Design of new fault diagnosis and fault tolerant control scheme for non-Gaussian singular stochastic distribution systems

New fault diagnosis (FD) and fault tolerant control (FTC) algorithms for non-Gaussian singular stochastic distribution control (SDC) systems are presented in this paper. Different from general SDC systems, in singular SDC systems, the relationship between the weights and the control input is expressed by a singular state space model, which increases the difficulty in the FD and FTC design. The proposed approach relies on an iterative learning observer (ILO) for fault estimation. The fault may be constant, fast-varying or slow-varying. Based on the estimated fault information, the fault tolerant controller can be designed to make the post-fault probability density function (PDF) still track the given distribution. Simulations are given to show the effectiveness of the proposed FD and FTC algorithms.     

Minimum rational entropy fault tolerant control for non-Gaussian singular stochastic distribution control systems using T-S fuzzy modelling

In this paper, a new fault diagnosis (FD) and fault tolerant control (FTC) algorithm for a non-Gaussian nonlinear singular stochastic distribution control (SDC) system is studied. The rational square-root fuzzy logic model is used to approximate the output probability density function of non-Gaussian processes and a Takagi-Sugeno (T-S) fuzzy model is employed to transform the non-Gaussian nonlinear SDC system into a fuzzy SDC system. An adaptive fuzzy fault diagnosis observer is constructed to achieve reconstruction of system state and fault. Based on the estimated fault information, the controller is reconfigured by minimising the performance index with regard to the rational entropy subjected to mean constraint. Minimum rational entropy fault tolerant control is introduced to make the output of the past-fault SDC system still have the minimum uncertainty. Simulation results are provided to demonstrate the validity of the FD and minimum rational entropy FTC algorithm.     

基于有理平方根逼近的非高斯随机分布系统的故障诊断和容错控制

随机分布系统指的是输入为常规向量而输出为系统输出的概率密度函数所描述的一类随机系统．该类系统控制算法的目标是选择一个控制输入使得系统的实际输出概率密度函数尽可能跟踪一个事先给定的概率密度函数．本文对采用有理平方根B样条逼近其输出概率密度函数的非高斯动态随机分布系统,提出了一种基于非线性自适应观测器的故障诊断方法．该方法可快速有效地诊断出非高斯随机分布系统故障．通过对故障系统的重组,使故障后系统的输出概率密度函数仍能跟踪给定的分布,实现了该随机系统的容错控制,提高了随机系统的可靠性．     

Robust fault diagnosis for non-Gaussian stochastic systems based on the rational square-root approximation model

The task of robust fault detection and diagnosis of stochastic distribution control （SDC） systems with uncertainties is to use the measured input and the system output PDFs to still obtain possible faults information of the system. Using the rational square-root B-spline model to represent the dynamics between the output PDF and the input, in this paper, a robust nonlinear adaptive observer-based fault diagnosis algorithm is presented to diagnose the fault in the dynamic part of such systems with model uncertainties. When certain conditions are satisfied, the weight vector of the rational square-root B-spline model proves to be bounded. Conver- gency analysis is performed for the error dynamic system raised from robust fault detection and fault diagnosis phase. Computer simulations are given to demon- strate the effectiveness of the proposed algorithm.     

Stochastic Distribution Control of Singular Systems: Output PDF Shaping

This paper presents a new algorithm designed to control the shape of the output probability density function (PDF) of singular systems subjected to non-Gaussian input. The aim is to select a control input uk such that the output PDF is made as close as possible to a given PDF. Based on the B-spline neural network approximation of the output PDF, the control algorithm is formulated by extending the developed PDF control strategies of non-singular systems to singular systems. It has been shown that under certain conditions the stability of the closed-loop system can be guaranteed. Simulation examples are given to show the effectiveness of the proposed control algorithm.     

Fault diagnosis and fault-tolerant control for non-Gaussian nonlinear stochastic systems via entropy optimisation

ABSTRACT

In this paper, the fault diagnosis (FD) and fault tolerant control (FTC) problems are studied for non-linear stochastic systems with non-Gaussian disturbance and fault. Unlike classical FD algorithms, the minimum entropy FD is adopted to minimise the residual entropy and control the shape of the probability density function (PDF) of the residual signal. The observation error system can be proved to be locally and ultimately bounded in the mean square sense. Since entropy can be used to characteriSe the uncertainty of the tracking error for non-Gaussian stochastic systems, the FTC controller is obtained by minimising the performance function with regard to the entropy of the tracking error in this paper. The PDF of the output tracking error is approximated by the B-spline model. An illustrative example is utilised to demonstrate the effectiveness of the FD and FTC algorithm, and satisfactory results have been obtained.     

Novel MPC‐Based Fault Tolerant Tracking Control Against Sensor Faults

The problem of active fault‐tolerant tracking control with control input and system output constraints is studied for a class of discrete‐time systems subject to sensor faults. A time‐varying fault‐tolerant observer is first developed to estimate the real system state from the faulty sensor output and control input signals. Then by using the estimated state at each time step, a model predictive control (MPC)‐based fault‐tolerant tracking control scheme is presented to guarantee the desired tracking performance and the given input and output constraints on the faulty system. In comparison with many existing fault‐tolerant MPC methods, its main contribution is that the proposed state estimator is designed by the simple and online numerical computation to tolerate the possible sensor faults, so that the regular MPC algorithm without fault information can be adopted for the online calculation of fault‐tolerant control signal. The potential recursive infeasibility and computational complexity due to the faults are avoided in the scheme. Additionally, the closed‐loop stability of the post‐fault system is discussed. Simulative results of an electric throttle control system verify the effectiveness of the proposed method.     

Robust fault diagnosis and fault‐tolerant control for non‐Gaussian uncertain stochastic distribution control systems

The purpose of fault diagnosis of stochastic distribution control systems is to use the measured input and the system output probability density function to obtain the fault estimation information. A fault diagnosis and sliding mode fault‐tolerant control algorithms are proposed for non‐Gaussian uncertain stochastic distribution control systems with probability density function approximation error. The unknown input caused by model uncertainty can be considered as an exogenous disturbance, and the augmented observation error dynamic system is constructed using the thought of unknown input observer. Stability analysis is performed for the observation error dynamic system, and the H_∞ performance is guaranteed. Based on the information of fault estimation and the desired output probability density function, the sliding mode fault‐tolerant controller is designed to make the post‐fault output probability density function still track the desired distribution. This method avoids the difficulties of design of fault diagnosis observer caused by the uncertain input, and fault diagnosis and fault‐tolerant control are integrated. Two different illustrated examples are given to demonstrate the effectiveness of the proposed algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

Control performance‐based fault detection and fault‐tolerant control schemes for a class of nonlinear systems

The objective of this paper is to develop performance‐based fault detection (FD) and fault‐tolerant control (FTC) schemes for a class of nonlinear systems. To this end, the representation forms of nonlinear systems with faults and the controller parameterization forms are studied first with the aid of the nonlinear factorization technique. Then, based on the stable kernel representation and the stable image representation of the faulty nonlinear system, the stability performance of the closed‐loop system is addressed, respectively. The so‐called fault‐tolerant margin is defined to evaluate the system fault‐tolerant ability. On this basis, two performance‐based FD schemes are developed aiming at detecting the system performance degradation caused by system faults. Furthermore, to recover the system stability performance, two performance‐based FTC strategies are proposed based on the information provided by the FD unit. In the end, a numerical example and a case study on the three‐tank system are given to demonstrate the proposed results.     

Adaptive Fault Tolerant Control of Multi-time-scale Singularly Perturbed Systems

This paper studies the fault tolerant control, adaptive approach, for linear time-invariant two-time-scale and three-time-scale singularly perturbed systems in presence of actuator faults and external disturbances. First, the full order system will be controlled using ε-dependent control law. The corresponding Lyapunov equation is ill-conditioned due to the presence of slow and fast phenomena. Secondly, a time-scale decomposition of the Lyapunov equation is carried out using singular perturbation method to avoid the numerical stiffness. A composite control law based on local controllers of the slow and fast subsystems is also used to make the control law ε-independent. The designed fault tolerant control guarantees the robust stability of the global closed-loop singularly perturbed system despite loss of effectiveness of actuators. The stability is proved based on the Lyapunov stability theory in the case where the singular perturbation parameter is sufficiently small. A numerical example is provided to illustrate the proposed method.     

基于故障诊断观测器的输出反馈容错控制设计

针对自适应故障诊断观测器需要误差系统满足苛刻的严格正实条件(Strictly positive real, SPR)和难于处理输出存在扰动的不确定性系统等问题, 提出了一种新型的增广故障诊断观测器的设计方法, 不仅显著地拓宽了自适应故障诊断观测器的适用范围, 而且其具有处理系统扰动的良好性能. 在故障估计的基础上, 提出了动态输出反馈容错控制的设计方法, 避免了基于观测器的状态反馈容错控制的设计难点. 同时, 故障诊断观测器和输出反馈容错控制是分开设计的, 并且又考虑了各自的性能, 简化了设计过程. 最后, 通过仿真实验验证了所提方法的有效性.     

Design of fault diagnosis filters and fault-tolerant control for aclass of nonlinear systems

This paper presents a set of algorithms for fault diagnosis and fault tolerant control strategy for affine nonlinear systems subjected to an unknown time-varying fault vector. First, the design of fault diagnosis filter is performed using nonlinear observer techniques, where the system is decoupled through a nonlinear transformation and an observer is used to generate the required residual signal. By introducing an extra input to the observer, a direct estimation of the time-varying fault is obtained when the residual is controlled, by this extra input, to zero. The stability analysis of this observer is proved and some relevant sufficient conditions are obtained. Using the estimated fault vector, a fault tolerant controller is established which guarantees the stability of the closed loop system. The proposed algorithm is applied to a combined pH and consistency control system of a pilot paper machine, where simulations are performed to show the effectiveness of the proposed approach     

Adaptive neural model-based fault tolerant control for multi-variable processes

An adaptive neural network model-based fault tolerant control approach for unknown non-linear multi-variable dynamic systems is proposed. A multi-layer Perceptron network is used as the process model and is adapted on-line using the extended Kalman filter to learn changes in process dynamics. In this way, the adaptive model will learn the post-fault dynamics caused by actuator or component faults. Then, the inversion of the neural model is used as a controller to maintain the system stability and control performance after fault occurrence. The convergence of the model inversion control is proved using Lyapunov method. The proposed method is applied to the simulation of a two-input two-output continuous-stirred tank reactor to demonstrate the effectiveness of the approach. Several actuator and component faults are simulated on the continuously stirred tank reactor process when the system is under the proposed fault tolerant control. The results have shown a fast recovery of tracking performance and the maintained stability.     

基于小波变换与等价空间的无人机作动器故障检测

基于等价空间的故障检测可实现残差对初始状态与输入全解耦,在实际工程系统中取得了广泛应用.然而,为了确保故障诊断系统性能,高阶的等价空间导致残差在线计算量大,且制约了可检测故障信号的频率范围.本文提出一种基于小波变换与等价空间结合的无人机作动器故障检测方法,将故障检测问题归结为小波基函数选取和等价空间向量的优化设计,使产生的残差信号满足了干扰鲁棒性与故障灵敏性比率型性能指标的最小化,并通过引入平稳小波变换对残差进行多尺度滤波,利用小波变换的时频局部化特性和快速算法,在满足故障检测系统性能的前提下有效降低了等价空间阶数,一定程度上实现了较宽频率范围内作动器故障信号的检测,克服了传统等价空间方法的不足.最后,以无人机作动器故障检测为例,通过仿真实验验证了本文方法的有效性.     

一类非线性系统的故障重构与容错控制

针对一类满足Lipschitz条件的仿射非线性系统,提出一种执行器故障重构与容错控制方法。通过非奇异变化矩阵对系统进行降阶,设计出滑模故障重构观测器,优化滑模策略,使滑模故障重构观测器渐进估计系统的状态,并给出稳定性分析。运用等价输出控制方法直接获取故障信息,实现执行器故障的检测与重构。设计出主动容错控制器,通过补偿控制,完成执行器故障的容错控制。最后通过数值仿真验证了方法的可行性与有效性。     

非均匀采样数据系统时变故障估计与调节最优集成设计

针对一类发生连续时变故障的非均匀采样数据系统,建立了一套主动容错控制最优设计方案. 首先,为了实现基于非均匀离散采样输出对连续故障的估计,同时鉴于现有自适应故障诊断方法无法直接推广于非均匀采样数据系统,提出一种连续时间增广观测器最优设计方法,既能保证故障估计误差快速收敛同时又对外界干扰鲁棒;并且提出一个迭代算法对故障估计延迟与系统鲁棒性进行权衡;进一步地,基于所获得的故障信息,并考虑估计误差和时变故障内采样特性对容错控制带来的不利因素,设计基于状态反馈的非均匀采样容错控制器来快速恢复故障系统性能;最后,通过对四容水箱基准实例的仿真来验证所提方法的有效性.     

Aero‐Engine DCS Fault‐Tolerant Control with Markov Time Delay Based On Augmented Adaptive Sliding Mode Observer

With a focus on aero‐engine distributed control systems (DCSs) with Markov time delay, unknown input disturbance, and sensor and actuator simultaneous faults, a combined fault tolerant algorithm based on the adaptive sliding mode observer is studied. First, an uncertain augmented model of distributed control system is established under the condition of simultaneous sensor and actuator faults, which also considers the influence of the output disturbances. Second, an augmented adaptive sliding mode observer is designed and the linear matrix inequality (LMI) form stability condition of the combined closed‐loop system is deduced. Third, a robust sliding mode fault tolerant controller is designed based on fault estimation of the sliding mode observer, where the theory of predictive control is adopted to suppress the influence of random time delay on system stability. Simulation results indicate that the proposed sliding mode fault tolerant controller can be very effective despite the existence of faults and output disturbances, and is suitable for the simultaneous sensor and actuator faults condition.     

Observer‐based fault diagnosis and self‐restore control for systems with measurement delays

The problems of fault diagnosis and fault‐tolerant control are considered for systems with measurement delays. In contrast to the present fault diagnosis and fault‐tolerant control approaches, which consider only the input delay and/or state delay, the main contribution of this paper consists of proposing a new observer‐based reduced‐order fault diagnoser construction approach and a design approach to dynamic self‐restore fault‐tolerant control law for systems with measurement delays. First, the time‐delay system is transformed into a delay‐free system in form by a special functional‐based delay‐free transformation approach for measurement delays. Then, the fault diagnosis is realized online via the proposed reduced‐order fault diagnoser. Using the results of fault diagnosis, two dynamic self‐restore control laws are designed to make the system isolated from faults. A numerical example demonstrates the feasibility and validity of the proposed scheme. © 2012 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

基于概率密度函数的时滞依赖故障检测与诊断

针对包含时滞的随机分布系统,提出了一种基于概率密度函数（PDF）的时滞依赖故障检测与诊断方法。建立了基于PDF信息的故障检测残差,利用故障检测与诊断理论,设计了基于线性矩阵不等式的故障检测观测器和故障估计器,并且通过了稳定性分析,实现了对该系统的故障检测以及估计。通过数值仿真,证明了该方法的有效性。