scholarly journals A Reduced-Order TS Fuzzy Observer Scheme with Application to Actuator Faults Reconstruction

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Design Procedure ◽  
Matching Condition ◽  
Lyapunov Theory ◽  
Observer Design ◽  
Linear Matrix ◽  
Actuator Fault ◽  
Actuator Faults ◽  
Reduced Order ◽  
Fuzzy Observer ◽  
Fault Reconstruction

This paper focuses on the principle for designing reduced-order fuzzy-observer-based actuator fault reconstruction for a class of nonlinear systems. The problem addressed can be indicated as an approach for a kind of reduced-order fuzzy observer design with special gain matrix structure that depends on a given matching condition specification. Using the Lyapunov theory, the stability conditions are obtained and expressed in terms of linear matrix inequalities, and the conditions for asymptotic estimation of actuator faults are derived. Simulation results illustrate the observer design procedure and demonstrate the actuator fault reconstruction effectiveness and performance.

scholarly journals Robust Fault Estimation Using the Intermediate Observer: Application to the Quadcopter

Sensors ◽  
2020 ◽  
Vol 20 (17) ◽  
pp. 4917
Author(s):  
Ngoc Phi Nguyen ◽  
Tuan Tu Huynh ◽  
Xuan Phu Do ◽  
Nguyen Xuan Mung ◽  
Sung Kyung Hong
Keyword(s):  
Estimation Algorithm ◽  
Lyapunov Theory ◽  
Observer Design ◽  
Balance Method ◽  
System Stability ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Actuator Faults ◽  
Control Effectiveness ◽  
System States

In this paper, an actuator fault estimation technique is proposed for quadcopters under uncertainties. In previous studies, matching conditions were required for the observer design, but they were found to be complex for solving linear matrix inequalities (LMIs). To overcome these limitations, in this study, an improved intermediate estimator algorithm was applied to the quadcopter model, which can be used to estimate actuator faults and system states. The system stability was validated using Lyapunov theory. It was shown that system errors are uniformly ultimately bounded. To increase the accuracy of the proposed fault estimation algorithm, a magnitude order balance method was applied. Experiments were verified with four scenarios to show the effectiveness of the proposed algorithm. Two first scenarios were compared to show the effectiveness of the magnitude order balance method. The remaining scenarios were described to test the reliability of the presented method in the presence of multiple actuator faults. Different from previous studies on observer-based fault estimation, this proposal not only can estimate the fault magnitude of the roll, pitch, yaw, and thrust channel, but also can estimate the loss of control effectiveness of each actuator under uncertainties.

Robust Tracking Control for Takagi–Sugeno Fuzzy Systems With Unmeasurable Premise Variables: Application to Tank System

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
H. Ghorbel ◽  
A. El Hajjaji ◽  
M. Souissi ◽  
M. Chaabane
Keyword(s):  
Tracking Control ◽  
Fuzzy Systems ◽  
Design Procedure ◽  
Control Design ◽  
Linear Matrix ◽  
Robust Tracking Control ◽  
Fuzzy Observer ◽  
Tank System ◽  
System States ◽  
Takagi Sugeno

In this paper, a robust fuzzy observer-based tracking controller for continuous-time nonlinear systems presented by Takagi–Sugeno (TS) models with unmeasurable premise variables, is synthesized. Using the H∞ norm and Lyapunov approach, the control design for TS fuzzy systems with both unmeasurable premises and system states is developed to guarantee tracking performance of closed loop systems. Sufficient relaxed conditions for synthesis of the fuzzy observer and the fuzzy control are driven in terms of linear matrix inequalities (LMIs) constraints. The proposed method allows simplifying the design procedure and gives the observer and controller gains in only one step. Numerical simulation on a two tank system is provided to illustrate the tracking control design procedure and to confirm the efficiency of the proposed method.

scholarly journals Observer Design for Simultaneous State and Fault Estimation for a Class of Discrete-time Descriptor Linear Models

2021 ◽  
Vol 229 ◽  
pp. 01020
Author(s):  
Kaoutar Ouarid ◽  
Abdellatif El Assoudi ◽  
Jalal Soulami ◽  
El Hassane El Yaagoubi
Keyword(s):  
Discrete Time ◽  
Linear Models ◽  
Estimation Error ◽  
Equivalent Form ◽  
Observer Design ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Sensor Faults ◽  
Actuator Faults ◽  
Algebraic Equations

This paper investigates the problem of observer design for simultaneous states and faults estimation for a class of discrete-time descriptor linear models in presence of actuator and sensor faults. The idea of the present result is based on the second equivalent form of implicit model [1] which permits to separate the differential and algebraic equations in the considered singular model, and the use of an explicit augmented model structure. At that stage, an observer is built to estimate simultaneously the unknown states, the actuator faults, and the sensor faults. Next, the explicit structure of the augmented model is established. Then, an observer is built to estimate simultaneously the unknown states, the actuator faults, and the sensor faults. By using the Lyapunov approach, the convergence of the state estimation error of the augmented system is analyzed, and the observer’s gain matrix is achieved by solving only one linear matrix inequality (LMI). At long last, an illustrative model is given to show the performance and capability of the proposed strategy.

scholarly journals Design of Reduced-Order Multiple Observers for Uncertain Systems with Unknown Inputs

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Mihai Lungu
Keyword(s):  
Linear Time ◽  
Design Procedure ◽  
Lyapunov Theory ◽  
Design Algorithm ◽  
Reduced Order ◽  
Unknown Inputs ◽  
Linear Time Invariant ◽  
Reduced Order Observer ◽  
Multiple Observer ◽  
Takagi Sugeno

The paper presents the design of a new reduced-order multiple observer for the estimation of the state associated with Takagi-Sugeno systems with unknown inputs, this being only the second reduced-order multiple observer ever designed. The design of reduced-order multiple observers which can achieve the finite-time state reconstruction for nonlinear systems described by multiple models is a niche area problem; the author of this paper continuing his work started with the introduction of the reduced-order multiple observer concept. The new multiple observer is a combination of a typical reduced-order observer for linear-time invariant multivariable systems and a full-order multiple observer for Takagi-Sugeno systems. The sufficient stability conditions of the observer are derived via the Lyapunov theory and its robustness is improved by means of a novel and efficient method which cancels the negative effect of the uncertainties appearing in the system. To validate the suggested design algorithm, the steps of the design procedure have been summarized and software implemented for the concrete case of a light aircraft lateral-directional motion.

scholarly journals Observer Design for a Class of Nonlinear Descriptor Systems: A Takagi-Sugeno Approach with Unmeasurable Premise Variables

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
J. Soulami ◽  
A. El Assoudi ◽  
M. Essabre ◽  
M. Habibi ◽  
E. El Yaagoubi
Keyword(s):  
Differential Equations ◽  
State Estimation ◽  
Ordinary Differential Equations ◽  
Differential Algebraic Equations ◽  
The State ◽  
Lyapunov Theory ◽  
Observer Design ◽  
Descriptor Systems ◽  
Fuzzy Observer ◽  
Takagi Sugeno

The Takagi-Sugeno (T-S) fuzzy observer for dynamical systems described by ordinary differential equations is widely discussed in the literature. The aim of this paper is to extend this observer design to a class of T-S descriptor systems with unmeasurable premise variables. In practice, the computation of solutions of differential-algebraic equations requires the combination of an ordinary differential equations (ODE) routine together with an optimization algorithm. Therefore, a natural way permitting to estimate the state of such a system is to design a procedure based on a similar numerical algorithm. Beside some numerical difficulties, the drawback of such a method lies in the fact that it is not easy to establish a rigorous proof of the convergence of the observer. The main result of this paper consists in showing that the state estimation problem for a class of T-S descriptor systems can be achieved by using a fuzzy observer having only an ODE structure. The convergence of the state estimation error is studied using the Lyapunov theory and the stability conditions are given in terms of linear matrix inequalities (LMIs). Finally, an application to a model of a heat exchanger pilot process is given to illustrate the performance of the proposed observer.

scholarly journals Actuator Fault Diagnosis for Discrete-Time Systems via Augmenting State Approach

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Yongchao Wang ◽  
Shangmin Qi ◽  
Yujun Hu ◽  
Shenghui Guo ◽  
Darong Huang
Keyword(s):  
Fault Diagnosis ◽  
Interval Estimation ◽  
Descriptor System ◽  
Linear Matrix ◽  
Reconstruction Method ◽  
Actuator Fault ◽  
Actuator Faults ◽  
System Matrix ◽  
Interval Observer ◽  
Time Systems

For the problem of the actuator fault diagnosis in the control systems, this paper presents a novel method by using an interval estimation approach to detect the faults and reconstruct them. In order to make estimations of the unavoidable measurement noise, a descriptor system form is built. Firstly, a full-order interval observer is developed to detect actuator faults for its sensitiveness to them. Then, a reduced-order one, which is robust to actuator faults, is presented. This method does not need the boundary information of faults; thus, the design condition is more relaxed. In order to make the interval observer stable and cooperative, linear matrix inequalities and a time-varying transformation are employed to ensure the error system matrix to be Schur and nonnegative. Based on the interval estimation results of the aforementioned method, an interval reconstruction method of actuator faults is proposed. Finally, results of the two simulation examples verify the proposed methods are effective and accurate.

Full-Order and Reduced-Order Exponential Observers for Discrete-Time Nonlinear Systems With Incremental Quadratic Constraints

2018 ◽  
Vol 141 (4) ◽  
Author(s):  
Wei Zhang ◽  
Younan Zhao ◽  
Masoud Abbaszadeh ◽  
Mingming Ji
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Exponential Convergence ◽  
Estimation Error ◽  
Observer Design ◽  
Linear Matrix ◽  
Discrete Time System ◽  
Quadratic Constraints ◽  
Reduced Order ◽  
Reduced Order Observer

This paper considers the observer design problem for a class of discrete-time system whose nonlinear time-varying terms satisfy incremental quadratic constraints. We first construct a circle criterion based full-order observer by injecting output estimation error into the observer nonlinear terms. We also construct a reduced-order observer to estimate the unmeasured system state. The proposed observers guarantee exponential convergence of the state estimation error to zero. The design of the proposed observers is reduced to solving a set of linear matrix inequalities. It is proved that the conditions under which a full-order observer exists also guarantee the existence of a reduced-order observer. Compared to some previous results in the literature, this work considers a larger class of nonlinearities and unifies some related observer designs for discrete-time nonlinear systems. Finally, a numerical example is included to illustrate the effectiveness of the proposed design.

Reduced-Order Observer Design for Discrete-Time Descriptor Systems With Unknown Inputs: An Linear Matrix Inequality Approach

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Shenghui Guo ◽  
Fanglai Zhu
Keyword(s):  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Observer Design ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Unknown Input ◽  
Matrix Inequality ◽  
Reduced Order ◽  
Unknown Inputs ◽  
Reduced Order Observer

Reduced-order observer design methods for both linear and nonlinear discrete-time descriptor systems based on the linear matrix inequality (LMI) approach are investigated. We conclude that the conditions under which a full-order observer exists can also guarantee the existence of a reduced-order observer. By choosing a special reduced-order observer gain matrix, a reduced-order unknown input observer is proposed for linear system with unknown inputs, and then an unknown input reconstruction is provided for some special cases. We also extend above results to the cases of nonlinear systems. Finally, three numerical comparative simulation examples are given to illustrate the effectiveness and merits of proposed methods.

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