Integrated design of fault reconstruction and fault-tolerant control against actuator faults using learning observers

This paper addresses the problem of integrated fault reconstruction and fault-tolerant control in linear systems subject to actuator faults via learning observers (LOs). A reconfigurable fault-tolerant controller is designed based on the constructed LO to compensate for the influence of actuator faults by stabilising the closed-loop system. An integrated design of the proposed LO and the fault-tolerant controller is explored such that their performance can be simultaneously considered and their coupling problem can be effectively solved. In addition, such an integrated design is formulated in terms of linear matrix inequalities (LMIs) that can be conveniently solved in a unified framework using LMI optimisation technique. At last, simulation studies on a micro-satellite attitude control system are provided to verify the effectiveness of the proposed approach.     

Fault detection and isolation design for uncertain nonlinear systems based on full-order,reduced-order and high-order high-gain sliding-mode observers

This paper considers the observer-based fault detection and isolation design problems when the observer matching condition is not satisfied. Based on the relative degree concept, an auxiliary output vector that may satisfy the observer matching condition is constructed. Since the auxiliary output vector contains unknown information, we use a high-order high-gain sliding-mode observer to exactly estimate not only the auxiliary outputs, but also their derivatives in a finite time. Then, an adaptive robust full-order observer is developed to serve as an actuator fault detection observer. For the actuator fault reconstruction purpose, a reduced-order observer is proposed to estimate the system states even if there are some actuator faults and an actuator fault reconstruction method is provided to reach the fault isolation purpose. A numerical simulation example is used to illustrate the effectiveness of the proposed methods.     

Adaptive Sliding Mode Observer‐Based Robust Fault Reconstruction for a Helicopter With Actuator Fault

This paper proposes a design method of robust fault reconstruction for a 3‐DOF helicopter with actuator faults and disturbance. The model of the 3‐DOF helicopter considered in this paper is an affine nonlinear system. An adaptive sliding mode observer is firstly proposed such that the actuator fault can be reconstructed through the adaptive law online. Then, based on linear matrix inequalities (LMI), a feasible algorithm is explored to solve the designed parameters. Finally, a simulation study of the 3‐DOF helicopter is presented to show the effectiveness of the scheme.     

ROBUST FAULT DETECTION AND ISOLATION FOR UNCERTAIN LINEAR RETARDED SYSTEMS

A robust fault detection and isolation scheme is proposed for uncertain continuous linear systems with discrete state delays for both additive and multiplicative faults. Model uncertainties, disturbances and noises are represented as unstructured unknown inputs. The proposed scheme consists of a Luenberger observer for fault detection and a group of adaptive observers, one for each class of faults, for fault isolation. The threshold determination and fault isolation are based on a multi‐observer strategy. Robustness to model uncertainties and disturbances can be guaranteed for the scheme by selecting proper thresholds. All the signals, i.e., the fault estimate and the state and output estimation errors of each isolation observer can be shown to be uniformly bounded, and the estimate of the fault by the matched observer is shown to be satisfactory in the sense of extended H₂ norm. Furthermore, the sensitivity to fault and the fault isolability condition are analyzed also in the paper. Simulations of a heating process for detecting and isolating an actuator gain fault and an additive fault show the proposed scheme is effective.     

Robust fault and icing diagnosis in unmanned aerial vehicles using LPV interval observers

This paper proposes a linear parameter varying (LPV) interval unknown input observer for the robust fault diagnosis of actuator faults and ice accretion in unmanned aerial vehicles (UAVs) described by an uncertain model. The proposed interval observer evaluates the set of values for the state, which are compatible with the nominal fault‐free and icing‐free operation and can be designed in such a way that some information about the nature of the unknown inputs affecting the system can be obtained, thus allowing the diagnosis to be performed. The proposed strategy has several advantages. First, the LPV paradigm allows taking into account operating point variations. Second, the noise rejection properties are enhanced by the presence of the integral term. Third, the interval estimation property guarantees the absence of false alarms. Linear matrix inequality–based conditions for the analysis/design of these observers are provided in order to guarantee the interval estimation of the state and the boundedness of the estimation. The developed theory is supported by simulation results, obtained with the uncertain model of a Zagi Flying Wing UAV, which illustrate the strong appeal of the methodology for identifying correctly unexpected changes in the system dynamics due to actuator faults or icing.     

A model for multi-label classification and ranking of learning objects

This paper describes an approach that uses multi-label classification methods for search tagged learning objects (LOs) by Learning Object Metadata (LOM), specifically the model offers a methodology that illustrates the task of multi-label mapping of LOs into types queries through an emergent multi-label space, and that can improve the first choice of learners or teachers. In order to build the model, the paper also proposes and preliminarily investigates the use of multi-label classification algorithm using only the LO features. As many LOs include textual material that can be indexed, and such indexes can also be used to filter the objects by matching them against user-provided keywords, we then did experiments using web classification with text features to compare the accuracy with the results from metadata (LO feature).     

A Robust Fault Estimation Scheme for a Class of Nonlinear Systems

This paper presents an observer‐based robust fault estimation scheme for a class of nonlinear systems. We consider the system where the fault enters both the state and output equations via unmeasurable nonlinear functions, for which currently no fault estimation scheme exists. The proposed scheme exploits the special structures and information embedded in the fault‐dependent nonlinear functions. We propose a design method to minimize the ?₂ gain from the disturbances to the fault estimation, and provide conditions for the existence of such observers. The effectiveness of this scheme is demonstrated on a nonlinear single‐link flexible joint robot system with disturbances.     

Fault reconstruction for delay systems via least squares and time‐shifted sliding mode observers

In this article, we address the problem of fault reconstruction in delayed systems by introducing a time‐shifted sliding mode observer (SMO). While time‐varying delays of arbitrary duration are considered in the measured output signal, the actuator fault is parametrized as a weighted sum of known regressor functions with unknown coefficients. The prediction scheme utilizes the variation of constants formula to obtain the present time estimate of the unmeasured state. The fault is also identified at present time by means of the continuous‐time Least Squares approaches. Ideal sliding mode can be guaranteed in theory, even in the presence of such adverse delays, since there is no chattering in the output estimation error of the SMO. An application to petroleum engineering with numerical simulations is presented to show the effectiveness of the proposed method.     

Nonlinear Luenberger‐like observers for nonlinear MIMO systems

This paper deals with the design of observers for a class of continuous time nonlinear multi‐input multi‐output systems with nonlinear outputs. Geometric tools are used to transform the original system into an appropriate observer canonical form. Furthermore, a pole placement technique is used to obtain a desired transient response of resulting error dynamics. The observer design is presented for two cases. In both cases, it is shown that the observer gain can be obtained from the solution of a Riccati equation. An illustrative example of state estimation in induction motors is presented to explain the proposed observer design. The performance of the method is also verified by numerical simulations. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Fault estimation observer design for discrete‐time systems in finite‐frequency domain

This paper proposes a framework of fault estimation observer design in finite‐frequency domain for discrete‐time systems. First, under the multiconstrained idea, a full‐order fault estimation observer in finite‐frequency domain is designed to achieve fault estimation by using the generalized Kalman–Yakubovich–Popov lemma to reduce conservatism generated by the entire frequency domain. Then, a reduced‐order fault estimation observer is constructed, which results in a new fault estimator to realize fault estimation using current output information. Furthermore, by introducing slack variables, improved results on full‐order fault estimation observer and reduced‐order fault estimation observer design with finite‐frequency specifications are obtained such that different Lyapunov matrices can be separately designed for each constraint. Simulation results are presented to illustrate the advantages of the theoretic results obtained. Copyright © 2014 John Wiley & Sons, Ltd.     

一种基于全维和降维观测器的故障检测和重构方法

针对不确定性非线性系统,讨论基于观测器的执行器故障的检测和重构方法.首先,通过设计滑模全维观测器,产生对干扰具有鲁棒性、对故障具有敏感性的残差,来达到故障检测的目的;然后,设计能直接消去干扰和故障影响的降维观测器来达到状态渐近收敛估计,并在此基础上,提出故障重构方法;基于微分方程的数值解方法和函数微分的数值解方法,给出一种故障重构的数值解方法;最后,对一个实际模型进行仿真,结果表明了该方法的实用性.     

基于扰动估计的飞行控制系统传感器故障重构

针对飞行控制系统的传感器故障重构问题,讨论了基于扰动估计的传感器故障检测与重构方法。首先,通过建立观测器,对已有系统的干扰进行估计;其次,通过干扰的估计值来建立系统的鲁棒观测器;最后,再通过对系统建立多个降维鲁棒观测器来隔离并重构传感器故障。采用某飞机横侧向模型进行仿真验证,仿真表明基于扰动估计的鲁棒观测器能够有效地对传感器故障进行隔离与重构。     

Preserving order observers for nonlinear systems

Preserving Order Observers provide an estimation that is always above or below the true variable, and in the absence of uncertainties/perturbations, the estimation converges asymptotically to the true value of the variable. In this paper, we propose a novel methodology to design preserving order observers for a class of nonlinear systems in the nominal case or when perturbations/uncertainties are present. This objective is achieved by combining two important systemic properties: dissipativity and cooperativity. Dissipativity is used to guarantee the convergence of the estimation error dynamics, whereas cooperativity of the error dynamics assures the order‐preserving properties of the observer. The use of dissipativity for observer design offers a big flexibility in the class of nonlinearities that can be considered while keeping the design simple: it leads in many situations to the solution of a linear matrix inequality (LMI). Cooperativity of the observer leads to an LMI. When both properties are considered simultaneously, the design of the observer can be reduced, in most cases, to the solution of both a bilinear matrix inequality and an LMI. Because a couple of preserving order observers, one above and one below, provide an interval observer, the proposed methodology unifies several interval observers design methods. The design methodology has been validated experimentally in a three‐tanks system, and it has also been tested numerically and compared with an example from the literature.Copyright © 2013 John Wiley & Sons, Ltd.     

Near optimal interval observers bundle for uncertain bioreactors

In this paper we design an interval observer for the estimation of unmeasured variables of uncertain bioreactors. The observer is based on a bounded error observer, as proposed in [Lemesle, V., & Gouzé, J.-L. (2005). Hybrid bounded error observers for uncertain bioreactor models. Bioprocess and Biosystems Engineering, 27, 311-318], that makes use of a loose approximation of the bacterial kinetics. We first show how to generate guaranteed upper and lower bounds on the state, provided that known intervals for the initial condition and the uncertainties are available. These so-called framers depend on a tuning gain. They can be run in parallel and the envelope provides the best estimate. An optimality criterion is introduced leading to the definition of an optimal observer. We show that this criterion provides directly a gain set containing the best framers. The method is applied to the estimation of the total biomass of an industrial wastewater treatment plant, demonstrating its efficiency.     

Actuator Fault Reconstruction for Systems with Monotone Nonlinearities

This paper considers observer‐based fault reconstruction for systems with monotone nonlinearities. The nonlinear term in the observer error dynamics satisfies a sector property. Using Lyapunov redesign techniques, a continuous nonlinear error feedback is designed according to the slope property of the nonlinear term to stabilize the error dynamics. Hence, the convergence of observer error is independent of the Lipschitz constant. If the observer error converges to zero asymptotically, then the continuous error feedback can be used to reconstruct the faults. As an extension, an adaptive scheme is developed for systems where the arguments of nonlinear functions are perturbed by unknown parameters. Finally, simulations of an electric driving system are presented to show the effectiveness of the schemes.     

Adaptive Lipschitz Observer Design for a Mammalian Model

This paper deals with observer designs for a proposed mathematical model of circadian rhythms which exist in almost every living organism. A 7th order model for mammalian circadian rhythms which captures the main dynamic features is considered in this paper. A recent result of one‐sided Lipschitz observer design in the literature is applied to this mammalian model to show a possibility of reducing measurements for circadian models in system biology. The mammalian model presented may contain an uncertainty parameter. An adaptive design of the Lipschitz observer is then applied to deal with this case. Besides detailed designs of both observers, detailed analysis is also performed for nonlinear functions in the mammalian model to show that the Lipschitz observers can indeed be applied. Several simulation studies of the proposed observers are carried out with the results shown in this paper.     

State estimation and unknown input reconstruction via both reduced-order and high-order sliding mode observers

This paper considers the problems of the simultaneous estimation of the system states and the unknown inputs for linear systems when the so-called observer matching condition is not satisfied. An auxiliary output vector is introduced so that the observer matching condition is satisfied with respect to it. A high-order sliding mode observer is considered to get the exact estimates of both the auxiliary outputs and their derivatives in a finite time based on the system measured outputs. After this, a reduced-order observer is constructed by using the estimated auxiliary outputs as the new system outputs. The reduced-order observer is able to asymptotically estimate the system states without suffering the influence of the unknown inputs. A kind of unknown input reconstruction method based on both the state and the auxiliary output derivative estimates is developed. Finally, a numerical simulation example is given to illustrate the effectiveness of the proposed methods.     

High‐order sliding‐mode observer for linear time‐varying systems with unknown inputs

In this article, an observer for linear time variant systems affected by unknown inputs is suggested. The proposed observer combines the deterministic least squares filter and the high‐order sliding‐mode differentiator to provide exact state reconstruction in spite of bounded unknown inputs and system instability. The cascade structure of the algorithm provides a correct state reconstruction for the class of linear time variant systems that satisfy the structural property of strong observability. Simulations illustrate the performance of the proposed algorithm. Copyright © 2016 John Wiley & Sons, Ltd.