Robust fault detection in linear systems based on PI observers

A parametric approach for robust fault detection in linear systems with unknown disturbances is presented. The residual is generated using full-order proportional-integral (PI) observers. The approach is based on a result for PI observer design recently proposed. In terms of the design degrees of freedom provided by the parametric PI observer design and a group of introduced parameter vectors, a sufficient and necessary condition for PI observer design with disturbance decoupling is established. By properly constraining the design parameters according to this proposed condition, the effect of the disturbance to the residual signal is decoupled, and a simple algorithm is presented. The presented approach offers all the degrees of design freedom. A numerical example illustrates the effect of the proposed approach.     

鲁棒Luenberger观测器设计

观测器控制系统中的观测器条件是系统的状态观测值渐近收敛于系统真实状态的根本 条件.本文首先提出了Luenberger观测器设计的一种参数方法,然后根据使观测器条件误差 为最小的准则,考虑了具有参数摄动的系统的鲁棒Luenberget观测器设计问题,给出了简单、 有效的算法.仿真结果说明了本文方法的有效性.     

Robust fault detection in linear systems based on full-order state observers

A parametric approach to robust fault detection in linear systems with unknown disturbances is presented. The residual is generated using full-order state observers （FSO）. Based on an analytical solution to a type of Sylvester matrix equations, the parameterization of the observer gain matrix is given. In terms of the design degrees of freedom provided by the parametric observer design and a group of introduced parameter vectors, a sufficient and necessary condition for fullorder state observer design with disturbance decoupling is then established. By properly constraining the design parameters according to this proposed condition, the effect of the disturbance on the residual signal is also decoupled, and a simple algorithm is developed. The presented approach offers all the degrees of design freedom. Finally, a numerical example illustrates the effect of the proposed approach.     

Robust fault detection in linear systems based on full-order state observers

A parametric approach to robust fault detection in linear systems with unknown disturbances is presented. The residual is generated using full-order state observers (FSO). Based on an analytical solution to a type of Sylvester matrix equations, the parameterization of the observer gain matrix is given. In terms of the design degrees of freedom provided by the parametric observer design and a group of introduced parameter vectors, a sufficient and necessary condition for fullorder state observer design with disturbance decoupling is then established. By properly constraining the design parameters according to this proposed condition, the effect of the disturbance on the residual signal is also decoupled, and a simple algorithm is developed. The presented approach offers all the degrees of design freedom. Finally, a numerical example illustrates the effect of the proposed approach.     

线性系统对偶Luenberger观测器设计

提出了线性系统对偶Luenberger观测器的参数化设计方法.基于一类广义Sylvester矩阵方程的显式参数化解,根据一些自由参数给出了对偶Luenberger观测器所有增益矩阵的参数化表达.该设计方法能提供所有的设计自由度,它们能进一步用来实现系统的其他性能指标.数值例子显示了该方法的设计过程.     

Zonotopic fault detection observer design for Takagi–Sugeno fuzzy systems

This paper considers zonotopic fault detection observer design in the finite-frequency domain for discrete-time Takagi–Sugeno fuzzy systems with unknown but bounded disturbances and measurement noise. We present a novel fault detection observer structure, which is more general than the commonly used Luenberger form. To make the generated residual sensitive to faults and robust against disturbances, we develop a finite-frequency fault detection observer based on generalised Kalman–Yakubovich–Popov lemma and P-radius criterion. The design conditions are expressed in terms of linear matrix inequalities. The major merit of the proposed method is that residual evaluation can be easily implemented via zonotopic approach. Numerical examples are conducted to demonstrate the proposed method.     

一种鲁棒故障检测与分离的参数化方法

针对具有未知干扰输入的多变量线性系统,提出一种鲁棒故障检测与分离的完全参数化方法。利用最近的结果,基于Luenberger未知输入观测器矩阵的特征值及一组自由参数向量,分别给出了系统干扰解耦和故障分离的充要条件。通过适当选择满足一些约束的自由参数,仅使用单一观测器实现了鲁棒故障检测与分离设计。该方法提供了所有设计自由度。一个数值例子证明了该方法的有效性。     

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     

采样数据系统最优诊断观测器设计

研究采样数据(sampled-data,SD)系统最优诊断观测器的直接设计方法.首先从传递函数角度分析一般离散时间系统诊断观测器的Luenberger条件,由此构造出SD诊断观测器,并推导出其混杂动态关系.然后将SD故障检测问题定义为一个特定的比值型优化问题,并应用互内外分解法和代数方法构制其最优诊断观测器,使得产生的离散时间残差对连续时间未知输入具有鲁棒性,但对故障却是敏感的.仿真结果验证了所提设计方法的有效性.     

矩阵方程AX-EXF=BY的通解及其应用

给出矩阵方程AX—EXY=BY的一个完全解析的、具有显式表达式和完全自由度的参数解(X,Y)．这里假设矩阵束(E,A B)为R-能控的,F为任意的方阵．相比于现有结论,求解算法不要求矩阵A和F具有特殊的形式,且对它们的特征值没有任何的限制,此外,本文给出的通解还具有结构简洁的特点,作为一个应用,给出了广义系统正常Luenberger函数观测器的一种参数化的设计方法,算例证明了方法的有效性．     

A robust controller for trajectory tracking of a DC motor pendulum system

This work presents a solution to the output feedback trajectory tracking problem for an uncertain DC motor pendulum system under the effect of an unknown bounded disturbance. The proposed algorithm uses a Proportional Derivative (PD) controller plus a novel on-line estimator of the unknown disturbance. The disturbance estimator is obtained by coupling a standard second-order Luenberger observer with a third-order sliding modes differentiator. The Luenberger observer provides estimates of the motor angular position and velocity. Moreover, an ideal disturbance estimator in terms of the Luenberger observer error and its first and second time derivatives is obtained from the observer error formulae; these time derivatives are not available from measurements. Subsequently, the sliding modes third-order differentiator allows obtaining estimates of these time derivatives in finite time. The estimates replace the real values of the first and second time derivatives in the ideal disturbance estimator thus producing a practical disturbance estimator, and also permit obtaining an estimate of the motor angular velocity. A depart from previous approaches is the fact that the disturbance is not directly estimated by the Luenberger observer or the third-order differentiator. Numerical simulations and real-time experiments validate the effectiveness of the proposed approach.     

Robust fault diagnosis scheme in a class of nonlinear system based on UIO and fuzzy residual

In this study, a novel robust fault diagnosis scheme is developed for a class of nonlinear systems when both fault and disturbance are considered. The proposed scheme includes both component and sensor fault with nonlinear system that transferred to nonlinear Takagi-Sugeno (T-S) model. It considers a larger category of nonlinear system when fuzzification is used for only nonlinear distribution matrices. In fact the proposed method covers nonlinear systems could not transform to linear T-S model. This paper studies the problem of robust fault diagnosis based on two fuzzy nonlinear observers, the first one is a fuzzy nonlinear unknown input observer (FNUIO) and the other is a fuzzy nonlinear Luenberger observer (FNLO). This approach decouples the faulty subsystem from the rest of the system through a series of transformations. Then, the objective is to design FNUIO to guarantee the asymptotic stability of the error dynamic using the Lyapunov method; meanwhile, FNLO is designed for faulty subsystem to generate fuzzy residual signal based on a quadratic Lyapunov function and some matrices inequality convexification techniques. FNUIO affects only the fault free subsystem and completely removes any unknown inputs such as disturbances when residual signal is generated by FNLO is affected by component or sensor fault. This novelty and using nonlinear system in T-S model make the proposed method extremely effective from last decade literature. Sufficient conditions are established in order to guarantee the convergence of the state estimation error. Thus, a residual generator is determined on the basis of LMI conditions such that the estimation error is completely sensitive to fault vector and insensitive to the unknown inputs. Finally, an numerical example is given to show the highly effectiveness of the proposed fault diagnosis scheme.     

线性系统的干扰解耦观测器设计

此文提出线性系统的Luenberger函数观测器关于干扰解耦的条件,指出它与环路复现 (LTR)的关系.并结合Luenberger观测器设计的一种参数化方法,给出了线性系统干扰解 耦Luenberger观测器的一种简单、有效的设计方法.     

State estimation for linear hybrid systems with periodic jumps and unknown inputs

In order to solve the state estimation problem for linear hybrid systems with periodic jumps and unknown inputs, some hybrid observers are proposed. The proposed observers admit a Luenberger‐like structure and the synthesis is given in terms of linear matrix inequalities (LMIs). Therefore, the proposed observer designs are completely constructive and provide some input‐to‐state stability properties with respect to unknown inputs. It is worth mentioning that the structure of the hybrid observers, as well as the structure of the LMIs, depends on some observability properties of the flow and jump dynamics, respectively. Then, in order to compensate the effect of the unknown inputs, a hybrid sliding‐mode observer is added to the Luenberger‐like observer structure, providing exponential convergence to zero of the state estimation error despite certain class of unknown inputs. The existence of the hybrid observers and the unknown input hybrid observer is guaranteed if and only if the hybrid system is observable and strongly observable, respectively. Some numerical examples illustrate the feasibility of the proposed estimation approach.     

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.     

基于诊断观测器的最优事件触发故障检测

提出一种基于诊断观测器的最优事件触发故障检测方法.首先,针对自适应混合事件触发下的远程监控系统,发展一种数值代数结合型的低阶诊断观测器参数矩阵计算方法,以满足残差生成中的Luenberger条件;然后,通过评估事件触发传输误差、干扰和故障对残差信号的影响,构建$H_{\infty     

On the application of the {1}-inverse to the design of general structured unknown input observers

This paper presents a concise and straightforward formulation of the unknown input observer (UIO) problem based on the general structured observer. By employing the simplest generalized inverse of matrices, the {1}-inverse, we develop constructive design procedures for the UIO design that provide necessary and sufficient conditions for both full-order and reduced-order general structured UIOs. Moreover, corresponding configurations for continuous-time systems are also derived, and consequently this paper renders the complete solutions for general structured UIO design. Furthermore, we show that the general structured UIO is structurally and numerically equivalent to the UIO in the configuration of Luenberger observer. Examples are included to illustrate the validity of the proposed methodology.     

矩阵方程AX-EXF=BY的通解及其应用

给出矩阵方程 AX-EXY=BY的一个完全解析的、具有显式表达式和完全自由度的参数解 (X,Y) .这里假设矩阵束 (E,A,B) 为R-能控的, F为任意的方阵.相比于现有结论,求解算法不要求矩阵A和F具有特殊的形式,且对它们的特征值没有任何的限制.此外,本文给出的通解还具有结构简洁的特点.作为一个应用,给出了广义系统正常Luenberger函数观测器的一种参数化的设计方法.算例证明了方法的有效性.