Nonlinear sliding mode high-gain observers for fault estimation

A robust high gain observer for state and unknown inputs/faults estimations for a special class of nonlinear systems is developed in this article. Ensuring the observability of the faults/unknown inputs with respect to the outputs, the faults can be estimated from the sliding surface. Under a Lipschitz condition for the nonlinear part, the high gain observers are designed under some regularity assumptions. In the sliding mode, the convergence of the estimation error dynamics is proven similar to the analysis of high-gain observers.     

自适应广义滑模观测器之状态估计和故障重构

针对一类同时具有执行机构故障和输出扰动的不确定性系统,提出了一种自适应广义滑模观测器,实现系统状态的估计和执行机构故障的重构.首先,进行系统变换及状态增广构成一类奇异系统,使得执行机构故障和输出扰动解耦,且输出扰动成为增广系统的状态之一;随后,受未知输入观测器和滑模观测器的启发,设计了一种广义滑模观测器,放宽了传统方法对输出维数的严格约束,并通过融入自适应技术放宽了对故障和不确定性上界已知的要求;最后,利用等效误差注入的思想实现故障重构.针对可重复使用运载器再入段进行的仿真实例,验证了所提方法的有效性.     

Development and application of sliding mode LPV fault reconstruction schemes for the ADDSAFE Benchmark

This paper describes the development and the evaluation of a robust sliding mode observer fault detection scheme applied to an aircraft benchmark problem as part of the ADDSAFE project. The ADDSAFE benchmark problem which is considered in this paper is the yaw rate sensor fault scenario. A robust sliding mode sensor fault reconstruction scheme based on an LPV model is presented, where the fault reconstruction signal is obtained from the so-called equivalent output error injection signal associated with the observer. The development process includes implementing the design using AIRBUS׳s the so-called SAO library which allows the automatic generation of flight certifiable code which can be implemented on the actual flight control computer. The proposed scheme has been subjected to various tests and evaluations on the Functional Engineering Simulator conducted by the industrial partners associated with the ADDSAFE project. These were designed to cover a wide range of the flight envelope, specific challenging manoeuvres and realistic fault types. The detection and isolation logic together with a statistical assessment of the FDD schemes are also presented. Simulation results from various levels of FDD developments (from tuning, testing and industrial evaluation) show consistently good results and fast detection times.     

Disturbance decoupled fault reconstruction using sliding mode observers

This paper investigates and presents conditions that guarantee disturbance decoupled fault reconstruction using sliding mode observers, which are less stringent than those of previous work, and show that disturbance reconstruction is not necessary. An aircraft model validates the ideas proposed in this paper. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

New results in robust actuator fault reconstruction for linear uncertain systems using sliding mode observers

This paper presents a robust actuator fault reconstruction scheme for linear uncertain systems using sliding mode observers. In existing work, fault reconstruction via sliding mode observers is limited to either linear certain systems subject to unknown inputs, relative degree one systems or a specific class of relative degree two systems. This paper presents a new method that is applicable to a wider class of systems with relative degree higher than one, and can also be used for systems with more unknown inputs than outputs. The method uses two sliding mode observers in cascade. Signals from the first observer are processed and used to drive the second observer. Overall, this results in actuator fault reconstruction being feasible for a wider class of systems than using existing methods. A simulation example verifies the claims made in this paper. Copyright © 2007 John Wiley & Sons, Ltd.     

Robust estimation of voltage parameters via a sliding mode observer

Grid voltage parameters are essential for the real-time control and protection in power systems. Current approaches mainly focus on the phase-locked loop methods, but which are slow and sensitive to voltage variations and disturbances. In this paper, the estimation of grid voltage parameters is recast as an observer design problem. A second-order sliding mode observer (SMO) is designed to estimate the grid voltage parameters based on the exosystem model. Moreover, the asymptotic stability of the closed-loop SMO is proved. Simulation and experimental results are presented to illustrate the effectiveness of the proposed approach, which achieves fast response and accurate estimation     

Fault tolerant sliding mode control for T-S fuzzy stochastic time-delay system via a novel sliding mode observer approach

In this paper, a fault estimation and fault-tolerant control problem for a class of T-S fuzzy stochastic time-delay systems with actuator and sensor faults is investigated. A novel sliding mode observer is proposed, which can simultaneously estimate the system states, actuator and sensor faults with good accuracy. Based on the state and actuator fault estimation, a new sliding mode control scheme is developed, which can effectively eliminate the influence of actuator fault. Sufficient conditions for the existence of the proposed observer and fault-tolerant sliding mode controller are provided in terms of linear matrix inequality, and moreover, the reachability of the sliding mode surface can be guaranteed under the proposed control scheme. The propose sliding mode observer and fault-tolerant sliding mode controller can overcome the restrictive assumption that the input matrix of all local modes is the same. Finally, a numerical example is provided to verify the effectiveness of the proposed sliding mode observer and fault-tolerant sliding mode control technique.     

基于鲁棒自适应滑模观测器的多故障重构

针对一类不确定非线性系统, 基于滑模观测器研究执行器和传感器同时故障时的鲁棒重构问题. 引入线性变换矩阵并添加后置滤波器构建增维系统, 综合??_∞ 控制将鲁棒滑模观测器增益矩阵设计方法, 转化为LMI 约束下的多目标凸优化问题. 在滑模增益中添加了自适应律, 确保状态估计误差渐近稳定, 同时滑模运动经有限时间到达滑模面, 在此基础上给出执行器和传感器故障同时重构算法. 最后通过数值算例表明了所提出方法的有效性.

     

A sliding mode observer-based strategy for fault detection,isolation, and estimation in a class of Lipschitz nonlinear systems

This article investigates the design and application of a sliding mode observer (SMO) strategy for actuator as well as sensor fault detection, isolation, and estimation (FDIE) problem for a class of uncertain Lipschitz nonlinear systems. Actuator FDIE is addressed by regrouping the system's inputs into a structure suitable for SMO design. Similarly, by filtering the regrouped outputs, a similar system structure can be developed for sensor FDIE problem. Once in the suitable form and under certain assumptions, nonlinear SMOs are proposed for actuator and sensor FDIE. A systematic LMI-based design approach for the proposed SMO is presented. Additionally, the article addresses four problems, namely: (P1) What are the conditions for isolating single and/or multiple faults? (P2) What is the maximum number of faults that can be isolated simultaneously? (P3) How should one design SMO-based FDI approach in order to achieve multiple fault isolation using as few observers as possible? (P4) How can one estimate the shape of the faults? To solve the above problems, a new concept called fault isolation index (FIX) is proposed for actuator and sensor FDIE. It is proved that fault isolation can only be achieved if FIX?≠?0, and also that the maximum number of faults that can be isolated is equal to FIX. Using the proposed fault isolation strategy and by treating some healthy inputs or outputs as unknown inputs, a systematic FDIE design scheme using a bank of nonlinear SMOs, which provides a solution for the four problems is provided. An example is used to illustrate the proposed ideas. The simulation results show that the proposed FDIE scheme can successfully detect and isolate both slowly and fast-changing actuator faults. It is also shown that accurate estimation of actuator faults can be achieved.     

Observer based fault reconstruction schemes using terminal sliding modes

ABSTRACT

Two state/fault estimation methods using terminal sliding mode (TSM) concepts are presented in this paper. In contrast with conventional sliding modes, which guarantee asymptotic convergence of non-output estimation errors and faults, TSMs enable finite time convergence of estimation errors for faults and all the states. The minimum-phase condition, as a common condition required for fault estimation, is released in the proposed methods. Method I implements fractional power of the so-called switching term to make it robust against matched faults and disturbances. Compared with previous terminal scheme, this method covers a wider class of systems. In Method II, fractional power sliding variable is considered to achieve finite time convergence of estimation errors and their derivatives. In contrast with Method I, this approach is also robust against unmatched faults. Finally, the methods are applied to an unstable aircraft model.     

Interpolating sliding mode observer for a ball and beam system

ABSTRACT

A principle of interpolating sliding mode observer is introduced in this paper. The observer incorporates multiple linear observers through interpolation of multiple estimates, which is treated as a type of adaptation. The principle is then applied to the ball and beam system for observation of the slope of the beam from the measurement of the ball position. The linearised model of the ball and beam system using multiple linearisation points is developed. The observer dynamics implemented in Matlab/Simulink Real Time Workshop environment. Experiments conducted on the ball and beam experimental setup demonstrate excellent performance of the designed novel interpolating (adaptive) observer.     

On robust regulation via sliding mode for nonlinear systems

A robust control scheme for the output tracking of nonlinear systems is proposed. The scheme is based on the nonlinear regulator theory and the sliding mode approach. It is shown that if perturbations and/or uncertainties appear on the system, the sliding mode controller is able to perform approximate asymptotic tracking, in the sense that the output tracking error remains bounded, provided the upper bounds of the uncertain terms are known.     

Extended results on robust state estimation and fault detection

A common requirement implicit in the current methods for the design of robust state estimators and robust fault detection filters is that the first Markov matrix must be non-zero, and indeed, full rank. We relax both of these restrictions in this paper to allow the applicability to a wider range of systems. The extended results are then applied to an aircraft fault detection for which the restrictive condition is not satisfied.     

New results in robust functional state estimation using two sliding mode observers in cascade

This paper presents a functional observer scheme using two sliding mode observers in cascade. A coordinate transformation is performed on the system such that existing sliding mode observer theory can be directly applied to achieve functional state estimation. The necessary and sufficient existence conditions for the scheme (in terms of the original system matrices) are also investigated, and they are found to be less stringent than earlier work on functional state estimation using one sliding mode observer; this could have benefits in terms of cost and simplicity. A numerical example verifies the effectiveness of the scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive-gain second-order sliding mode observer design for switching power converters

In this paper, an adaptive-gain, Second Order Sliding Mode (SOSM) observer for multi-cell converters is designed by considering it as a type of hybrid system. The objective is to reduce the number of voltage sensors by estimating the capacitor voltages from measurement of the load current. The proposed observer is proven to be robust in the presence of perturbations with unknown boundaries. As the states of the system are only partially observable, a recent concept known as Z(T_N)-observability is used to address the switching behavior. Multi-rate simulation results demonstrate the effectiveness and the robustness of the proposed observer with respect to output measurement noise and system uncertainty (load variations).     

采用鲁棒滑模观测器实现一类混沌系统的同步

提出一种鲁棒滑模观测器，并应用于一类混沌系统的同步，该鲁棒滑模观测器通过滑模与相应的控制策略来实现，可调整观测器跟踪系统状态的收敛速度，实现两个混沌系统的同步，将所提出的鲁棒滑模状态观测器用于一类存在参数摄动和／或干扰的混沌系统的同步具有鲁棒性，该鲁棒滑模状态观测器不仅能实现低维的混沌系统的同步，而且能实现超混沌系统的同步，以Chua’s电路和超混沌Roessler系统为例给出了设计过程和仿真实验，其结果验证了所提出方法的有效性。     

Extremum seeking with sliding mode gradient estimation and asymptotic regulation for a class of nonlinear systems

This paper presents a model-based extremum seeking approach for a class of single-input–single-output nonlinear systems, with the analytic form of the performance function unknown a priori. We focus on a practically implementable design with robustness to model uncertainties and disturbances. A discrete-time sliding mode gradient estimator is developed for estimating the gradient of the performance profile. Based on the estimate, a variable structure output feedback regulator is proposed to enforce the system states toward the optimal trajectory. We analyze convergence conditions of the switching system toward a neighborhood of the optimal trajectory, and establish an ultimate bound on the size of the neighborhood. The robustness of the proposed controller is discussed with respect to measurement noise.     

Robust sliding mode observer-based actuator fault detection and isolation for a class of nonlinear systems

In this article, an actuator fault detection and isolation scheme for a class of nonlinear systems with uncertainty is considered. The uncertainty is allowed to have a nonlinear bound which is a general function of the state variables. A sliding mode observer is first established based on a constrained Lyapunov equation. Then, the equivalent output error injection is employed to reconstruct the fault signal using the characteristics of the sliding mode observer and the structure of the uncertainty. The reconstructed signal can approximate the system fault signal to any accuracy even in the presence of a class of uncertainty. Finally, a simulation study on a nonlinear aircraft system is presented to show the effectiveness of the scheme.     

一种新颖的鲁棒模糊滑模观测器设计及干扰重构方法

针对一类由T-S模糊模型描述的不确定非线性系统,提出一种新颖的鲁棒模糊滑模观测器设计和干扰重构方法.首先,给出一种T-S模糊模型的等价形式.其次,在考虑滑模匹配条件不满足、状态不可测的情况下,利用高增益估计器构造辅助变量.为避免其峰化问题,提出基于高增益估计器的鲁棒滑模观测器.然后,基于所提出的等价形式,给出一类不确定非线性系统的鲁棒模糊滑模观测器设计方法.并证明其不但对系统的未知干扰具有鲁棒性,而且能保证状态估计残差在有限的时间内收敛于任意小的邻域,并可应用等价输出误差介入原理重构出系统的干扰.最后,将该方法应用于双关节机械臂的控制仿真实验.结果表明所提方法的有效性.     

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.