Fault isolation filter design for linear time-invariant systems

This paper is concerned with the problem of detecting and isolating multiple faults by a full-order observer of the plant state. We first obtain the fault isolability condition from the dual concept, namely static-state feedback decoupling. A new full-state observer design method is then developed to isolate simultaneous multiple faults. The method can isolate m simultaneous faults with m output measurements (such that the isolability condition is satisfied) under zero initial error of state estimation. Asymptotic fault isolation results can also be obtained using the same observer design if the number of invariant eigenvalues is (n-m), and if they are stable, where n represents the system order, m is the number of faults in the system. In both cases m can be up to the system order n     

Fault detection and isolation for linear parameter-varying systems with time-delays: a geometric approach

Fault detection and isolation(FDI) problems for linear parameter-varying(LPV) systems with state time-delays are studied in this paper. By defining the concept of unobservability subspace and designing its calculation algorithm, the geometric approach is introduced to the time-delay LPV systems. Utilizing Wirtinger-based integral inequality, we obtain a sufficient condition to solve the so-called H∞-based residual generation problem for the LPV systems. In this paper, we consider two cases: the ...     

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.     

Fault detection and isolation in nonlinear systems

This paper deals with fault detection and identification in dynamic systems when the system dynamics can be modeled by smooth nonlinear differential equations including affine, bilinear or linear parameter varying (LPV) systems. Two basic approaches will be considered, these apply differential algebraic and differential geometric tools.In the differential algebraic approach the state elimination methods will be used to derive nonlinear parity relations. In the specific case when a reconstruction of the fault signal is needed the dynamic inversion based approach will be investigated. This approach will also be studied from geometric point of view. The geometric approach, as proposed by Isidori and De Persis, is suitable to extend the detection filter and unknown input observer design approaches (well elaborated for LTI systems) to affine nonlinear systems.Beyond the development of the theory of fault detection and identification it is equally important to offer computable methods and to analyze the robustness properties against uncertainties. Both the observer based and the inversion based approaches will be elaborated for LPV systems that may offer computational tools inherited from linear systems and also allow to design for robustness utilizing results from robust filtering and disturbance attenuation.     

Actuator fault detection and isolation in linear systems

A scheme for the detection and isolation of actuator faults in linear systems is proposed. A bank of unknown input observers is constructed to generate residual signals which will deviate in characteristic ways in the presence of actuator faults. Residual signals are unaffected by the unknown inputs acting on the system and this decreases the false alarm and miss probabilities. The results are illustrated through a simulation study of actuator fault detection and isolation in a pilot plant doubleeffect evaporator.     

Fault detection for linear discrete-time systems with output quantisation

This paper is concerned with the problem of fault detection for a class of linear discrete-time quantised feedback systems, and system outputs are, respectively, quantised by a uniform quantiser and a non-uniform quantiser. A novel unified method is proposed to deal with the two different types of quantisation errors, i.e. the quantisation errors are considered as unknown inputs of the residual generator. Then, an optimal residual generator is constructed to guarantee a suitable trade-off between the sensitivity to faults and the robustness against disturbances as well as quantisation errors. In order to detect the occurrence of faults, the generated residual signal is evaluated, and then two different thresholds based on the stochastic properties of quantisation errors are designed for these two quantisers. In addition, the false alarm rate is introduced to evaluate the fault detection performance. Finally, two examples are given to illustrate the feasibility of the proposed approach.     

Fault detection of linear discrete-time periodic systems

In this note, an approach to the design of optimal fault detection systems for linear discrete-time periodic systems is proposed, which leads to an optimized compromise between robustness to unknown disturbances and sensitivity to faults. The needed computation mainly consists in solving a difference periodic Riccati system. The proposed approach is finally illustrated by a numerical example.     

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.     

Fault detection for linear distributed-parameter systems using finite-dimensional functional observers

In this article, finite-dimensional residual generators are directly designed for Riesz-spectral systems with bounded input and output operators to detect faults. This is achieved by using finite-dimensional observers, that can estimate linear functionals of the state without spillover. These observers allow for a decoupling of the unknown disturbances from the estimation error dynamics under mild assumptions. Then, a finite-dimensional residual generator is obtained by approximately decoupling the state from the residual, that is generated by the observer states and the outputs. It is shown that the resulting approximation error can be made small by increasing the observer order. Then, fault detection with the finite-dimensional residual generator can be assured by introducing a time-varying threshold. A faulty Euler–Bernoulli beam with structural damping illustrates the proposed finite-dimensional fault detection approach.     

Fault detection and isolation for nonlinear non-affine uncertain systems via sliding-mode techniques

This paper considers the fault detection and isolation problem for nonlinear uncertain non-affine systems. The proposed approach is based on an output-feedback stabilisation strategy, which exploits a Luenberger-like nonlinear observer. As a main result, a residual-based fault detection and isolation approach is developed, which relies on the measurable output, some of its derivatives, which are provided exactly by a uniform high-order sliding-mode differentiator, and the observer’s state. The proposed methodology is able to detect some possible components and actuators faults, and to isolate, under some mild conditions, the actuator faults from those ones in components. Simulation results illustrate the feasibility of the proposed approach.     

一类随机不确定线性系统鲁棒故障检测问题研究

将一类受乘性随机噪声影响线性系统的基于观测器的残差产生器设计归结为随机意义下的H∞-滤波问题,应用线性矩阵不等式技术．推导问题可解的充分条件,给出观测器增益矩阵的求解方法．另外,根据给定的残差评价函数和闻值,判断故障的发生并估计故障的误报率;或给定残差评价函数和容许故障误报率,通过适当的选取阈值把实际的故障误报率限定在容许的范围内．仿真算例验证了所给算法的有效性．     

Fault detection for discrete piecewise linear systems with infinite distributed time-delays

In this paper, the fault detection problem is investigated for a class of discrete-time piecewise linear systems with external disturbances and infinite distributed time-delays. As a modelling framework, piecewise linear system often arise when piecewise linear components are encountered, such as dead-zone, saturation, relays and hysteresis. The time-delays are assumed to be infinitely distributed in the discrete-time domain. The aim of this paper is to detect the possible faults and to estimate the system state. For this purpose, firstly, stability analysis is given based on a piecewise smooth Lyapunov function. Afterward, an appropriate approach of fault detection and filter design problem is provided to achieve a satisfactory balance between the disturbances attenuation level γ and the sensitivity to the fault for piecewise linear systems. As a consequence, a sufficient condition is obtained in terms of the linear matrix inequalities such that, for all admissible infinite distributed time-delays and external disturbances, the system is guaranteed to be asymptotically stable and the residual is guaranteed to satisfy H_∞ filtering performance and fault detection performance. At last, a simulation example is provided to demonstrate the applicability and effectiveness of the fault detection filtering scheme proposed in this paper.     

Fault detection for a class of linear systems with integral measurements

This paper discusses the parity space-based fault detection (FD) method for a class of linear discrete-time systems with integral measurements.The integral meas...     

Balancing transformations for unstable nonminimal linear systems

It is shown that an unstable nonminimal continuous (discrete) realization (A, B, C) can be transformed via a similarity transformation into a balanced one if and only if the product of the controllability, observability Gramians is similar to a real diagonal matrix Λ. If, in addition, the eigenvalues of A , say λ, satisfy the relation λ_i+λ _j≠0(λ_iλ_j≠1) then the matrix Λ will always be positive semidefinite, and a balanced realization with its minimal part in the internally balanced form can always be obtained     

Statistical detection and isolation of additive faults in linear time-varying systems

This paper describes a statistical approach to fault detection and isolation for linear time-varying (LTV) systems subject to additive faults with time-varying profiles. The proposed approach combines a generalized likelihood ratio (GLR) test with a recursive filter that cancels out the dynamics of the monitored fault effects. To our knowledge, the proposed recursive filter is new for the considered faults. The resulting algorithm handles fault isolation with weaker assumptions than usual, in particular regarding the requirements on the number of sensors and on the stability of the monitored system. Numerical results for leakage detection in a gas transportation network illustrate the effectiveness of the proposed method.     

Fault detection and isolation for networked control systems with finite frequency specifications

The fault detection and isolation (FDI) problem with finite frequency specifications is addressed in this paper under the framework of geometric approach for networked control systems subject to communication constraints and packet losses. The considered communication constraint is that only one of the transmission nodes is allowed to gain access to the shared channel. Also, those transmission nodes are scheduled to transmit data according to a specified stochastic protocol. Then by virtues of the common unobservable subspace and the finite frequency stochastic H _? index, a novel FDI scheme is developed in which a set of FDI filters that perform the FDI task with only partially available measurements are designed such that each residual is only sensitive to one fault in certain frequency domain and decoupled from the others. Further, less conservative conditions including some previous existing results have been presented to construct the FDI filters. Finally, an example is given to illustrate the effectiveness of the proposed method.Copyright © 2012 John Wiley & Sons, Ltd.     

Path-following for linear systems with unstable zero dynamics

A constructive solution to the path-following problem for MIMO linear systems with unstable zero dynamics is developed. While the original control variable steers the system output along the path, the path parameter θ is used as an additional control to stabilize zero dynamics with a feedback law which is nonlinear due to the path constraint. A sufficient condition for solvability of the path-following problem is given in terms of the geometric properties of the path. When this condition is satisfied, an arbitrary small L₂ norm of path-following error can be achieved, thus avoiding performance limitations of the standard reference tracking problem imposed by unstable zero dynamics.     

Parametric identification of unstable linear systems

Identification of an unstable subsystem operating in a stable closed-loop in the presence of noise, is considered. The Equation Error- -Input Covariance (EEIC) method is shown to be applicable. The method can be implemented on-line except for the case where the identified system has poles or zeros on the imaginary axis. A simulated example demonstrates the results.