一种基于LMI的鲁棒故障诊断滤波器设计

研究了一类含有扰动的线性系统鲁棒故障诊断滤波器设计问题. 文中引入一种能同时体现残差对扰动信号鲁棒性和对故障信号灵敏性的性能指标, 利用H_∞理论把求解滤波器的问题转化为H_∞优化设计问题. 应用线性矩阵不等式(LMI)技术, 对此性能指标进行优化, 给出并证明了该设计问题解的存在性条件和滤波器增益阵的求解方法, 最后, 通过仿真实例验证了方法的有效性.     

A robust deconvolution scheme for fault detection and isolation of uncertain linear systems: an LMI approach

Optimal H_∞ deconvolution filter theory is exploited for the design of robust fault detection and isolation (FDI) units for uncertain polytopic linear systems. Such a filter is synthesized under frequency domain conditions which ensure guaranteed levels of disturbance attenuation, residual decoupling and deconvolution performance in prescribed frequency ranges. By means of the Projection Lemma, a quasi-convex formulation of the problem is obtained via LMIs. A FDI logic based on adaptive thresholds is also proposed for reducing the generation of false alarms. The effectiveness of the design technique is illustrated via a numerical example.     

基于多目标约束的鲁棒故障检测滤波器设计

针对包含未知输入的线性时不变系统,研究了其鲁棒故障检测滤波器设计问题。由于故障信号往往分布在有限频域段内,设计的目标包括使特定有限频域段上的复合性能指标最小化以及满足区域极点配置的要求。一个基于LMI的方法被提出用于解决该设计问题。该方法的优点在于求解过程中可以获取给定有限频域段上的频域指标的真实值,并可求得满足目标的最优解。因此,设计的故障检测滤波器可以获得良好的故障检测性能。一个基于某国产歼击机的设计实例验证了该方法的有效性。     

An LMI approach to design robust fault detection filter for uncertain LTI systems

In this paper, the robust fault detection filter design problem for uncertain linear time-invariant (LTI) systems with both unknown inputs and modelling errors is studied. The basic idea of our study is to use an optimal residual generator (assuming no modelling errors) as the reference residual model of the robust fault detection filter design for uncertain LTI systems with modelling errors and, based on it, to formulate the robust fault detection filter design as an H_∞ model-matching problem. By using some recent results of H_∞ optimization, a solution of the optimization problem is then presented via a linear matrix inequality (LMI) formulation. The main results include the development of an optimal reference residual model, the formulation of robust fault detection filter design problem, the derivation of a sufficient condition for the existence of a robust fault detection filter and a construction of it based on the LMI solution parameters, the determination of adaptive threshold for fault detection. An illustrative design example is employed to demonstrate the effectiveness of the proposed approach.     

Observer-based fault detection and isolation filter design for linear time-invariant systems

In this paper we consider a model-based fault detection and isolation problem for linear time-invariant dynamic systems subject to faults and disturbances. We use a state observer scheme that cancels the system dynamics and defines a residual vector signal that is sensitive only to faults and disturbances. We then design a stable fault detection and isolation filter such that the ?_∞-norm of the transfer matrix function from disturbances to the residual is minimised (for fault detection) subject to the constraint that the transfer matrix function from faults to residual is equal to a pre-assigned diagonal transfer matrix (for isolation of possibly simultaneous occurring faults). Our solution is given in the form of linear matrix inequalities using state-space techniques, as well as a model matching problem using matrix factorisation techniques. A numerical example is given to illustrate the efficiency of the fault detection and isolation filter.     

Design and analysis of robust fault detection filter using LMI tools

In this paper, the robust fault detection filter design problem for linear time invariant (LTI) systems with unknown inputs and modeling uncertainties is studied. The basic idea of our study is to formulate the robust fault detection filter design as a H_∞ model-matching problem. A solution of the optimal problem is then presented via a linear matrix inequality (LMI) formulation. The main results include the formulation of robust fault detection filter design problems, the derivation of a sufficient condition for the existence of a robust fault detection filter and construction of a robust fault detection filter based on the iterative of LMI algorithm.     

An LMI approach to the evaluation of alarm thresholds

A new approach is presented for selecting alarm thresholds in a simple fault detection system. Bounds are computed on the magnitudes of the minimum detectable fault and the maximum non-detectable fault. The use of the 2-norm for this calculation results in a linear matrix inequality (LMI) problem. An example is presented and a filter design is proposed that enhances the ability to distinguish between a fault and a disturbance. © 1998 John Wiley & Sons, Ltd.     

Asynchronous fault detection filter design approach for discrete‐time switched linear systems

This paper is concerned with the problem of the fault detection filter design for discrete‐time switched linear systems with average dwell‐time. The designed fault detection filters are also switched systems, which are assumed to be asynchronously switched with the original switched systems. Improved results on the weighted l₂ performance and the H _? performance are first given, and the multiple Lyaounov‐like functions during matched period and unmatched period for the running time of one subsystem are used. By the aid of multiple Lyapunov‐like functions combined with Projection Lemma, the FD filters are designed such that the augmented systems under asynchronous switching are exponentially stable, and the residual signal generated by the filters achieves the weighted l₂‐gain for disturbances and guarantees the H _? performance for faults. Sufficient conditions are formulated by linear matrix inequalities, and the filter gains are characterized in terms of the solution of a convex optimization problem. Finally, examples are provided to demonstrate the effectiveness of the proposed design method. Copyright © 2012 John Wiley & Sons, Ltd.     

Active fault detection and isolation of discrete-time linear time-varying systems: a set-membership approach

Active fault detection and isolation (AFDI) is used for detection and isolation of faults that are hidden in the normal operation because of a low excitation signal or due to the regulatory actions of the controller. In this paper, a new AFDI method based on set-membership approaches is proposed. In set-membership approaches, instead of a point-wise estimation of the states, a set-valued estimation of them is computed. If this set becomes empty the given model of the system is not consistent with the measurements. Therefore, the model is falsified. When more than one model of the system remains un-falsified, the AFDI method is used to generate an auxiliary signal that is injected into the system for detection and isolation of faults that remain otherwise hidden or non-isolated using passive FDI (PFDI) methods. Having the set-valued estimation of the states for each model, the proposed AFDI method finds an optimal input signal that guarantees FDI in a finite time horizon. The input signal is updated at each iteration in a decreasing receding horizon manner based on the set-valued estimation of the current states and un-falsified models at the current sample time. The problem is solved by a number of linear and quadratic programming problems, which result in a computationally efficient algorithm. The method is tested on a numerical example as well as on the pitch actuator of a benchmark wind turbine.     

A single dynamic observer-based module for design of simultaneous fault detection,isolation and tracking control scheme

The problem of simultaneous fault detection, isolation and tracking (SFDIT) control design for linear systems subject to both bounded energy and bounded peak disturbances is considered in this work. A dynamic observer is proposed and implemented by using the H_∞/H_?/L₁ formulation of the SFDIT problem. A single dynamic observer module is designed that generates the residuals as well as the control signals. The objective of the SFDIT module is to ensure that simultaneously the effects of disturbances and control signals on the residual signals are minimised (in order to accomplish the fault detection goal) subject to the constraint that the transfer matrix from the faults to the residuals is equal to a pre-assigned diagonal transfer matrix (in order to accomplish the fault isolation goal), while the effects of disturbances, reference inputs and faults on the specified control outputs are minimised (in order to accomplish the fault-tolerant and tracking control goals). A set of linear matrix inequality (LMI) feasibility conditions are derived to ensure solvability of the problem. In order to illustrate and demonstrate the effectiveness of our proposed design methodology, the developed and proposed schemes are applied to an autonomous unmanned underwater vehicle (AUV).     

An LMI approach to robust fault estimation for a class of nonlinear systems

The paper presents a robust fault estimation approach for a class of nonlinear discrete‐time systems. In particular, two sources of uncertainty are present in the considered class of systems, that is, an unknown input and an exogenous external disturbance. Thus, apart from simultaneous state and fault estimation, the objective is to decouple the effect of an unknown input while minimizing the influence of the exogenous external disturbance within the framework. The resulting design procedure guarantees that a prescribed disturbance attenuation level is achieved with respect to the state and fault estimation error while assuring the convergence of the observer. The core advantage of the proposed approach is its simplicity by reducing the fault estimation problem to matrix inequalities formulation. In addition, the design conditions ensure the convergence of the observer with guaranteed performance. The effectiveness of the proposed approach is demonstrated by its application to a twin rotor multiple‐input multiple‐output system. Copyright © 2015 John Wiley & Sons, Ltd.     

新的基于LMI的鲁棒故障检测滤波器设计方法*

提出一种新的基于LMI的滤波器设计方法,能够解决在线性时不变系统中进行故障检测时所遇到的多目标优化问题。通常在故障检测中,H∞范数用于描述残差对于外界干扰的鲁棒性,而H指标用于描述残差对于故障的灵敏度。通过引入残差的误差值,将多个指标（H∞和H指标）统一转换成H∞范数,从而将故障检测滤波器的设计问题转换成对H∞范数优化问题;然后用一种新颖的基于LMI的方法来求解;最后,将本算法应用于某导弹发生故障的纵向平面模型,仿真结果表明了该算法能有效、及时地检测出故障。     

A risk adjusted approach to robust simultaneous fault detection and isolation

This paper addresses the problem of detecting and isolating faults in noisy MIMO uncertain-systems, subject to structured dynamic uncertainty. Its main result shows that this problem can be efficiently solved using a combination of sampling and LMI optimization tools. These results are illustrated with two examples and benchmarked against existing methods.     

Robust fault detection filter design for uncertain LTI systems based on new bounded real lemma

This paper concerns the problem of robust fault detection filter design for uncertain linear time-invariant (LTI) systems with both model uncertainty and disturbances. Firstly, the fault detection filter design is formulated to H _∞ model-matching problem. Secondly, based on a new bounded real lemma, a sufficient condition for the existence of the robust fault detection filter is constructed in term of linear matrix inequalities (LMIs). Owing on the introduction of the tuning parameter and slack variables in obtained LMI condition, the proposed design method can provide higher fault detection sensitivity performance than the existing one. Finally, an illustrative example is employed to demonstrate the effectiveness of the proposed approach. Recommended by Editorial Board member Bin Jiang under the direction of Editor Jae Weon Choi. This work was supported by Postdoctoral Fundation of Jiangsu Province under grant 0901026c and Key Laboratory of Education Ministry for Image Processing and Intelligent Control under grant 200805. Tao Li received the Ph.D. degree in the Research Institute of Automation Southeast University, China. Now He is a postdoctoral researcher with the same university. His current research interests include time-delay systems, neural networks, robust control, fault detection and diagnosis. Lingyao Wu received the Ph.D. degree in the Research Institute of Automation Southeast University, China. Now He is an Assistant Professor in the Research Institute of Automation Southeast University. His current research interests include time-delay systems, neural networks, robust control, fault detection and diagnosis. Xinjiang Wei was born in Dongying, China, in 1977. He received the B.S. degrees from Yantai Normal University, China in 1999, M.S. degrees from Bohai University in 2002, and the Ph.D. degree in Department of Information from Northeastern University in 2005. From 2006 to Present, he was with Ludong University as an Associate Professor. From 2006 to 2009, he was a Postdoctoral Fellow at Southeast University. His research interests include robust control, nonlinear control, and fuzzy control.     

不确定飞行控制系统中断故障检测与分离

研究不确定飞行控制系统执行器中断故障检测与分离问题,同时设计了状态反馈控制器和检测器,在保证闭环控制系统稳定的前提下,通过设计的检测器对系统状态进行重组以产生残差进而检测执行器的中断故障。此外,通过设计一组分离器,可以确定出执行器发生故障的位置。最后,通过研究一个飞行控制系统模型验证了所提出方法的有效性。     

Fault detection and isolation for discrete-time switched linear systems based on average dwell-time method

This article is concerned with the problem of fault detection and isolation (FDI) for discrete-time switched linear systems based on the average dwell-time method. The proposed FDI framework consists of a bank of FDI filters, which are divided into N groups for N subsystems. The FDI filters belonging to one group correspond to the faults for a subsystem, and generate a residual signal to guarantee the fault sensitivity performance for the subsystem, the fault attenuation performance for other subsystems and the disturbance attenuation performance for all subsystems. Different form employing the weighting matrices to restrict the frequency ranges of faults for each subsystem, the finite-frequency H _? performance for switched systems is first defined. Sufficient conditions are established by linear matrix inequalities (LMIs), and the filter gains are characterised in terms of the solution of a convex optimisation problem. Two examples are used to demonstrate the effectiveness of the proposed design method.     

Subspace aided data-driven design of robust fault detection and isolation systems

This paper deals with subspace method aided data-driven design of robust fault detection and isolation systems. The basic idea is to identify a primary form of residual generators directly from test data and then make use of performance indices to make uniform the design of different type robust residuals. Four algorithms are proposed to design fault detection, isolation and identification residual generators. Each of them can achieve robustness to unknown inputs and sensitivity to sensor or actuator faults. Their existence conditions and multi-fault identification problem are briefly analyzed as well and the application of the method proposed is illustrated by a simulation study on the vehicle lateral dynamic system.     

A new iterative approach for multi-objective fault detection observer design and its application to a hypersonic vehicle

This paper addresses the multi-objective fault detection observer design problems for a hypersonic vehicle. Owing to the fact that parameters’ variations, modelling errors and disturbances are inevitable in practical situations, system uncertainty is considered in this study. By fully utilising the orthogonal space information of output matrix, some new understandings are proposed for the construction of Lyapunov matrix. Sufficient conditions for the existence of observers to guarantee the fault sensitivity and disturbance robustness in infinite frequency domain are presented. In order to further relax the conservativeness, slack matrices are introduced to fully decouple the observer gain with the Lyapunov matrices in finite frequency range. Iterative linear matrix inequality algorithms are proposed to obtain the solutions. The simulation examples which contain a Monte Carlo campaign illustrate that the new methods can effectively reduce the design conservativeness compared with the existing methods.     

基于观测器的非线性不确定系统鲁棒故障检测新方法

针对非线性不确定系统的鲁棒故障检测问题,提出了一种采用统计理论的新方法.通过设计全阶故障观测器产生残差信号,将鲁棒故障检测观测器设计问题转化为H∞优化问题;利用H∞范数描述故障检测的鲁棒性,保证系统的抗干扰能力,同时引入H_范数,确保对故障信号的灵敏度;应用线性矩阵不等式技术给出了该设计问题解存在的条件和求解方法.将统计理论用于故障检测阈值的确定,充分考虑了残差信号的随机特性,使故障决策更加准确和可靠.最后通过仿真实例验证了本文方法的有效性.     

Set-theoretic methods in robust detection and isolation of sensor faults

This paper proposes a sensorfault detection and isolation (FDI) approach based on interval observers and invariant sets. In fault detection (FD), both interval observer-based and invariant set-based mechanisms are used to provide real-time fault alarms. In fault isolation (FI), the proposed approach also uses these two different mechanisms. The former, based on interval observers, aims to isolate faults during the transient-state operation induced by faults. If the former does not succeed, the latter, based on both interval observers and invariant sets, is started to guarantee FI after the system enters into steady state. Besides, a collection of invariant set-based FDI conditions are established by using all available system-operating information provided by all interval observers. In order to reduce computational complexity, a method to remove all available but redundant/unnecessary system-operating information is incorporated into this approach. If the considered faults satisfy the proposed FDI conditions, it can be guaranteed that they are detectable and isolable after their occurrences. This paper concludes with a case study based on a subsystem of a wind turbine benchmark, which can illustrate the effectiveness of this FDI technique.