Nonlinear robust fault reconstruction and estimation using a sliding mode observer

This paper considers fault detection and estimation issues for a class of nonlinear systems with uncertainty, using an equivalent output error injection approach. A particular design of sliding mode observer is presented for which the parameters can be obtained using LMI techniques. A fault estimation approach is presented to estimate the fault and the estimation error is dependent on the bounds on the uncertainty. For a special class of uncertainty, a fault reconstruction scheme is presented where the reconstructed signal can approximate the fault signal to any accuracy. The proposed fault estimation/reconstruction signals are only based on the available plant input/ouput information and can be calculated on-line. Finally, a simulation study on a robotic arm system is presented to show the effectiveness of the scheme.     

噪声方差不确定约束系统的滚动时域估计

针对噪声方差不确定的约束系统,讨论了一种鲁棒滚动时域估计(MHE)方法.首先,根据噪声方差不确定模型,找到满足所有不确定性的最小方差上界,在线性矩阵不等式(LMI)框架下求解优化问题,得到近似到达代价的表达形式;然后再融合预测控制的滚动优化原理,把系统的硬约束直接表述在优化问题中,在线优化性能指标,估计出当前时刻系统的状态.仿真时与鲁棒卡尔曼滤波方法进行比较,结果表明了该方法的有效性.     

Design of a novel knowledge-based fault detection and isolation scheme

In this paper, a real-time fault detection and isolation (FDI) scheme for dynamical systems is developed, by integrating the signal processing technique with neural network design. Wavelet analysis is applied to capture the fault-induced transients of the measured signals in real-time, and the decomposed signals are pre-processed to extract details about a fault. A Regional Self-Organizing feature Map (R-SOM) neural network is synthesized to classify the fault types. The R-SOM neural network adopts two regions adjustment in the learning algorithm, thus it has high precision in clustering and matching, especially when the noise, disturbance and other uncertainties exist in the systems. As a result, the proposed FDI scheme is robust and accurate. The design is implemented on a stirred tank system and satisfactory online testing results are obtained.     

Fault detection and isolation for uncertain closed‐loop systems based on adaptive and switching approaches

This paper deals with the fault detection and isolation (FDI) problem for uncertain closed‐loop systems with external disturbances and nonlinear perturbations. To address the system uncertainties and the nonlinear perturbations in different faulty models, adaptive and switching techniques are introduced to construct a bank of FDI observers, such that one of them can match the current system, and the corresponding observer estimate errors can converge asymptotically to zero. An effective FDI scheme is then presented by introducing some model‐matching indexes. Moreover, the introduced switching laws liberate the equality constraints often used in the existing FDI approaches, which are hard to satisfy if the system matrices include uncertainties. Finally, a simulation example of F/A‐18A automatic carrier landing system is used to illustrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

A gain-varying UIO approach with adaptive threshold for FDI of nonlinear F16 systems

A discrete gain-varying unknown input observer (UIO) method is presented for actuator fault detection and isolation (FDI) problems in this paper. A novel residual scheme together with a moving horizon threshold is proposed. This design methodology is applied to a nonlinear F16 system with polynomial aerodynamics coefficient expressions, where the coefficient expressions for the F16 system and UIOs may be slightly different. The simulation results illustrate that a satisfactory FDI performance can be achieved even when the F16 system is under the environment of model uncertainties, exogenous noise and measurement errors.     

基于RBF神经网络观测器的非线性系统鲁棒故障检测方法

针对一类仿射非线性动态系统，提出一种基于网络非线性观测器的鲁棒故障检测与隔离的新方法，采用ＲＢＦ神经网络逼近观测器系统中的非线性项，提高了状态估计的精度，证明了状态估计误差稳定且渐近收敛到零；同时提出了一种新的网络权值调整指标方法，提高了神经网络故障分类器的泛化能力，从而保证该方法对监测系统的建模 外部扰动具有良好的鲁棒性。     

一类基于神经网络非线性观测器的鲁棒故障检测

针对一类仿射非线性动态系统,提出了一种基 于神经网络非线性观测器的鲁棒故障检测与隔离的新方法．该方法采用神经网络逼近观测器 系统中的非线性项,提高了状态估计的精度,并从理论上证明了状态估计误差稳定且渐近收 敛到零;另一方面引入神经网络分类器进行故障的模式识别,通过在神经网络输入端加入噪 声项来进行训练,提高神经网络的泛化逼近能力,从而保证对被监测系统的建模误差和外部 扰动具有良好的鲁棒性．最后,利用本文方法针对某型歼击机结构故障进行仿真验证,仿真 结果表明本文方法是有效的．     

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.     

Robust l1 estimation using the Popov-Tsypkin multiplier with application to robust fault detection

This paper considers the design of robust l₁ estimators based on multiplier theory (which is intimately related to mixed structured singular value theory) and the application of robust l₁ estimators to robust fault detection. The key to estimator-based, robust fault detection is to generate residuals which are robust against plant uncertainties and external disturbance inputs, which in turn requires the design of robust estimators. Specifically, the Popov-Tsypkin multiplier is used to develop an upper bound on an l₁ cost function over an uncertainty set. The robust l₁ estimation problem is formulated as a parameter optimization problem in which the upper bound is minimized subject to a Riccati equation constraint. A continuation algorithm that uses quasi-Newton BFGS (the algorithm of Broyden, Fletcher, Goldfab and Shanno) corrections is developed to solve the minimization problem. The estimation algorithm has two stages. The first stage solves a mixed-norm H₂/l₁ estimation problem. In particular, it is initialized with a steady-state Kalman filter and, by varying a design parameter from 0 to 1, the Kalman filter is deformed to an l₁ estimator. In the second stage the l₁ estimator is made robust. The robust l₁ estimation framework is then applied to the robust fault detection of dynamic systems. The results are applied to a simplified longitudinal flight control system. It is shown that the robust fault detection procedure based on the robust l₁ estimation methodology proposed in this paper can reduce false alarm rates.     

基于智能解析余度的容错飞控系统设计

常规的解析余度容错方法容易受到不确定因素和随机干扰的影响,本文以飞行控制系统为研究对象,提出基于智能解析余度的容错飞行控制系统设计方案,使用径向基神经网络的在线学习和全局逼近的性能,建立飞行控制系统传感器之间的解析余度关系,利用不相同传感器之间的解析关系进行残差分析从而进行传感器的故障隔离与信号重构.这样有效地抑制了测量噪声和模型不确定性.应用某型飞机进行仿真,实现了传感器的在线故障隔离与重构,验证了该方法的有效性.     

Robust output tracking control for the systems with uncertainties

A new robust tracking control is proposed for the minimum phase dynamical systems with parameter uncertainties and unmatched disturbance, where only the input-output measurement of the system is employed. The system parameters may vary slightly around their corresponding nominal values. The disturbance is assumed to be bounded. However, the upper and lower bounds are unknown. First, the frame of the control law is presented. Then, a special bounded signal is generated by the disturbance and the model uncertainties are estimated by a new non-linear method, where the upper and lower bounds of the special signal are adaptively updated online. Finally, the robust tracking control is synthesized by using the estimate of the special signal. The output tracking error can be made as small as necessary by choosing the design parameters. The attraction of the proposed method lies in its robustness to uncertainties and its ease of implementation. Example and simulation results are presented to show the effectiveness of the proposed algorithm.     

A novel reduced-basis method with upper and lower bounds for real-time computation of linear elasticity problems

This paper presents a novel reduced-basis method for analyzing problems of linear elasticity in a systematical, rapid and reliable fashion for solutions with both upper and lower bounds to the exact solution in the form of energy norm or compliance output. The lower bound of the solution output is obtained form the well-known reduced-basis method based on the Galerkin projection used in the finite element method, which is termed as GP_RBM. For the upper bound, a new reduced-basis approach is developed by the combination of the reduced-basis method and a smoothed Galerkin projection used in the linearly conforming point interpolation method, and it is thus termed as SGP_RBM. To examine the present SGP_RBM, we first conduct a theoretical study on the very important upper bound property. Reduced-basis models for both GP_RBM and SGP_RBM are constructed with the aid of an asymptotic error estimation and greedy adaptive procedure. The GP_RBM and the newly proposed SGP_RBM are applied to analyze a cantilever beam with an oblique crack to verify the proposed RBM technique in terms of accuracy, convergence, bound properties and computational savings. Both theoretical analysis and numerical results have demonstrated that the present method is a very efficient method for real-time solutions providing exact output bounds.     

A new nonlinear robust disturbance observer

This paper presents a new nonlinear robust disturbance observer by using only the input–output information for minimum phase dynamical systems with arbitrarily relative degrees. The model uncertainties, the nonlinear parts of the system are merged into the disturbance term, and are regarded as a part of the disturbance. The disturbance is assumed bounded. However, the upper and lower bounds are assumed unknown. The new disturbance observer is inspired by the VSS control theory, whereas the upper and lower bounds of the disturbance are adaptively updated. The estimation error of the disturbance can be made as small as necessary by choosing the design parameters. The attraction of the proposed method lies in its robustness to disturbance and easiness to be implemented. Example and simulation results show the effectiveness of the proposed algorithm.     

Robust filtering under stochastic parametric uncertainties

This paper is concerned with a polynomial approach to robust deconvolution filtering of linear discrete-time systems with random modeling uncertainties. The modeling errors appear in the coefficients of the numerators and denominators of both the input signal and system transfer function models in the form of random variables with zero means and known upper bounds of the covariances. The robust filtering problem is to find an estimator that minimizes the maximum mean square estimation error over the random parameter uncertainties and input and measurement noises. The key to our solution is to quantify the effect of the random parameter uncertainties by introducing two fictitious noises for which a simple way is given to calculate their covariances. The optimal robust estimator is then computed by solving one spectral factorization and one polynomial equation as in the standard optimal estimator design using a polynomial approach. An example of signal detection in mobile communication is given to illustrate the effectiveness of our approach.     

一类具有未知死区MIMO系统的自适应模糊控制

针对一类具有未知死区并具有下三角函数控制增益矩阵的不确定MIMO非线性系统, 根据滑模控制原理, 并利用Nussbaum函数的性质, 提出了一种自适应模糊控制器的设计方案. 该方案取消了函数控制增益符号已知和死区模型参数上界、下界已知的条件. 通过引入积分型李亚普诺夫函数及最优逼近误差与死区扰动上界的自适应补偿项,证明了闭环系统是稳定的,跟踪误差收敛到零. 仿真结果表明了该方法的有效性.     

基于神经网络的不确定机器人自适应滑模控制

提出一种机器人轨迹跟踪的自适应神经滑模控制。该控制方案将神经网络的非线性映射能力与变结构控制理论相结合,利用RBF网络自适应学习系统不确定性的未知上界,神经网络的输出用于自适应修正控制律的切换增益。这种新型控制器能保证机械手位置和速度跟踪误差渐近收敛于零。仿真结果表明了该方案的有效性。     

Active fault detection and isolation of discrete-time linear time-varying systems: a set-membership approach

Active fault detection and isolation (AFDI) is used for detection and isolation of faults that are hidden in the normal operation because of a low excitation signal or due to the regulatory actions of the controller. In this paper, a new AFDI method based on set-membership approaches is proposed. In set-membership approaches, instead of a point-wise estimation of the states, a set-valued estimation of them is computed. If this set becomes empty the given model of the system is not consistent with the measurements. Therefore, the model is falsified. When more than one model of the system remains un-falsified, the AFDI method is used to generate an auxiliary signal that is injected into the system for detection and isolation of faults that remain otherwise hidden or non-isolated using passive FDI (PFDI) methods. Having the set-valued estimation of the states for each model, the proposed AFDI method finds an optimal input signal that guarantees FDI in a finite time horizon. The input signal is updated at each iteration in a decreasing receding horizon manner based on the set-valued estimation of the current states and un-falsified models at the current sample time. The problem is solved by a number of linear and quadratic programming problems, which result in a computationally efficient algorithm. The method is tested on a numerical example as well as on the pitch actuator of a benchmark wind turbine.     

An Extended Zonotopic and Gaussian Kalman Filter (EZGKF) merging set-membership and stochastic paradigms: Toward non-linear filtering and fault detection

A framework merging the set-membership and the stochastic paradigms is formalized and used to design an Extended Zonotopic and Gaussian Kalman Filter (EZGKF) dealing with the robust state estimation and the fault detection of uncertain discrete-time nonlinear systems. The so-called Set-membership and Gaussian Mergers (SGM) are introduced and particularized to Zonotopes (ZGM). They provide a constructive and computationally efficient solution to propagate random uncertainties with incompletely specified probability distributions combining set-based support enclosures and upper covariance matrix bounds formalized as matrix inequalities. Based on a full time-varying LPV enclosure featuring structured state matrix uncertainties, and given some confidence level expressed in probabilistic terms (maximal false alarm rate), a detection test is developed and shown to merge the usually mutually exclusive benefits granted by set-membership techniques (robustness to the worst-case within specified bounds, domain computations) and stochastic approaches (taking noise distribution into account, probabilistic evaluation of tests). A numerical example illustrates the state estimation capabilities of EZGKF and the improved tradeoff between the sensitivity to faults and the robustness to disturbances/noises.     

An adaptive learning regulator for uncertain minimum phase systems with undermodeled unknown exosystems

The design of an adaptive learning regulator is addressed for uncertain minimum phase linear systems (with known bounds, known upper bound on system order, known relative degree, known high frequency gain sign) and for unknown exosystems (with unknown order, uncertain frequencies). On the basis of a known bound on system uncertainties and a known bound on the modeled exosystem frequencies, a new adaptive output error feedback control algorithm is proposed which guarantees exponential convergence of both the output and the control input errors into residual bounds which decrease as the exosystem modeling error decreases. Exponential convergence of both errors to zero is obtained when the regulator exactly models all exosystem excited frequencies, while asymptotic convergence of both errors to zero is achieved when the actual exosystem is overmodeled by the regulator. The new algorithm generalizes existing learning controllers since, in the case of periodic references and/or disturbances, the knowledge of the period is not required.     

A hierarchical multiple-model approach for detection and isolation of robotic actuator faults

Modern robotic systems perform elaborate tasks in complicated environments and have close interactions with humans. Therefore fault detection and isolation (FDI) schemes must be carefully designed and implemented on robotic systems in order to guarantee safe and reliable operations. In this paper, we propose a hierarchical multiple-model FDI (HMM-FDI) scheme to detect and isolate actuator faults of robot manipulators. The proposed algorithm performs FDI in stages and refines the associated model set at each stage. Consequently only a small number of models are required to detect and isolate various types of unexpected actuator faults, including abrupt faults, incipient faults, and simultaneous faults. In addition, the computational load is alleviated due to the reduced-sized model set. The relation between the fault detection stage of the HMM-FDI scheme and the likelihood ratio test is explicitly revealed and theoretical upper bounds of the false alarm and missed detection probabilities are evaluated. Then we conduct experiments to demonstrate the ability of the HMM-FDI scheme in successful and immediate detection and isolation of actuator faults.