorithm is then used to reconstruct the fault signal. The performance of the proposed observer is validated through a hardware-in-loop emulator. The experimental results illustrate the feasibility and effectiveness of the proposed approach for application to fuel cell air-feed systems.

152 citations


Cites background from "Brief paper: Nonlinear robust fault..."

  • ...To overcome this, Tan and Edwards [21] proposed an FDI scheme for a class of 1063-6536 © 2014 IEEE....

    [...]

  • ...On the basis of the work by Edwards et al. [19], Tan and Edwards [20] proposed a sensor fault reconstruction method for well-modeled linear systems through the linear matrix inequality (LMI) technique....

    [...]

  • ...Yan and Edwards [23] proposed a precise fault reconstruction scheme, using equivalent output error injection, for a class of nonlinear systems with uncertainty....

    [...]

  • ...Edwards and Tan [13] and Alwi and Edwards [14] proposed fault reconstruction methods which estimate the magnitude and shape of faults in addition to detection and isolation....

    [...]

  • ...This constraint was relaxed by Yan and Edwards [1], where the fault distribution vector and the structure matrix of the uncertainty are allowed to be functions of the system’s output and input....

    [...]

References
More filters
Book
17 Aug 1995
TL;DR: This paper reviewed the history of the relationship between robust control and optimal control and H-infinity theory and concluded that robust control has become thoroughly mainstream, and robust control methods permeate robust control theory.
Abstract: This paper will very briefly review the history of the relationship between modern optimal control and robust control. The latter is commonly viewed as having arisen in reaction to certain perceived inadequacies of the former. More recently, the distinction has effectively disappeared. Once-controversial notions of robust control have become thoroughly mainstream, and optimal control methods permeate robust control theory. This has been especially true in H-infinity theory, the primary focus of this paper.

6,945 citations

Book
01 Feb 1992
TL;DR: The theory and practical application of Lyapunov's Theorem, a method for the Study of Non-linear High-Gain Systems, are studied.
Abstract: I. Mathematical Tools.- 1 Scope of the Theory of Sliding Modes.- 1 Shaping the Problem.- 2 Formalization of Sliding Mode Description.- 3 Sliding Modes in Control Systems.- 2 Mathematical Description of Motions on Discontinuity Boundaries.- 1 Regularization Problem.- 2 Equivalent Control Method.- 3 Regularization of Systems Linear with Respect to Control.- 4 Physical Meaning of the Equivalent Control.- 5 Stochastic Regularization.- 3 The Uniqueness Problems.- 1 Examples of Discontinuous Systems with Ambiguous Sliding Equations.- 1.1 Systems with Scalar Control.- 1.2 Systems Nonlinear with Respect to Vector-Valued Control.- 1.3 Example of Ambiguity in a System Linear with Respect to Control ..- 2 Minimal Convex Sets.- 3 Ambiguity in Systems Linear with Respect to Control.- 4 Stability of Sliding Modes.- 1 Problem Statement, Definitions, Necessary Conditions for Stability ..- 2 An Analog of Lyapunov's Theorem to Determine the Sliding Mode Domain.- 3 Piecewise Smooth Lyapunov Functions.- 4 Quadratic Forms Method.- 5 Systems with a Vector-Valued Control Hierarchy.- 6 The Finiteness of Lyapunov Functions in Discontinuous Dynamic Systems.- 5 Singularly Perturbed Discontinuous Systems.- 1 Separation of Motions in Singularly Perturbed Systems.- 2 Problem Statement for Systems with Discontinuous control.- 3 Sliding Modes in Singularly Perturbed Discontinuous Control Systems.- II. Design.- 6 Decoupling in Systems with Discontinuous Controls.- 1 Problem Statement.- 2 Invariant Transformations.- 3 Design Procedure.- 4 Reduction of the Control System Equations to a Regular Form.- 4.1 Single-Input Systems.- 4.2 Multiple-Input Systems.- 7 Eigenvalue Allocation.- 1 Controllability of Stationary Linear Systems.- 2 Canonical Controllability Form.- 3 Eigenvalue Allocation in Linear Systems. Stabilizability.- 4 Design of Discontinuity Surfaces.- 5 Stability of Sliding Modes.- 6 Estimation of Convergence to Sliding Manifold.- 8 Systems with Scalar Control.- 1 Design of Locally Stable Sliding Modes.- 2 Conditions of Sliding Mode Stability "in the Large".- 3 Design Procedure: An Example.- 4 Systems in the Canonical Form.- 9 Dynamic Optimization.- 1 Problem Statement.- 2 Observability, Detectability.- 3 Optimal Control in Linear Systems with Quadratic Criterion.- 4 Optimal Sliding Modes.- 5 Parametric Optimization.- 6 Optimization in Time-Varying Systems.- 10 Control of Linear Plants in the Presence of Disturbances.- 1 Problem Statement.- 2 Sliding Mode Invariance Conditions.- 3 Combined Systems.- 4 Invariant Systems Without Disturbance Measurements.- 5 Eigenvalue Allocation in Invariant System with Non-measurable Disturbances.- 11 Systems with High Gains and Discontinuous Controls.- 1 Decoupled Motion Systems.- 2 Linear Time-Invariant Systems.- 3 Equivalent Control Method for the Study of Non-linear High-Gain Systems.- 4 Concluding Remarks.- 12 Control of Distributed-Parameter Plants.- 1 Systems with Mobile Control.- 2 Design Based on the Lyapunov Method.- 3 Modal Control.- 4 Design of Distributed Control of Multi-Variable Heat Processes.- 13 Control Under Uncertainty Conditions.- 1 Design of Adaptive Systems with Reference Model.- 2 Identification with Piecewise-Continuous Dynamic Models.- 3 Method of Self-Optimization.- 14 State Observation and Filtering.- 1 The Luenberger Observer.- 2 Observer with Discontinuous Parameters.- 3 Sliding Modes in Systems with Asymptotic Observers.- 4 Quasi-Optimal Adaptive Filtering.- 15 Sliding Modes in Problems of Mathematical Programming.- 1 Problem Statement.- 2 Motion Equations and Necessary Existence Conditions for Sliding Mode.- 3 Gradient Procedures for Piecewise Smooth Function.- 4 Conditions for Penalty Function Existence. Convergence of Gradient Procedure.- 5 Design of Piecewise Smooth Penalty Function.- 6 Linearly Independent Constraints.- III. Applications.- 16 Manipulator Control System.- 1 Model of Robot Arm.- 2 Problem Statement.- 3 Design of Control.- 4 Design of Control System for a Two-joint Manipulator.- 5 Manipulator Simulation.- 6 Path Control.- 7 Conclusions.- 17 Sliding Modes in Control of Electric Motors.- 1 Problem Statement.- 2 Control of d. c. Motor.- 3 Control of Induction Motor.- 4 Control of Synchronous Motor.- 18 Examples.- 1 Electric Drives for Metal-cutting Machine Tools.- 2 Vehicle Control.- 3 Process Control.- 4 Other Applications.- References.

5,422 citations


"Brief paper: Nonlinear robust fault..." refers background in this paper

  • ...where eq denotes the equivalent output error injection signal required to maintain the sliding motion (Edwards & Spurgeon, 1998; Utkin, 1992), and (·) is defined by (e1, z, ẑ, u) := A3e1 + G2(T −1z, u) − G2(T −1ẑ, u)....

    [...]

  • ...This shows that a reachability condition is satisfied: see Utkin (1992) for example....

    [...]

  • ...…(21) and (44): (e1, z, ẑ, u) + E2 (T −1z, u, t) + D2f (y, u, t) − eq = 0, (45) where eq denotes the equivalent output error injection signal required to maintain the sliding motion (Edwards & Spurgeon, 1998; Utkin, 1992), and (·) is defined by (e1, z, ẑ, u) := A3e1 + G2(T −1z, u) − G2(T −1ẑ, u)....

    [...]

  • ...Sliding mode techniques, however, have good robustness and are completely insensitive to so-called matched uncertainty (Edwards & Spurgeon, 1998; Utkin, 1992)....

    [...]

Journal Article

4,506 citations

Book
27 Sep 2011
TL;DR: Robust Model-Based Fault Diagnosis for Dynamic Systems targets both newcomers who want to get into this subject, and experts who are concerned with fundamental issues and are also looking for inspiration for future research.
Abstract: There is an increasing demand for dynamic systems to become safer and more reliable This requirement extends beyond the normally accepted safety-critical systems such as nuclear reactors and aircraft, where safety is of paramount importance, to systems such as autonomous vehicles and process control systems where the system availability is vital It is clear that fault diagnosis is becoming an important subject in modern control theory and practice Robust Model-Based Fault Diagnosis for Dynamic Systems presents the subject of model-based fault diagnosis in a unified framework It contains many important topics and methods; however, total coverage and completeness is not the primary concern The book focuses on fundamental issues such as basic definitions, residual generation methods and the importance of robustness in model-based fault diagnosis approaches In this book, fault diagnosis concepts and methods are illustrated by either simple academic examples or practical applications The first two chapters are of tutorial value and provide a starting point for newcomers to this field The rest of the book presents the state of the art in model-based fault diagnosis by discussing many important robust approaches and their applications This will certainly appeal to experts in this field Robust Model-Based Fault Diagnosis for Dynamic Systems targets both newcomers who want to get into this subject, and experts who are concerned with fundamental issues and are also looking for inspiration for future research The book is useful for both researchers in academia and professional engineers in industry because both theory and applications are discussed Although this is a research monograph, it will be an important text for postgraduate research students world-wide The largest market, however, will be academics, libraries and practicing engineers and scientists throughout the world

3,826 citations


"Brief paper: Nonlinear robust fault..." refers background or methods in this paper

  • ...In the last few decades, various modelbased approaches have been developed (Chen & Patton, 1999), and in particular observer-based techniques have obtained much attention....

    [...]

  • ...The comprehensive survey paper (Frank, 1987) provides an overview of observer-based approaches, and many results have been established (see e.g. Chen & Patton, 1999; Frank & Ding, 1997; Shields, 2005; Xu & Zhang, 2004 and the references therein)....

    [...]

  • ...All rights reserved. doi:10.1016/j.automatica.2007.02.008 a very effective method for FDI both in theory and practice (Chen & Patton, 1999)....

    [...]

Book
27 Aug 1998
TL;DR: This text provides the reader with a grounding in sliding mode control and is appropriate for the graduate with a basic knowledge of classical control theory and some knowledge of state-space methods.
Abstract: In the formation of any control problem there will be discrepancies between the actual plant and the mathematical model for controller design. Sliding mode control theory seeks to produce controllers to over some such mismatches. This text provides the reader with a grounding in sliding mode control and is appropriate for the graduate with a basic knowledge of classical control theory and some knowledge of state-space methods. From this basis, more advanced theoretical results are developed. Two industrial case studies, which present the results of sliding mode controller implementations, are used to illustrate the successful practical application theory.

3,355 citations


"Brief paper: Nonlinear robust fault..." refers background or methods in this paper

  • ...By the same reasoning as used in Edwards and Spurgeon (1998), and employing further changes of coordinates, the system matrix can be made to have the structure in (7) whilst preserving the structures of the input and output distribution matrices....

    [...]

  • ...1 of Edwards and Spurgeon (1998). From Edwards and Spurgeon (1998), it is easy to see that the nonnegative integer l in Lemma 1 above denotes the number of invariant zeros of the triple (A, [E D], C)....

    [...]

  • ...Sliding mode techniques, however, have good robustness and are completely insensitive to so-called matched uncertainty (Edwards & Spurgeon, 1998; Utkin, 1992)....

    [...]

  • ...From Edwards and Spurgeon (1998), it is easy to see that the nonnegative integer l in Lemma 1 above denotes the number of invariant zeros of the triple (A, [E D], C)....

    [...]

  • ...Therefore, the conclusion in Lemma 1 above cannot be directly obtained from Lemma 6.1 of Edwards and Spurgeon (1998)....

    [...]