Sliding-mode observers for systems with unknown inputs: A high-gain approach

Sliding-mode observers can be constructed for systems with unknown inputs if the so-called observer matching condition is satisfied. However, most systems do not satisfy this condition. To construct sliding-mode observers for systems that do not satisfy the observer matching condition, auxiliary outputs are generated using high-gain approximate differentiators and then employed in the design of sliding-mode observers. The state estimation error of the proposed high-gain approximate differentiator based sliding-mode observer is shown to be uniformly ultimately bounded with respect to a ball whose radius is a function of design parameters. Finally, the unknown input reconstruction using the proposed observer is analyzed and then illustrated with a numerical example.     

UIO design for singular delayed LPV systems with application to actuator fault detection and isolation

In this paper, the unknown input observer (UIO) design for singular delayed linear parameter varying (LPV) systems is considered regarding its application to actuator fault detection and isolation. The design procedure assumes that the LPV system is represented in the polytopic framework. Existence and convergence conditions for the UIO are established. The design procedure is formulated by means of linear matrix inequalities (LMIs). Actuator fault detection and isolation is based on using the UIO approach for designing a residual generator that is completely decoupled from unknown inputs and exclusively sensitive to faults. Fault isolation is addressed considering two different strategies: dedicated and generalised bank of observers’ schemes. The applicability of these two schemes for the fault isolation is discussed. An open flow canal system is considered as a case study to illustrate the performance and usefulness of the proposed fault detection and isolation method in different fault scenarios.     

On non-linear unknown input observers–applied to lateral vehicle velocity estimation on banked roads

Unknown input observers (UIOs) are observers that have stable error dynamics that are independent of unknown inputs. This paper studies such observers for non-linear systems, and shows that the error dynamics for a non-linear UIO has the same structure as the error dynamics of a non-linear observer without unknown inputs. This result is first used to provide synthesis inequalities for UIOs for a class of non-linear systems, and secondly, to inspire the design of an observer for estimation of vehicle lateral velocity on banked roads.     

匹配条件不满足时线性系统未知输入观测器设计

针对一类不满足观测器匹配条件的线性系统,讨论了未知输入观测器设计方法.首先,为了突破观测器匹配条件的限制,提出了一种与未知输入相对阶无关的辅助输出构造方法.然后,把未知输入看作系统状态的一部分,将原系统转化为一个不含未知输入的增维线性描述系统.针对这样的系统转化,对一系列等价前提条件进行了详细的讨论.之后,针对该增维线性描述系统,构造Luenberger观测器来估计原系统的状态和未知输入.同时,借助于高阶滑模微分器,来估计辅助输出中的未知信号.最后,对一个单连杆柔性机械手模型进行了数值仿真,仿真结果表明了方法的有效性.     

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.     

Robust Unknown Input Observer Design for Linear Uncertain Time Delay Systems with Application to Fault Detection

In this paper, a novel approach is proposed to design a robust fault detection observer for uncertain linear time delay systems. The system is composed of both norm‐bounded uncertainties and exogenous signals (noise, disturbance, and fault) which are considered to be unknown. The main contribution of this paper is to present unknown input observer (UIO)‐based fault detection system which shows the maximum sensitivity to fault signals and the minimum sensitivity to other signals. Since the system contains uncertainty terms, an H_∞ model‐matching approach is used in design procedure. The reference residual signal generator system is designed so that the fault signal has maximum sensitivity while the exogenous signals have minimum sensitivity on the residual signal. Then, the fault detection system is designed by minimizing the estimation error between the reference residual signal and the UIO residual signal in the sense of H_∞ norm. A sufficient condition for the existence of such a filter is exploited in terms of certain linear matrix inequalities (LMIs). Application of the proposed method in a numerical example and an engineering process are simulated to demonstrate the effectiveness of the proposed algorithm. Simulation results show the validity of the proposed approach to detect the occurrence of faults in the presence of modeling errors, disturbances, and noise.     

A note on interval observer design for unknown input estimation

This paper addresses the problem of interval observer design for unknown input estimation in linear time-invariant systems. Although the problem of unknown input estimation has been widely studied in the literature, the design of joint state and unknown input observers has not been considered within a set-membership context. While conventional interval observers could be used to propagate with some additional conservatism, unknown inputs by considering them as disturbances, the proposed approach allows their estimation. Under the assumption that the measurement noise and the disturbances are bounded, lower and upper bounds for the unmeasured state and unknown inputs are computed. Numerical simulations are presented to show the efficiency of the proposed approach.     

Unknown input observer for state affine systems: A necessary and sufficient condition

The problem of designing an unknown input observer for linear systems and its application to fault detection is widely studied in the literature. For nonlinear systems, only subclasses of nonlinear systems and sufficient conditions have been stated. In this paper an unknown input observer design for state affine systems is considered. Based on the geometric approach, a necessary and sufficient condition is given for the existence of an unknown input observer.     

Sliding-mode observers for nonlinear systems with unknown inputs and measurement noise

This paper deals with the design of observers for Lipschitz nonlinear systems with not only unknown inputs but also measurement noise when the observer matching condition is not satisfied. First, an augmented vector is introduced to construct an augmented system, and an auxiliary output vector is constructed such that the observer matching condition is satisfied and then a high-gain sliding mode observer is considered to get the exact estimates of both the auxiliary outputs and their derivatives in a finite time. Second, for nonlinear system with both unknown inputs and measurement noise, an adaptive robust sliding mode observer is developed to asymptotically estimate the system’s states, and then an unknown input and measurement noise reconstruction method is proposed. Finally, a numerical simulation example is given to illustrate the effectiveness of the proposed methods.     

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.     

A novel approach to the design of unknown input observers

A novel state estimator design scheme for linear dynamical systems driven by partially unknown inputs is presented. It is assumed that there is no information available about the unknown inputs, and thus no prior assumption is made about the nature of these inputs. A simple approach for designing a reduced-order unknown input observer (UIO) with pole-placement capability is proposed. By carefully examining the dynamic system involved and simple algebraic manipulations, it is possible to rewrite equations eliminating the unknown inputs from part of the system and to put them into a form where it could be partitioned into two interconnected subsystems, one of which is directly driven by known inputs only. This makes it possible to use a conventional Luenberger observer with a slight modification for the purpose of estimating the state of the system. As a result, it is also possible to state similar necessary and sufficient conditions to those of a conventional observer for the existence of a stable estimator and also arbitrary placement of the eigenvalues of the observer. The design and computational complexities involved in designing UIOs are greatly reduced in the proposed approach     

Unknown input observers for 2D state-space models

In this paper, dead-beat unknown input observers (UIOs) for two-dimensional (2D) state-space models are investigated. Dead-beat UIOs are observers which produce an exact estimate of the original system state trajectory, after a finite number of evolution steps, independently of the system and observer initial conditions and of the unknown disturbances that affect the system functioning. Necessary and sufficient conditions for the existence of dead-beat UIOs are provided, as well as a parameterization of all dead-beat UIO transfer matrices. Comparisons with Luenberger-type UIOs are also carried out, and the extension of the paper results to the case of asymptotic UIOs with a given rate of convergence and to Roesser models are finally discussed.     

状态估计与未知输入和可测噪声同时重构方法

针对一类不确定线性系统,讨论了状态估计及未知输入和可测噪声重构方法。首先,对仅具有未知输入的线性系统,讨论了观测器匹配条件不满足前提下的状态估计和未知输入重构问题;通过设计降维观测器和高阶滑模观测器,提出一种未知输入代数重构方法;然后,将以上结论上升到具有未知输入和可测噪声的线性系统,以此提出了状态估计及未知输入和可测噪声同时重构的方法;最后,通过对飞行器模型进行仿真,验证了所提出方法的有效性。     

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.     

基于辅助输出的线性系统状态和未知输入同时估计方法

在未知输入观测器匹配条件不满足的情况下, 针对一类线性时不变系统, 研究了同时估计系统 状态和未知输入的问题. 首先, 基于可测输出对未知输入的相关度的概念, 给出了辅助输出 的构造方法, 使得匹配条件得以满足. 为了处理辅助输出中的未知信息, 提出了一种高增益 观测器设计方法, 它不仅能估计辅助输出, 而且还能估计辅助输出的导数. 然后, 基于辅助 输出的估计值, 提出了一种降维观测器设计方法, 可以在不受未知输入影响的情况下估计系统 的状态; 接下来, 基于状态和辅助输出及其导数的估计值, 给出了未知输入估计. 最后, 对一个五 阶系统进行了数字仿真, 仿真结果表明所提出的方法是有效的.     

一种基于最优未知输入观测器的故障诊断方法

针对含有未知输入干扰和噪音的不确定动态系统,使用全阶未知输入观测器(Unknown input observer, UIO)来消除干扰项,实现状态估计, 结合Kalman滤波器算法来求解状态反馈矩阵,以使得输出残差信号的协方差最小,从而增强系统对噪声的鲁棒性,实现了 一种基于最优未知输入观测器的残差产生器.采用极大似然比(Generalized likelihood ratio, GLR)的方法对残差信号进行评估,通过设定的阈值来提高诊断率. 最后以风力发电机组传动系统出现加性传感器故障和乘性传感器故障为例, 进行了残差信号的仿真,仿真结果说明了该方法的有效性.     

Robust Fault Detection and Isolation Based on Finite-frequency H?/H∞ Unknown Input Observers and Zonotopic Threshold Analysis

This work proposes a robust fault detection and isolation scheme for discrete-time systems subject to actuator faults, in which a bank of H_?/H_∞ fault detection unknown input observers (UIOs) and a zonotopic threshold analysis strategy are considered. In observer design, finite-frequency H_? index based on the generalized Kalman-Yakubovich-Popov lemma and H_∞ technique are utilized to evaluate worst-case fault sensitivity and disturbance attenuation performance, respectively. The proposed H_?/H_∞ fault detection observers are designed to be insensitive to the corresponding actuator fault only, but sensitive to others. Then, to overcome the weakness of predefining threshold for FDI decision-making, this work proposes a zonotopic threshold analysis method to evaluate the generated residuals. The FDI decision-making relies on the evaluation with a dynamical zonotopic threshold. Finally, numerical simulations are provided to show the feasibility of the proposed scheme.      

基于UIOs的风力机传动系统多故障诊断

风力机故障诊断通过对机组运行数据进行提取、估计,以辨别出故障并获得故障信息.但目前风力机故障检测大多考虑单个故障发生的情况,而实际工程中无法避免多故障同时发生.通过设计未知输入观测器组,解决了风力机传动系统执行器和传感器的多故障诊断及隔离.针对不同故障类型各设计一组未知输入观测器.观测器组中的每个未知输入观测器产生一个残差信号,该残差不敏感于相应故障,但敏感于其他故障.通过对比观测器组中的残差信号可实现单一或多故障诊断.建立风力机传动系统故障模型,仿真分析得出该方法具有可行性.