Sensor bias fault isolation in a class of nonlinear systems

This note presents a robust fault isolation scheme for a class of nonlinear systems with sensor bias type of faults. The proposed fault diagnosis architecture consists of a fault detection estimator and a bank of isolation estimators, each corresponding to a particular output sensor. Based on the class of nonlinear systems and sensor bias faults under consideration, the stability and learning properties of the fault isolation estimators are obtained, adaptive thresholds are derived for the isolation estimators, and fault isolability conditions are rigorously investigated, characterizing the class of nonlinear faults that are isolable by the proposed scheme. A simulation example is used to illustrate the effectiveness of the sensor bias fault isolation methodology.     

Neural-network-based robust fault diagnosis in robotic systems

Fault diagnosis plays an important role in the operation of modern robotic systems. A number of researchers have proposed fault diagnosis architectures for robotic manipulators using the model-based analytical redundancy approach. One of the key issues in the design of such fault diagnosis schemes is the effect of modeling uncertainties on their performance. This paper investigates the problem of fault diagnosis in rigid-link robotic manipulators with modeling uncertainties. A learning architecture with sigmoidal neural networks is used to monitor the robotic system for any off-nominal behavior due to faults. The robustness and stability properties of the fault diagnosis scheme are rigorously established. Simulation examples are presented to illustrate the ability of the neural-network-based robust fault diagnosis scheme to detect and accommodate faults in a two-link robotic manipulator.     

Robust fault isolation for a class of non-linear input?output systems

The design and analysis of fault diagnosis methodologies for non-linear systems has received significant attention recently. This paper presents a robust fault isolation scheme for a class of non-linear systems with unstructured modelling uncertainty and partial state measurement. The proposed fault diagnosis architecture consists of a fault detection and approximation estimator and a bank of isolation estimators. Each isolation estimator corresponds to a particular type of fault in the fault class. A fault isolation decision scheme is presented with guaranteed performance. If at least one component of the output estimation error of a particular fault isolation estimator exceeds the corresponding adaptive threshold at some finite time, then the occurrence of that type of fault can be excluded. Fault isolation is achieved if this is valid for all but one isolation estimator. Based on the class of non-linear systems under consideration, fault isolability conditions are rigorously investigated, characterizing the class of non-linear faults that are isolable by the proposed scheme. Moreover, the non-conservativeness of the fault isolability conditions is illustrated by deriving a subclass of nonlinear systems and faults for which this condition is also necessary for fault isolability. A simulation example of a simple robotic system is used to show the effectiveness of the robust fault isolation methodology.     

Design and analysis of a fault isolation scheme for a class of uncertain nonlinear systems

This paper presents a unified fault isolation scheme for handling both process faults and sensor faults in a class of uncertain nonlinear systems. The proposed fault diagnosis architecture consists of a fault detection estimator and a bank of isolation estimators, each corresponding to a particular fault type. The design of the fault isolation decision scheme is based on the derivation of appropriate adaptive thresholds for each fault isolation estimator. Fault isolability conditions characterizing the class of process faults and sensor faults that are isolable by the proposed scheme are derived. A rigorous isolability analysis is presented via the use of the so-called fault mismatch functions, which are defined between pairs of possible faults. A simulation example is used to illustrate the proposed fault isolation scheme.     

A robust detection and isolation scheme for abrupt and incipientfaults in nonlinear systems

This paper presents a robust fault diagnosis scheme for abrupt and incipient faults in nonlinear uncertain dynamic systems. A detection and approximation estimator is used for online health monitoring. Once a fault is detected, a bank of isolation estimators is activated for the purpose of fault isolation. A key design issue of the proposed fault isolation scheme is the adaptive residual threshold associated with each isolation estimator. A fault that has occurred can be isolated if the residual associated with the matched isolation estimator remains below its corresponding adaptive threshold, whereas at least one of the components of the residuals associated with all the other estimators exceeds its threshold at some finite time. Based on the class of nonlinear uncertain systems under consideration, an isolation decision scheme is devised and fault isolability conditions are given, characterizing the class of nonlinear faults that are isolable by the robust fault isolation scheme. The nonconservativeness of the fault isolability conditions is illustrated by deriving a subclass of nonlinear systems and of faults for which these conditions are also necessary for fault isolability. Moreover, the analysis of the proposed fault isolation scheme provides rigorous analytical results concerning the fault isolation time. Two simulation examples are given to show the effectiveness of the fault diagnosis methodology     

Automated fault diagnosis in nonlinear multivariable systems usinga learning methodology

The paper presents a robust fault diagnosis scheme for detecting and approximating state and output faults occurring in a class of nonlinear multiinput-multioutput dynamical systems. Changes in the system dynamics due to a fault are modeled as nonlinear functions of the control input and measured output variables. Both state and output faults can be modeled as slowly developing (incipient) or abrupt, with each component of the state/output fault vector being represented by a separate time profile. The robust fault diagnosis scheme utilizes on-line approximators and adaptive nonlinear filtering techniques to obtain estimates of the fault functions. Robustness with respect to modeling uncertainties, fault sensitivity and stability properties of the learning scheme are rigorously derived and the theoretical results are illustrated by a simulation example of a fourth-order satellite model.     

Fault-tolerant cooperative output regulation for multi-vehicle systems with sensor faults

This paper presents a unified framework of fault diagnosis and fault-tolerant cooperative output regulation (FTCOR) for a linear discrete-time multi-vehicle system with sensor faults. The FTCOR control law is designed through three steps. A cooperative output regulation (COR) controller is designed based on the internal mode principle when there are no sensor faults. A sufficient condition on the existence of the COR controller is given based on the discrete-time algebraic Riccati equation (DARE). Then, a decentralised fault diagnosis scheme is designed to cope with sensor faults occurring in followers. A residual generator is developed to detect sensor faults of each follower, and a bank of fault-matching estimators are proposed to isolate and estimate sensor faults of each follower. Unlike the current distributed fault diagnosis for multi-vehicle systems, the presented decentralised fault diagnosis scheme in each vehicle reduces the communication and computation load by only using the information of the vehicle. By combing the sensor fault estimation and the COR control law, an FTCOR controller is proposed. Finally, the simulation results demonstrate the effectiveness of the FTCOR controller.     

基于LMI的非线性差分-代数系统的鲁棒故障诊断

针对非线性不确定差分-代数系统(DAS),提出了一种基于线性矩阵不等式(LMI)的故 障诊断方法.该方法首先利用已知的DAS标称模型构造一个由差分方程和代数方程组成的辅 助系统,然后基于状态差值与差分方程中的故障以及约束输出差值与代数方程中的故障之间的 关系,将故障辨识问题转化为参数估计问题,最后利用LMI方法对故障进行在线辨识.仿真结 果表明了该方法的有效性.     

Reduction of stable differential–algebraic equation systems via projections and system identification

Most large-scale process models derived from first principles are represented by nonlinear differential–algebraic equation (DAE) systems. Since such models are often computationally too expensive for real-time control, techniques for model reduction of these systems need to be investigated. However, models of DAE type have received little attention in the literature on nonlinear model reduction. In order to address this, a new technique for reducing nonlinear DAE systems is presented in this work. This method reduces the order of the differential equations as well as the number and complexity of the algebraic equations. Additionally, the algebraic equations of the resulting system can be replaced by an explicit expression for the algebraic variables such as a feedforward neural network. This last property is important insofar as the reduced model does not require a DAE solver for its solution but system trajectories can instead be computed with regular ODE solvers. This technique is illustrated with a case study where responses of several different reduced-order models of a distillation column with 32 differential equations and 32 algebraic equations are compared.     

Fault diagnosis of a class of nonlinear uncertain systems with Lipschitz nonlinearities using adaptive estimation

This paper presents a fault detection and isolation (FDI) scheme for a class of Lipschitz nonlinear systems with nonlinear and unstructured modeling uncertainty. This 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. A new FDI method is developed using adaptive estimation techniques. The FDI architecture consists of a fault detection estimator and a bank of fault isolation estimators. The fault detectability and isolability conditions, characterizing the class of faults that are detectable and isolable by the proposed scheme, are rigorously established. The fault isolability condition is derived via the so-called fault mismatch functions, which are defined to characterize the mutual difference between pairs of possible faults. A simulation example of a single-link flexible joint robot is used to illustrate the effectiveness of the proposed scheme.     

Fault estimation—a standard problem approach

This paper presents a range of optimization based approaches to fault diagnosis. A variety of fault diagnosis problems are reformulated in the so‐called standard problem set‐up introduced in the literature on robust control. Once the standard problem formulations are given, the fault diagnosis problems can be solved by standard optimization techniques. The proposed methods include (1) fault diagnosis (fault estimation, (FE)) for systems with model uncertainties; FE for systems with parametric faults, and FE for a class of nonlinear systems. Copyright © 2002 John Wiley & Sons, Ltd.     

Actuator fault diagnosis for a class of nonlinear systems and its application to a laboratory 3D crane

In this paper, an actuator fault diagnosis scheme is proposed for a class of affine nonlinear systems with both known and unknown inputs. The scheme is based on a novel input/output relation derived from the considered nonlinear systems and the use of the recently developed high-order sliding-mode robust differentiators. The main advantages of the proposed approach are that it does not require a design of nonlinear observer and applies to systems not necessarily detectable. Conditions are provided to characterize the feasibility of fault detection and isolation using the proposed scheme and the maximum number of isolatable actuator faults. The efficacy of the proposed actuator fault diagnosis approach is tested through experiments on a laboratory 3D Crane, and the experimental results show that the proposed actuator fault diagnosis approach is promising and can achieve fault detection and isolation satisfactorily.     

Robust nonlinear control of spacecraft formation flying using constraint forces

A robust nonlinear control method is presented for spacecraft precise formation flying.With the constraint forces and consid-ering nonlinearity and perturbations,the problem of the formation keeping is changed to the Lagrange systems with the holonomic constraints and the differential algebraic equations (DAE).The nonlinear control laws are developed by solving the DAE.Because the traditional numerical solving methods of DAE are very sensitive to the various errors and the resulting con-trol laws are not ro...     

Robust fault diagnosis for non-linear difference-algebraic systems

A new robust fault diagnosis method based on linear matrix inequality (LMI) for non-linear difference-algebraic systems (DAS) with uncertainties is proposed. Based on the known nominal model of DAS, it firstly constructs an auxiliary system consisting of a difference equation and an algebraic equation, then converts the problem of fault identification into the problem of parameter estimation, and finally realizes fault identification using an LMI method. This method can not only detect, isolate and identify faults for DAS, but also give the upper bounds of fault identification error. Simulation indicates that it can give satisfactory diagnostic results for both abrupt and incipient faults.     

Design of unknown input functional observers for nonlinear systems with application to fault diagnosis

This paper considers the design of low-order unknown input functional observers for robust fault detection and isolation of a class of nonlinear Lipschitz systems subject to unknown inputs. The proposed functional observers can be used to generate residual signals to detect and isolate actuator faults. By using the generalized inverse approach, the effect of the unknown inputs can be decoupled completely from the residual signals. Conditions for the existence and stability of reduced-order unknown input functional observer are derived. A design procedure for the generation of residual signals to detect and isolate actuator faults is presented using the proposed unknown-input observer-based approach. A numerical example is given to illustrate the proposed fault diagnosis scheme in nonlinear systems subject to unknown inputs.     

Robust Fault‐Tolerant Control of Launch Vehicle Via GPI Observer and Integral Sliding Mode Control

A robust fault‐tolerant attitude control scheme is proposed for a launch vehicle (LV) in the presence of unknown external disturbances, mismodeling dynamics, actuator faults, and actuator's constraints. The input‐output representation is employed to describe the rotational dynamics of LV rendering three independently decoupled second order single‐input‐single‐output (SISO) systems. In the differential algebraic framework, general proportional integral (GPI) observers are used for the estimations of the states and of the generalized disturbances, which include internal perturbations, external disturbances, and unknown actuator failures. In order to avoid the defects of the conventional sliding surface, a new nonlinear integral sliding manifold is introduced for the robust fault‐tolerant sliding mode controller design. The stability of the GPI observer and that of the closed‐loop system are guaranteed by Lyapunov's indirect and direct methods, respectively. The convincing numerical simulation results demonstrate the proposed control scheme is with high attitude tracking performance in the presence of various disturbances, actuator faults, and actuator constraints.     

Fault detection for nonlinear discrete-time systems via deterministic learning

Recently, an approach for the rapid detection of small oscillation faults based on deterministic learning theory was proposed for continuous-time systems. In this paper, a fault detection scheme is proposed for a class of nonlinear discrete-time systems via deterministic learning. By using a discrete-time extension of deterministic learning algorithm, the general fault functions (i.e., the internal dynamics) underlying normal and fault modes of nonlinear discrete-time systems are locally-accurately approximated by discrete-time dynamical radial basis function (RBF) networks. Then, a bank of estimators with the obtained knowledge of system dynamics embedded is constructed, and a set of residuals are obtained and used to measure the differences between the dynamics of the monitored system and the dynamics of the trained systems. A fault detection decision scheme is presented according to the smallest residual principle, i.e., the occurrence of a fault can be detected in a discrete-time setting by comparing the magnitude of residuals. The fault detectability analysis is carried out and the upper bound of detection time is derived. A simulation example is given to illustrate the effectiveness of the proposed scheme.     

Symbolic elimination in dynamic optimization based on block-triangular ordering

We consider dynamic optimization problems for systems described by differential-algebraic equations (DAEs). Such problems are usually solved by discretizing the full DAE. We propose techniques to symbolically eliminate many of the algebraic variables in a preprocessing step before discretization. These techniques are inspired by the causalization and tearing techniques often used when solving DAE initial value problems. Since sparsity is crucial for some dynamic optimization methods, we also propose a novel approach to preserving sparsity during this procedure. The proposed methods have been implemented in the open-source JModelica.org platform. We evaluate the performance of the methods on a suite of optimal control problems solved using direct collocation. We consider both computational time and probability of solving the problem in a timely manner. We demonstrate that the proposed methods often are an order of magnitude faster than the standard way of discretizing the full DAE, and also significantly increase probability of successful convergence.     

Distributed fault diagnosis for process and sensor faults in a class of interconnected input–output nonlinear discrete-time systems

This paper presents a distributed fault diagnosis scheme able to deal with process and sensor faults in an integrated way for a class of interconnected input–output nonlinear uncertain discrete-time systems. A robust distributed fault detection scheme is designed, where each interconnected subsystem is monitored by its respective fault detection agent, and according to the decisions of these agents, further information regarding the type of the fault can be deduced. As it is shown, a process fault occurring in one subsystem can only be detected by its corresponding detection agent whereas a sensor fault in a subsystem can be detected by either its corresponding detection agent or the detection agent of another subsystem that is affected by the subsystem where the sensor fault occurred. This discriminating factor is exploited for the derivation of a high-level isolation scheme. Moreover, process and sensor fault detectability conditions characterising quantitatively the class of detectable faults are derived. Finally, a simulation example is used to illustrate the effectiveness of the proposed distributed fault detection scheme.     

陈述式基于方程仿真模型的约简

为解决复杂多领域连续系统的高效仿真问题,研究了陈述式基于方程仿真模型的约简策略.基于符号处理技术,提出了一种模型约简方法.该方法从方程的规范转换入手,通过消除特定形式方程缩减系统规模,将整个方程系统规划分解为一个可顺序求解的子系统序列.给出的实例表明文中约简方法效果显著.文中策略与算法已在多领域物理系统混合建模与仿真平台EMWorks中实现.