Zonotopic fault detection observer design for Takagi–Sugeno fuzzy systems

This paper considers zonotopic fault detection observer design in the finite-frequency domain for discrete-time Takagi–Sugeno fuzzy systems with unknown but bounded disturbances and measurement noise. We present a novel fault detection observer structure, which is more general than the commonly used Luenberger form. To make the generated residual sensitive to faults and robust against disturbances, we develop a finite-frequency fault detection observer based on generalised Kalman–Yakubovich–Popov lemma and P-radius criterion. The design conditions are expressed in terms of linear matrix inequalities. The major merit of the proposed method is that residual evaluation can be easily implemented via zonotopic approach. Numerical examples are conducted to demonstrate the proposed method.     

Interval observer versus set‐membership approaches for fault detection in uncertain systems using zonotopes

This paper presents both analysis and comparison of the interval observer–based and set‐membership approaches for the state estimation and fault detection (FD) in uncertain linear systems. The considered approaches assume that both state disturbance and measurement noise are modeled in a deterministic context following the unknown but bounded approach. The propagation of uncertainty in the state estimation is bounded through a zonotopic set representation. Both approaches have been mathematically related and compared when used for state estimation and FD. A case study based on a two‐tanks system is employed for showing the relationship between both approaches while comparing their performance.     

Active fault detection based on set‐membership approach for uncertain discrete‐time systems

Active fault detection facilitates determination of the fault characteristics by injecting proper auxiliary input signals into the system. This article proposes an observer‐based on‐line active fault detection method for discrete‐time systems with bounded uncertainties. First, the output including disturbances, measurement noise and interval uncertainties at each sample time is enclosed in a zonotope. In order to reduce the conservativeness in the fault detection process, a zonotopic observer is designed to estimate the system states allowing to generate the output zonotopes. Then, a proper auxiliary input signal is designed to separate the output zonotopes of the faulty model from the healthy model that is injected into the system to facilitate the detection of small fault . Since the auxiliary input signal generation leads to a nonconvex optimization problem, it is transformed into a mixed integer quadratic programming problem. Finally, a case study based on a DC motor is used to show the effectiveness of the proposed method.     

Robust Fault Detection and Isolation Based on Finite-frequency H?/H∞ Unknown Input Observers and Zonotopic Threshold Analysis

This work proposes a robust fault detection and isolation scheme for discrete-time systems subject to actuator faults, in which a bank of H₋/H_∞ fault detection unknown input observers (UIOs) and a zonotopic threshold analysis strategy are considered. In observer design, finite-frequency H₋ index based on the generalized Kalman-Yakubovich-Popov lemma and H_∞ technique are utilized to evaluate worst-case fault sensitivity and disturbance attenuation performance, respectively. The proposed H₋/H_∞ fault detection observers are designed to be insensitive to the corresponding actuator fault only, but sensitive to others. Then, to overcome the weakness of predefining threshold for FDI decision-making, this work proposes a zonotopic threshold analysis method to evaluate the generated residuals. The FDI decision-making relies on the evaluation with a dynamical zonotopic threshold. Finally, numerical simulations are provided to show the feasibility of the proposed scheme.     

基于状态集员估计的主动故障检测

对于现代复杂控制系统, 微小故障往往很难发现. 在系统过程干扰和测量噪声未知但有界的前提下, 提出了一种新的基于状态集员估计的主动故障检测方法. 首先设计全对称多胞形卡尔曼滤波器对系统状态进行估计, 并利用全对称多胞形对受未知干扰影响的状态集合进行描述, 然后设计辅助输入信号使得加入辅助输入信号后正常模型的状态集合与故障模型的状态集合交集为空, 从而实现主动故障检测. 为了使得所设计的辅助输入信号对原系统影响最小, 需要求得最小的辅助输入信号, 本文将最优化问题转化为混合整数二次规划问题进行求解. 最后, 与基于输出集合的辅助输入信号设计方法对比, 仿真验证本文所提出的基于状态集合的主动故障检测方法由于未受下一时刻测量噪声的影响, 所求得的辅助输入信号更小, 保守性更低.     

Robust Unknown Input Observer Design for Linear Uncertain Time Delay Systems with Application to Fault Detection

In this paper, a novel approach is proposed to design a robust fault detection observer for uncertain linear time delay systems. The system is composed of both norm‐bounded uncertainties and exogenous signals (noise, disturbance, and fault) which are considered to be unknown. The main contribution of this paper is to present unknown input observer (UIO)‐based fault detection system which shows the maximum sensitivity to fault signals and the minimum sensitivity to other signals. Since the system contains uncertainty terms, an H_∞ model‐matching approach is used in design procedure. The reference residual signal generator system is designed so that the fault signal has maximum sensitivity while the exogenous signals have minimum sensitivity on the residual signal. Then, the fault detection system is designed by minimizing the estimation error between the reference residual signal and the UIO residual signal in the sense of H_∞ norm. A sufficient condition for the existence of such a filter is exploited in terms of certain linear matrix inequalities (LMIs). Application of the proposed method in a numerical example and an engineering process are simulated to demonstrate the effectiveness of the proposed algorithm. Simulation results show the validity of the proposed approach to detect the occurrence of faults in the presence of modeling errors, disturbances, and noise.     

线性离散系统的有限频域集员故障检测观测器设计

本文针对线性离散系统, 提出了一种新的有限频域执行器故障检测方法.利用中心对称多胞体近似未知扰动边界, 本文提出的中心对称多胞体集员故障检测观测器可实时估计残差范围.通过观测零点是否脱离残差生成的中心对称多胞体的范围, 判断故障是否发生.为了提高对干扰的鲁棒性和对故障的敏感性, 基于P半径准则和广义Kalman-Yakubovich-Popov引理, 本文给出了故障检测观测器的设计条件, 并将其转化为便于求解的矩阵不等式形式.最后, 车辆横向动态系统的仿真结果验证了所提方法的有效性.     

Fault detection for networked control systems subject to quantisation and packet dropout

This article addresses the stochastic fault detection (SFD) problem in finite-frequency domain for a class of networked control systems (NCSs) with respect to signal quantisation and data packet dropout. Considering a logarithmic quantiser and Markovian packet dropout, the NCS is modelled as a Markov jump linear system (MJLS) with quantisation error. Further, a new definition of finite-frequency stochastic H _? index is given, which gives a measurement of sensitivity. Subsequently, sufficient conditions are derived to guarantee that the MJLS can achieve such a performance. By virtue of the obtained conditions, the fault detection filters (FDFs) are designed in finite-frequency domain, which are valid in characterising the disturbance attenuation performance and finite-frequency fault sensitivity performance. Finally, a simulation example is given to illustrate the method and its effectiveness.     

A design of disturbance observer in standard H∞ control framework

The disturbance observer (DOB)‐based controller is widely used to estimate and suppress disturbance in motion control system. Because the low‐pass filter (Q‐filter) in DOB decides the performances of disturbance suppression, noise rejection, and robust stability against system uncertainties, design of Q‐filter is the principal task in DOB construction. This paper presents a systematic scheme for Q‐filter design based on H_∞ norm optimization. Cost function for optimization is proposed by considering performance and relative order condition of the Q‐filter. The norm minimization problem is then transformed to a standard H_∞ control problem. Furthermore, the relationship between performance and frequency weighting functions is investigated based on which selection of weighting functions is presented. Simulation results validate the global optimality and systematicness of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.     

Elegant antidisturbance fault‐tolerant control for stochastic systems with multiple heterogeneous disturbances

In this article, the elegant antidisturbance fault‐tolerant control (EADFTC) problem is studied for a class of stochastic systems in the simultaneous presence of multiple heterogeneous disturbances and time‐varying faults. The multiple heterogeneous disturbances include white noise, norm bounded uncertain disturbances and uncertain modeled disturbances with multiple nonlinearities and unknown amplitudes, frequencies, and phases. The time‐varying fault signals are caused by lose efficacy of actuator. To online estimate uncertain modeled disturbances and time‐varying faults, a novel composite observer structure consisting of the adaptive nonlinear disturbance observer and the fault diagnosis observer is constructed. The novel EADFTC strategy is proposed by integrating composite observer structure with adaptive disturbance observer‐based control theory and H_∞ technology. It is proved that all the signals of closed‐loop system are asymptotically bounded in mean square under the circumstances of multiple heterogeneous disturbances and time‐varying faults occur simultaneously. Finally, the effectiveness and availability of proposed strategy are demonstrated by means of the numerical simulation and a doubly fed induction generators system simulation, respectively.     

Composite DOBC with fuzzy fault‐tolerant control for stochastic systems with unknown nonlinear dynamics

A class of stochastic nonlinear systems with fault and multisource disturbances is concerned. The fault is a general bounded actuator fault, and the multiple disturbances include partial‐known information disturbance and white noise. A stochastic adaptive disturbance observer is constructed to estimate the partial‐known information disturbance, based on which the partial‐known information disturbance can be compensated in the feed‐foreword channel immediately. Also, the multiplicative white noise can be attenuated by the designed feedback controller. To make the composite system is satisfactory, a composite disturbance based‐observer control with fuzzy fault‐tolerant control is proposed. The pole placement and LMI method is applied to attenuate and reject the disturbance. Furthermore, the fault can be compensated simultaneously. To verify the feasibility and availability of the designed control scheme, a simulation example is shown finally.     

Finite-frequency fault detection for two-dimensional Fornasini–Marchesini dynamical systems

This paper is concerned with the fault detection problem for two-dimensional (2-D) discrete-time systems described by the Fornasini–Marchesini local state-space model. The goal of the paper is to design a fault detection filter to detect the occurrence of faults in finite-frequency domain. To this end, a finite-frequency H_? index is used to describe fault sensitivity performance, and a finite-frequency H_∞ index is used to describe disturbance attenuation performance. In light of the generalised Kalman–Yakubovich–Popov lemma for 2-D systems and matrix inequality techniques, convex conditions are derived for this fault detection problem. Based on these conditions, a numerical algorithm is put forward to construct a desired fault detection filter. Finally, a numerical example and an industrial example are given to illustrate the effectiveness of the proposed algorithm.     

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 Method Based on H−/H∞ Unknown Input Observer Design in Finite Frequency Domain

This paper proposes an actuator fault detection and isolation strategy based on a bank of unknown input observers with finite frequency specifications. In order to deal with actuator fault diagnosis problem, a bank of H _?/H _∞ unknown input observers are designed to generate residuals, which are insensitive to the corresponding faults but sensitive to the other actuators faults, and meanwhile robust against the unknown disturbances. In this paper, the actuator faults and unknown disturbances are considered to belong to finite frequency domains, and two finite frequency performance indices are used to measure the fault sensitivity and the disturbance robustness of the residuals. Furthermore, some parameters for extra design of freedom are introduced in the H _?/H _∞ unknown input observers design. Based on the generalised Kalman‐Yakubovich‐Popov (GKYP) lemma, the design conditions of the H _?/H _∞ unknown input observer are derived and formulated as linear matrix inequalities (LMIs). Finally, a VTOL aircraft model is used to demonstrate the performance of the proposed fault diagnosis scheme.     

Fault detection for switched positive systems under successive packet dropouts with application to the Leslie matrix model

In this paper, the problem of fault detection filter design is dealt with for a class of switched positive systems with packet dropouts on the channel between the sensors and the filters. The phenomena of packet dropouts are governed by a Bernoulli process, and a stochastic switched positive system is established based on the augmented states of the plants and filters. Two criteria are developed to evaluate the performance of the fault detection for the system under investigation. Sufficient conditions are established on the existence of the desired filters for the mean‐square stability with an L₁ disturbance attenuation level, and an index for the L_? fault sensitivity is also derived through constructing a switched Lyapunov function in term of linear programming. Two illustrative examples, one of which is concerned with the Leslie matrix model, are provided to show the effectiveness and applicability of the proposed results. Copyright © 2015 John Wiley & Sons, Ltd.     

Using set invariance to design robust interval observers for discrete‐time linear systems

Based on interval and invariant set computation, an interval version of the Luenberger state observer for uncertain discrete‐time linear systems is proposed in this work. This new interval observer provides a punctual estimation of the state vector and guaranteed bounds on the estimation error. An off‐line and an on‐line approach to characterize, in a guaranteed way, the estimation error are introduced. Compared with the existing approaches, the proposed interval observer design method is not restrictive in terms of required assumptions, complexity, and on‐line computation time. Furthermore, the convergence issue of the estimation error is well established and to reduce the conservatism of the estimated state enclosure induced by the bounded additive state disturbance and noise measurement, an H_∞ method to compute the optimal observer gain is proposed. The performance of the proposed state estimation approach are highlighted on different illustrative examples.     

Robust adaptive fault‐tolerant control of uncertain linear systems via sliding‐mode output feedback

This paper is concerned with the robust adaptive fault‐tolerant compensation control problem via sliding‐mode output feedback for uncertain linear systems with actuator faults and exogenous disturbances. Mismatched disturbance attenuation is performed via H_∞ norm minimization. By incorporating the matrix full‐rank factorization technique with sliding surface design successfully, the total failure of certain actuators can be coped with, under the assumption that redundancy is available in the system. Without the need for a fault detection and isolation mechanism, an adaptive sliding mode controller, where the gain of the nonlinear unit vector term is updated automatically to compensate the effects of actuator faults, is designed to guarantee the asymptotic stability and adaptive H_∞ performance of closed‐loop systems. The effectiveness of the proposed design method is illustrated via a B747‐100/200 aircraft model. Copyright © 2014 John Wiley & Sons, Ltd.     

H−/L∞ fault detection observer for linear parameter‐varying systems with parametric uncertainty

This paper considers H_?/L_∞ fault detection for discrete‐time linear parameter‐varying (LPV) systems with parametric uncertainty. In H_?/L_∞ fault detection scheme, residual generation and threshold computation are simultaneously designed. With consideration of H_?/L_∞ performance indices, the generated residual is sensitive to faults while robust against unknown disturbances. Furthermore, the L_∞ performance provides a time‐varying threshold for residual evaluation. This paper proposes a novel H_?/L_∞ fault detection observer design method to handle actuator fault detection for LPV systems with parametric uncertainty. Sufficient conditions of the fault detection observer design in the finite‐frequency domain are derived as linear matrix inequalities. Numerical simulations are used to illustrate the effectiveness and superiority of the proposed fault detection observer design approach.     

H∞ boundary control for a class of nonlinear stochastic parabolic distributed parameter systems

This paper addresses the problem of H_∞ boundary control for a class of nonlinear stochastic distributed parameter systems expressed by parabolic stochastic partial differential equations (SPDEs) of Itô type. A simple but effective H_∞ boundary static output feedback (SOF) control scheme with collocated boundary measurement is introduced to ensure the local exponential stability in the mean square sense with an H_∞ performance. By using the semigroup theory, the disturbance‐free closed‐loop well‐posedness analysis is first given. Then, based on the SPDE model, a general linear matrix inequality based H_∞ boundary SOF control design is provided via Lyapunov technique and infinite‐dimensional infinitesimal operator, such that the disturbance‐free closed‐loop system is locally exponentially stable in the mean square sense and the H_∞ performance of disturbance attenuation can also be achieved in the presence of disturbances. Finally, simulation results on a stochastic Fisher‐Kolmogorov‐Petrovsky‐Piscounov equation illustrate the effectiveness of the proposed method.