Observer-based residual generation for fault diagnosis for non-affine non-linear polynomial systems

This paper proposes an observer-based residual generator (OBRG) for diagnosing faults in a continuous non-affine system with polynomial non-linearities up to any finite degree where the fault and an unknown input affect both the system and part of the output. Firstly, given certain assumptions and the use of defined extended vectors, a parameterized polynomial system is considerred for which a compact set of sufficient conditions is given for the existence of a candidate OBRG. Conditions for error stability (by a Lyapunov method) and detectability are given. The calculation steps in the design of the OBRG are shown to involve the solution of three linear equations (with parameterizations) and the calculation of a set of constant matrices (for detectability of faults). A result is then given establishing that the design holds for a much wider class of systems. The residual design is applied to a real three-tank system.     

Quantitative fault estimation for a class of non-linear systems

This paper develops a methodology for actuator fault diagnostics and quantitative estimation of fault signals in a class of non-linear systems. The class of non-linear systems considered is one in which the non-linearity is an incremental quadratic type of non-linearity that includes Lipschitz, positive real and sector non-linear functions. The methodology provides for both state estimation and fault vector estimation. An LMI procedure can be utilized for explicit computation of the observer gains. The procedure developed can also be specialized to linear time invariant systems. Compared to previous results for LTI systems, the procedure developed herein does not require the LTI system to be minimum phase. The use of the developed methodology is demonstrated through two illustrative examples of real world physical applications.     

Observer-based fuzzy adaptive fault control for a class of MIMO nonlinear systems

In this paper, the fault-tolerant control (FTC) problem is investigated for a class of multi-input multiple output nonlinear systems with time-varying delays, and an active FTC method is proposed. The controlled system contains unknown nonlinear functions, unknown control gain functions and actuator faults, which integrates time-varying bias and gain faults. Then, fuzzy logic systems are used to approximate the unknown nonlinear functions and unknown control gain functions, fuzzy adaptive observers are used for fault detection and isolation. Further, based on the obtained information, an accommodation method is proposed for compensating the actuator faults. It is shown that all the variables of the closed-loop system are semi-globally uniformly bounded, the tracking error converges to an arbitrary small neighbourhood of the origin. A simulation is given to demonstrate the effectiveness of the proposed approach.     

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.     

Robust fault diagnosis for a class of nonlinear systems

Robust fault diagnosis based on adaptive observer is studied for a class of nonlinear systems up to output injection. Adaptive fault updating laws are designed to guarantee the stability of the diagnosis system. The upper bounds of the state estimation error and fault estimation error of the adaptive observer are given respectively and the effects of parameter in the adaptive updating laws on fault estimation accuracy are also discussed. Simulation example demonstrates the effectiveness of the proposed methods and the analysis results.     

Robust fault diagnosis for a class of nonlinear systems

Robust fault diagnosis based on adaptive observer is studied for a class of nonlinear systems up to output injection. Adaptive fault updating laws are designed to guarantee the stability of the diagnosis system. The upper bounds of the state estimation error and fault estimation error of the adaptive observer are given respectively and the effects of parameter in the adaptive updating laws on fault estimation accuracy are also discussed. Simulation example demonstrates the effectiveness of the proposed methods and the analysis results.     

Sensor fault diagnostics for a class of non-linear systems using linear matrix inequalities

This paper develops a systematic approach to fault diagnostic system design for sensor health monitoring in Lipschitz non-linear systems. The methodology applies to non-linear systems with three or more sensors in which the state is observable through any one of the sensor measurements. Two major issues are addressed in the paper—observer design for the non-linear system to ensure directional growth of residues for failure identification and use of linear matrix inequalities for explicit design of the observer gain. The use of the methodology is demonstrated through an illustrative example.     

Observer-based control of uncertain systems with non-linear uncertainties

Global asymptotic stabilization of nominally linear uncertain systems is considered where uncertain elements in the plant are modelled as cone bounded non-linearities. At first, a linear time-invariant state feedback law ensuring global asymptotic closed-loop stability is obtained. The algorithm which calculates such a feedback law is simple and straightforward. It does not involve repeated solutions of a parameter-dependent algebraic Riccati or any such non-linear equations. Any state feedback law thus developed can then be implemented via an observer specially designed to preserve the global asymptotic stability of the closed-loop system.     

Observer-based approach to fault detection and isolation fornonlinear systems

The design of a residual generator for fault detection and isolation (FDI) in nonlinear systems which are affine in the control signals and in the failure modes is studied, First, the problem statement used for linear systems is extended, and a set of sufficient conditions for the existence of a solution is given. Next, circumstances under which high-gain observers for uniformly observable systems can be used in the synthesis of the residual generator are provided     

Design of a fault diagnosis scheme for a class of singular nonlinear systems

A new fault detection and diagnosis approach is developed in this paper for a class of singular nonlinear systems via the use of adaptive updating rules. Both detection and diagnostic observers are established, where Lyapunov stability theory is used to obtain the required adaptive tuning rules for the estimation of the process faults. This has led to stable observation error systems for both fault detection and diagnosis. A simulated numerical example is included to demonstrate the use of the proposed approach and encouraging results have been obtained.     

Design of a fault diagnosis scheme for a class of singular nonlinear systems

A new fault detection and diagnosis approach is developed in this paper for a class of singular nonlinear systems via the use of adaptive updating rules. Both detection and diagnostic observers are established, where Lyapunov stability theory is used to obtain the required adaptive tuning rules for the estimation of the process faults. This has led to stable observation error systems for both fault detection and diagnosis. A simulated numerical example is included to demonstrate the use of the proposed approach and encouraging results have been obtained.     

Controller assessment for a class of non-linear systems

The use of autoregressive moving average (ARMA) models to assess the control loop performance for processes that are adequately described by the superposition of a linear dynamic model and linear stochastic or deterministic disturbance model is well known. In this paper, classes of non-linear dynamic/stochastic systems for which a similar result can be obtained are established for single-input single-output discrete system. For these systems, lower mean-square error bounds on performance, can be estimated from the closed-loop routine operating data by using non-linear autoregressive moving average with exogenous inputs (NARMAX) models. It is necessary to know the process time delay. The fitting of these models is greatly facilitated by using efficient algorithms, such as Orthogonal Least Squares or other fast orthogonal search algorithms. These models can also be used to assess the predictive importance of non-linearities over multiple-time horizons.     

基于观测器的非线性互连系统的自适应模糊控制

针对一类不确定非线性MIMO互连系统,提出一种自适应模糊控制算法.通过设计观测器来估计系统的状态,因此不要求假设系统的状态是可测的.给出的自适应律只对不确定界进行在线调节,从而大大减轻了在线计算负担.该算法能够保证闭环系统的所有信号是一致有界的,并且跟踪误差指数收敛到一个小的零邻域内.仿真结果表明了算法的可行性.     

Sensor bias fault diagnosis in a class of nonlinear systems

This note describes a robust sensor bias fault diagnosis architecture for dynamic systems represented by a class of nonlinear discrete-time models. The nonlinearity in the system nominal model is assumed to be a function of inputs and outputs only. Specifically, this note uses adaptive techniques to estimate an unknown sensor bias in the presence of modeling uncertainties. A simulation example is presented to illustrate the methodology. The robustness, sensitivity and stability properties of the bias fault diagnosis architecture are rigorously analyzed     

Observer-based fault-tolerant control for a class of nonlinear networked control systems

This paper presents a fault-tolerant control (FTC) scheme for nonlinear systems which are connected in a networked control system. The nonlinear system is first transformed into two subsystems such that the unobservable part is affected by a fault and the observable part is unaffected. An observer is then designed which gives state estimates using a Luenberger observer and also estimates unknown parameter of the system; this helps in fault estimation. The FTC is applied in the presence of sampling due to the presence of a network in the loop. The controller gain is obtained using linear-quadratic regulator technique. The methodology is applied on a mechatronic system and the results show satisfactory performance.     

Observer-based adaptive fuzzy control for a class of nonlinear time-delay systems

An observer-based adaptive fuzzy control is presented for a class of nonlinear systems with unknown time delays. The state observer is first designed, and then the controller is designed via the adaptive fuzzy control method based on the observed states. Both the designed observer and controller are independent of time delays. Using an appropriate Lyapunov-Krasovskii functional, the uncertainty of the unknown time delay is compensated, and then the fuzzy logic system in Mamdani type is utilized to approximate the unknown nonlinear functions. Based on the Lyapunov stability theory, the constructed observer-based controller and the closed-loop system are proved to be asymptotically stable. The designed control law is independent of the time delays and has a simple form with only one adaptive parameter vector, which is to be updated on-line. Simulation results are presented to demonstrate the effectiveness of the proposed approach.     

一类非线性离散切换系统基于观测器的指数镇定

对一类离散非线性切换系统, 考虑了基于观测器的指数镇定问题. 借助微分中值定理(DMVT), 将非线性切换系统转化为线性参数(LPV)切换系统. 当状态变量不完全可获得时, 基于多Lyapunov函数方法, 给出系统在基于观测器的输出反馈控制器下指数镇定的充分条件. 所设计的滞后切换规则能够避免产生滑动模态. 并且将结果推广到系统方程含有不确定性的情况. 最后, 仿真例子说明了设计方法的有效性.     

Genetic programming based approaches to identification and fault diagnosis of non-linear dynamic systems

System identification is one of the most important research directions. It is a diverse field which can be employed in many different areas. One of them is the model-based fault diagnosis. Thus, the problems of system identification and fault diagnosis are closely related. Unfortunately, in both cases, the research is strongly oriented towards linear systems, while the problem of identification and fault diagnosis of non-linear dynamic systems still remains open. There are, of course, many more or less sophisticated approaches to this problem, although they are not as reliable and universal as those related to linear systems, and the choice of the method to be used depends on the application. The purpose of this paper is to provide a new system identification framework based on a genetic programming technique. Moreover, a fault diagnosis scheme for non-linear systems is proposed. In particular, a new fault detection observer is presented, and the Lyapunov approach is used to show that the proposed observer is convergent under certain conditions. It is also shown how to use the genetic programming technique to increase the convergence rate of the observer. The final part of this paper contains numerical examples concerning identification of chosen parts of the evaporation station at the Lublin Sugar Factory S.A., as well as state estimation and fault diagnosis of an induction motor.