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.     

Unknown inputs observer for a class of nonlinear uncertain systems: An LMI approach

This paper deals with the simultaneous estimation of states and unknown inputs for a class of Lipschitz nonlinear systems using only the measured outputs. The system is assumed to have bounded uncertainties that appear on both the state and output matrices. The observer design problem is formulated as a set of linear constraints which can be easily solved using linear matrix inequalities (LMI) technique. An application based on manipulator arm actuated by a direct current (DC) motor is presented to evaluate the performance of the proposed observer. The observer is applied to estimate both state and faults.     

非线性摄动系统的鲁棒故障诊断滤波器设计ILMI算法

The robust fault detection filter design for uncertain linear systems with nonlinear perturbations is formulated as a two-objective optimization problem. Solvable conditions for the exis- tence of such a robust fault detection filter are given in terms of matrix inequalities (MIs), which can be solved by applying iterative linear matrix inequality (ILMI) techniques. Particularly, compared with two existing LMI methods, the developed algorithm is more generalized and less conservative. An illustrative example is given to show the effectiveness of the proposed method.     

Observer design and output feedback stabilization for linear singular time-delay systems with unknown inputs

The design of a functional observer and reduced-order observer with internal delay for linear singular timedelay systems with unknown inputs is discussed. The sufficient conditions of the existence of observers, which are normal linear time-delay systems, and the corresponding design steps are presented via linear matrix inequality（LMI）. Moreover, the observer-based feedback stabilizing controller is obtained. Three examples are given to show the effectiveness of the proposed methods.     

Robust H ∞ filter design for time-delay systems with saturation

This paper investigates the H∞ filtering problem for a class of linear continuous-time systems with both time delay and saturation. Such systems have time delay in their state equations and saturation in their output equations, and their process and measurement noises have unknown statistical characteristics and bounded energies. Based on the Lyapunov-Krasovskii stability theorem and the linear matrix inequalities (LMIs) technique, a generalized dynamic filter architecture is proposed, and a filter design method is developed. The linear H∞ filter designed by the method can guarantee the H∞ performance. The parameters of the designed filter can be obtained by solving a kind of LMI. An illustrative example shows that the design method proposed in this paper is very effective.     

Observer-based robust stabilization for uncertain systems with unknown time-varying delay

This paper focuses on the problem of robust stabilization for a class of linear systems with uncertain parameters and time varying delays in states. The parameter uncertainty is continuous, time varying, and norm-bounded. The state delay is unknown and time varying. The states of the system are not all measurable and an observer is constructed to estimate the states. If a linear matrix inequality (LMI) is solvable, the gains of the controller and observer can be obtained from the solution of the LMI. The observer and controller are dependent on the size of time delay and on the size of delay derivative. Finally, an example is given to illustrate the effectiveness of the proposed control method.     

Development of nonlinear disturbance observer based control and nonlinear PID: A personal note

This paper gives an overview of early development of nonlinear disturbance observer design technique and the disturbance observer based control (DOBC) design. Some critical points raised in the development of the methods have been reviewed and discussed which are still relevant for many researchers or practitioners who are interested in this method. The review is followed by the development of a new type of nonlinear PID controller for a robotic manipulator and its experimental tests. It is shown that, under a number of assumptions, the DOBC consisting of a predictive control method and a nonlinear disturbance observer could reduce to a nonlinear PID with special features. Experimental results show that, compared with the predictive control method, the developed controller significantly improves performance robustness against uncertainty and friction. This paper may trigger further research and interests in the development of DOBC and related methods, and building up more understanding between this group of control methods with comparable ones (particularly control methods with integral action).     

Prediction method for energy consumption per ton of fused magnesium furnaces using data driven and mechanism model

This paper gives an overview of early development of nonlinear disturbance observer design technique and the disturbance observer based control (DOBC) design. Some critical points raised in the development of the methods have been reviewed and discussed which are still relevant for many researchers or practitioners who are interested in this method. The review is followed by the development of a new type of nonlinear PID controller for a robotic manipulator and its experimental tests. It is shown that, under a number of assumptions, the DOBC consisting of a predictive control method and a nonlinear disturbance observer could reduce to a nonlinear PID with special features. Experimental results show that, compared with the predictive control method, the developed controller significantly improves performance robustness against uncertainty and friction. This paper may trigger further research and interests in the development of DOBC and related methods, and building up more understanding between this group of control methods with comparable ones (particularly control methods with integral action).     

Observer-based H-infinity output feedback control with feedback gain and observer gain variations for Delta operator system

Considering that the controller feedback gain and the observer gain are of additive norm-bounded variations, a design method of observer-based H-infinity output feedback controller for uncertain Delta operator systems is proposed in this paper. A sufficient condition of such controllers is presented in linear matrix inequality （LMI） forms. A numerical example is then given to illustrate the effectiveness of this method, that is, the obtained controller guarantees the closed-loop system asymptotically stable and the expected H-infinity performance even if the controller feedback gain and the observer gain are varied.     

非线性系统观测器的设计:LMI方法

对满足Lipschitz条件的非线性系统给出了全维、降维观测器存在的充分条件并分别进行了证明,重点设计了新形式的降维状态观测器,观测器增益矩阵的获得完全取决于线性矩阵不等式(LMI)的解的情况,应用线性矩阵不等式工具箱使得设计更加方便,消除了增益矩阵选取的盲目性.通过对实际模型的仿真分析可知,两种观测器的状态估计误差均能渐近收敛到零,表明了该方法的有效性.     

时滞Lipschitz非线性系统观测器设计

给出了满足Lipschitz条件的离散非线性时滞系统的全维、降维观测器的设计方法和误差收敛的充分条件,并分别进行了证明.全维观测器通过将带有非线性项的矩阵不等式转化为两步线性矩阵不等式解出两个增益矩阵.降维观测器则通过解线性矩阵不等式(LMI)方便地获得观测器的增益矩阵,消除了增益矩阵选取的盲目性.通过对同一模型的仿真分析,两种观测器的状态估计误差均能迅速收敛到0,表明了所提出方法的有效性.     

Robust reduced-order sliding mode observer design

In this article, a triple state and output variable transformation-based method combined with linear matrix inequality (LMI) techniques to design a new robust reduced-order sliding mode observer for perturbed linear multiple-input and multiple-output systems is developed. The state and output variables of the original system are triple transformed into suitable canonical form coordinates to facilitate the design of a reduced-order observer. The existing transformations are summarised in this study and presented systematically. A new combined observer configuration is proposed and compared with another type of observers. Global asymptotical stability LMI and sliding mode existence conditions for the coupled observer error system are derived using Lyapunov full quadratic form. Reaching and sliding modes of motion of decoupled observer error system are discussed as well. Two numerical and simulation examples are given to illustrate the usefulness of the proposed design techniques.     

Observer design and output feedback stabilization for linear singular time-delay systems with unknown inputs

The design of a functional observer and reduced-order observer with internal delay for linear singular timedelay systems with unknown inputs is discussed. The sufficient conditions of the existence of observers, which are normal linear time-delay systems, and the corresponding design steps are presented via linear matrix inequality(LMI). Moreover, the observer-based feedback stabilizing controller is obtained. Three examples are given to show the effectiveness of the proposed methods.     

Robust observer design for nonlinear uncertain systems with LQ regulators

For a class of uncertain systems with linear nominal dynamics and nonlinear uncertainties, it has been shown (Katayama and Sasaki 1987) that linear quadratic (LQ) state feedback regulators can be used to provide robust asymptotic stability. In this paper, we study the combined observer-controller design problem, based on the linear state feedback regulator proposed by Katayama and Sasaki (1987), so that only output feedback is needed. Both full-order and reduced-order observers are considered. For the full-order observer, we propose an algorithm to synthesize the robust observer gain matrix. It is shown that with the observer it is still possible to achieve robust asymptotic stability. For the reduced-order observer, some conditions are derived to guarantee the robust asymptotic stabilizability of the uncertain systems. The trade-off between the magnitudes of controller and observer gains is clear in our approach. An example is used to illustrate the design process of the robust controller with full-order as well as reduced-order observers.     

含未知输入的时滞系统的函数观测器及输出反馈镇定

考虑了含未知输入的时滞系统的线性函数观测器设计.在一个不失一般性的秩条件假定下,以线性矩阵不等式(LMI)的形式给出了观测器存在的时滞无关型及时滞相关型判据,进而得到函数观测器改进的设计方法.此外,还讨论了降维状态观测器的设计,给出了基于观测器的反馈镇定控制器,实现了闭环的特征根分离及内稳定.具体算例说明了本文方法的有效性.     

Finite-time-observer design for nonlinear impulsive systems with impact perturbation

This paper investigates the observer design problem of nonlinear impulsive systems with impact perturbation. By using the concept of normal form, this paper proposes a full-order finite-time observer, which guarantees the finite-time convergence independent of the impact perturbation. A reduced-order observer is additionally developed for the proposed normal form. An illustrative example is given in order to illustrate the capability of the proposed method.     

A note on observers for Lipschitz nonlinear systems

This note deals with the design of reduced-order observers for Lipschitz nonlinear systems. It shows that the conditions under which a full-order observer exists also guarantee the existence of a reduced-order observer. A design method of the reduced-order observer that is dependent on the solution of the Riccati equation is then presented and an example is given to illustrate effects of the design method.