scholarly journals State and fault estimation based on fuzzy observer for a class of Takagi-Sugeno singular models

2022 ◽  
Vol 25 (1) ◽  
pp. 172
Author(s):  
Kaoutar Ouarid ◽  
Mohamed Essabre ◽  
Abdellatif El Assoudi ◽  
El Hassane El Yaagoubi
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Theory ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Engineering Practice ◽  
Sensor Faults ◽  
Matrix Inequalities ◽  
Decomposition Approach ◽  
New Approach ◽  
Takagi Sugeno

Singular nonlinear systems have received wide attention in recent years, and can be found in various applications of engineering practice. On the basis of the Takagi-Sugeno (T-S) formalism, which represents a powerful tool allowing the study and the treatment of nonlinear systems, many control and diagnostic problems have been treated in the literature. In this work, we aim to present a new approach making it possible to estimate simultaneously both non-measurable states and unknown faults in the actuators and sensors for a class of continuous-time Takagi-Sugeno singular model (CTSSM). Firstly, the considered class of CTSSM is represented in the case of premise variables which are non-measurable, and is subjected to actuator and sensor faults. Secondly, the suggested observer is synthesized based on the decomposition approach. Next, the observer’s gain matrices are determined using the Lyapunov theory and the constraints are defined as linear matrix inequalities (LMIs). Finally, a numerical simulation on an application example is given to demonstrate the usefulness and the good performance of the proposed dynamic system.

scholarly journals Simultaneous state and fault estimation for Takagi-Sugeno implicit models with Lipschitz constraints

2021 ◽  
Vol 11 (1) ◽  
pp. 100-108
Author(s):  
Manal Ouzaz ◽  
Abdellatif El Assoudi ◽  
Jalal Soulami ◽  
El Hassane El Yaagoubi
Keyword(s):  
Estimation Error ◽  
The State ◽  
Lyapunov Theory ◽  
Observer Design ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Sensor Faults ◽  
Algebraic Equations ◽  
The Stability ◽  
Takagi Sugeno

This paper presents a state and fault observer design for a class of Takagi-Sugeno implicit models (TSIMs) with unmeasurable premise variables satisfying the Lipschitz constraints. The fault variable is constituted by the actuator and sensor faults. The actuator fault affects the state and the sensor fault affects the output of the system. The approach is based on the separation between dynamic and static relations in the TSIM. Firstly, the method begins by decomposing the dynamic equations of the algebraic equations. Secondly, the fuzzy observer design that satisfies the Lipschitz conditions and permits to estimate simultaneously the unknown states, actuator and sensor faults is developed. The aim of this approach for the observer design is to construct an augmented model where the fault variable is added to the state vector. The exponential convergence of the state estimation error is studied by using the Lyapunov theory and the stability condition is given in term of only one linear matrix inequality (LMI). Finally, numerical simulation results are given to highlight the performances of the proposed method by using a TSIM of a single-link flexible joint robot.

Fault-tolerant controller design with fault estimation capability for a class of nonlinear systems using generalized Takagi-Sugeno fuzzy model

2019 ◽  
Vol 41 (15) ◽  
pp. 4218-4229 ◽  
Author(s):  
Alireza Navarbaf ◽  
Mohammad Javad Khosrowjerdi
Keyword(s):  
Nonlinear Systems ◽  
Controller Design ◽  
Fault Tolerant ◽  
Fuzzy Model ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Wide Range ◽  
Satisfy Lipschitz Condition ◽  
Unknown Disturbances ◽  
Takagi Sugeno

In this paper, a new design approach to construct a fault-tolerant controller (FTC) with fault estimation capability is proposed using a generalized Takagi-Sugeno (T-S) fuzzy model for a class of nonlinear systems in the presence of actuator faults and unknown disturbances. The generalized T-S fuzzy model consists of some local models with multiplicative nonlinear terms that satisfy Lipschitz condition. Besides covering a very wide range of nonlinear systems with a smaller number of local rules in comparison with the conventional T-S fuzzy model and hence having less computational burden, the existence of the multiplicative nonlinear term solves the uncontrollability issues that the other generalized T-S fuzzy models with additive nonlinear terms dealt with. A state/fault observer designed for the considered generalized T-S fuzzy model and then, a dynamic FTC law based on the estimated fault information is proposed and sufficient design conditions are given in terms of linear matrix inequalities (LMIs). It can be shown that the number of LMIs are less than that of previously proposed methods and then feasibility of our method is more likely. The effectiveness of the proposed FTC approach is verified using a nonlinear mass-spring-damper system.

scholarly journals Stable Fault Tolerant Controller Design for Takagi–Sugeno Fuzzy Model-Based Control Systems via Linear Matrix Inequalities: Three Conical Tank Case Study

Energies ◽  
2019 ◽  
Vol 12 (11) ◽  
pp. 2221 ◽  
Author(s):  
Himanshukumar R. Patel ◽  
Vipul A. Shah
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Control Systems ◽  
Linear Models ◽  
Fault Tolerant ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Fuzzy Models ◽  
Takagi Sugeno

This paper deals with a methodical design approach of fault-tolerant controller that gives assurance for the the stabilization and acceptable control performance of the nonlinear systems which can be described by Takagi–Sugeno (T–S) fuzzy models. Takagi–Sugeno fuzzy model gives a unique edge that allows us to apply the traditional linear system theory for the investigation and blend of nonlinear systems by linear models in a different state space region. The overall fuzzy model of the nonlinear system is obtained by fuzzy combination of the all linear models. After that, based on this linear model, we employ parallel distributed compensation for designing linear controllers for each linear model. Also this paper reports of the T–S fuzzy system with less conservative stabilization condition which gives decent performance. However, the controller synthesis for nonlinear systems described by the T–S fuzzy model is a complicated task, which can be reduced to convex problems linking with linear matrix inequalities (LMIs). Further sufficient conservative stabilization conditions are represented by a set of LMIs for the Takagi–Sugeno fuzzy control systems, which can be solved by using MATLAB software. Two-rule T–S fuzzy model is used to describe the nonlinear system and this system demonstrated with proposed fault-tolerant control scheme. The proposed fault-tolerant controller implemented and validated on three interconnected conical tank system with two constraints in terms of faults, one issed to build the actuator and sond is system component (leak) respectively. The MATLAB Simulink platform with linear fuzzy models and an LMI Toolbox was used to solve the LMIs and determine the controller gains subject to the proposed design approach.

A Simple, Natural and Effective Framework of Nonlinear Systems Control and its Application to Aerial Robots

2014 ◽  
Vol 26 (2) ◽  
pp. 140-147 ◽  
Author(s):  
Motoyasu Tanaka ◽  
◽  
Hiroshi Ohtake ◽  
Kazuo Tanaka ◽  
Keyword(s):  
Nonlinear Systems ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Design Problems ◽  
Model Based Control ◽  
Aerial Robots ◽  
Control Framework ◽  
Systems Control ◽  
Takagi Sugeno

This paper presents a simple, natural and effective framework of nonlinear systems control and its application to aerial robots. First, we present a framework of Takagi-Sugeno fuzzy model-based control and also discuss its feature. Next, a number of design problems for the control framework are formulated as numerically feasibility problems of representing in terms of linear matrix inequalities. Finally, we provide two applications of the control framework to aerial robots. The control results of aerial robots show the utility of the control framework.

scholarly journals An Adaptive Observer Design for Nonlinear Systems Affected by Unknown Disturbance with Simultaneous Actuator and Sensor Faults. Application to a CSTR

2021 ◽  
Vol 12 (4) ◽  
pp. 4847-4856
Keyword(s):  
Nonlinear Behavior ◽  
Lyapunov Theory ◽  
Observer Design ◽  
Adaptive Observer ◽  
Linear Matrix ◽  
Sensor Faults ◽  
Continuous Stirred Tank Reactor ◽  
Continuous Stirred Tank ◽  
Unknown Disturbance ◽  
Takagi Sugeno

Continuous Stirred Tank Reactor (CSTR) is an important system in the chemical and biological industries. It's characterized by a complex nonlinear behavior and is usually affected by faults and disturbances. Therefore, the states and faults estimation of a CSTR is always a challenging task for automated process researchers and engineers. This paper proposes an adaptive observer. This paper proposes an adaptive observer in order to estimate states and actuator and sensor faults simultaneously under unknown disturbance. Firstly, the approach of the Takagi-Sugeno multi-model is proposed to transform the complex nonlinear model into several simple linear sub-models. However, the states of the considered isotherm CSTR are not completely measurable, so the multi-model is represented with non-measurable premise variables. Then, in order to transform the considered system into a system with an unknown input, a mathematical transformation is introduced to describe the sensor faults as actuator faults. The proposed observer is designed, and the exponential stability conditions are studied with the Lyapunov theory and L2 optimization and formulated in terms of linear matrix inequalities. Finally, to improve the effectiveness of the proposed observer, a numerical simulation is carried out on a CSTR.

scholarly journals Robust Fault Estimation and Fault-Tolerant Control Based on Sliding Mode Observer for Takagi–Sugeno Fuzzy Systems Subject to Actuator and Sensor Faults

2020 ◽  
Vol 9 (8) ◽  
pp. 145-154
Keyword(s):  
Fault Tolerant ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Fault Tolerant Control ◽  
Lyapunov Stability Theory ◽  
Sliding Mode Observer ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Sensor Faults ◽  
Takagi Sugeno

In this paper, the problems of fault estimation and fault-tolerant control for Takagi-Sugeno fuzzy system affected by simultaneous actuator faults, sensor faults and external disturbances are investigated. Firstly, an adaptive fuzzy sliding-mode observer is designed to simultaneously estimate system states and both actuator and sensor faults. Then, based on the online estimation information, a static output feedback fault-tolerant controller is designed to compensate for the effect of faults and to stabilize the closed-loop system. Moreover, sufficient conditions for the existence of the proposed observer and controller with an H∞ performance are derived based on Lyapunov stability theory and expressed in terms of linear matrix inequalities. Finally, a nonlinear inverted pendulum with cart system application is given illustrate the validity of the proposed method.

scholarly journals LMI based fuzzy observer design for Takagi-Sugeno models containing vestigial nonlinear terms

2014 ◽  
Vol 24 (1) ◽  
pp. 39-52 ◽  
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Nonlinear Systems ◽  
Continuous Time ◽  
Observer Design ◽  
System Model ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Fuzzy Observer ◽  
Quadratic Inequalities ◽  
Lyapunov Stability Criterion ◽  
Takagi Sugeno

Abstract The paper deals with the problem of full order fuzzy observer design for the class of continuous-time nonlinear systems, represented by Takagi-Sugeno models containing vestigial nonlinear terms. On the basis of the Lyapunov stability criterion and the incremental quadratic inequalities, two design conditions for this kind of system model are outlined in the terms of linear matrix inequalities. A numerical example is given to illustrate the procedure and to validate the performances of the proposed approach.

scholarly journals Stabilizing Fuzzy Output Control for a Class of Nonlinear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Nonlinear Systems ◽  
Design Method ◽  
Design Procedure ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Output Control ◽  
Output Controller ◽  
Control Scheme ◽  
Lyapunov Matrix ◽  
Takagi Sugeno

The paper presents new conditions suitable in design of a stabilizing output controller for a class of continuous-time nonlinear systems, represented by Takagi-Sugeno models. Taking into account the affine properties of the TS model structure and applying the fuzzy control scheme relating to the parallel distributed output compensators, the sufficient design conditions are outlined in terms of linear matrix inequalities. The proposed procedure decouples the Lyapunov matrix and the system parameter matrices in the LMIs and guarantees global stability of the system. Simulation result illustrates the design procedure and demonstrates the performances of the proposed design method.

scholarly journals An H∞ sliding mode observer for Takagi–Sugeno nonlinear systems with simultaneous actuator and sensor faults An

2015 ◽  
Vol 25 (3) ◽  
pp. 547-559 ◽  
Author(s):  
Ali Ben Brahim ◽  
Slim Dhahri ◽  
Fayçal Ben Hmida ◽  
Anis Sellami
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode ◽  
Design Method ◽  
Estimation Error ◽  
Sliding Mode Observer ◽  
Linear Matrix ◽  
Sensor Faults ◽  
Fault Reconstruction ◽  
The Stability ◽  
Takagi Sugeno

Abstract This paper considers the problem of robust reconstruction of simultaneous actuator and sensor faults for a class of uncertain Takagi-Sugeno nonlinear systems with unmeasurable premise variables. The proposed fault reconstruction and estimation design method with H∞ performance is used to reconstruct both actuator and sensor faults when the latter are transformed into pseudo-actuator faults by introducing a simple filter. The main contribution is to develop a sliding mode observer (SMO) with two discontinuous terms to solve the problem of simultaneous faults. Sufficient stability conditions in terms linear matrix inequalities are achieved to guarantee the stability of the state estimation error. The observer gains are obtained by solving a convex multiobjective optimization problem. Simulation examples are given to illustrate the performance of the proposed observer

scholarly journals Finite-Frequency Observer-Based Fault Estimation and Fault-Tolerant Control for Wind Turbine

2020 ◽  
Vol 12 (3) ◽  
pp. 571-585
Author(s):  
Ayoub EL BAKRI ◽  
◽  
Ismail Boumhidi ◽  
Keyword(s):  
Linear Matrix Inequalities ◽  
Fault Tolerant ◽  
Lyapunov Theory ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Finite Frequency ◽  
Second Stage ◽  
Suggested Strategy ◽  
Simulation Results

This paper deals with the design problem of a robust fault estimation (FE)/ faulttolerant control (FTC) scheme for wind turbines (WT) in the finite frequency domain (FF). First, an adaptive fuzzy H∞ observer is constructed to simultaneously reconstruct the WT states and faults within the FF range. Throughout the observer analysis, it is only assumed that faults, uncertainties, and disturbances are bounded, which coincide with the practical requirements. In the second stage, based on the observer information, an active FTC method is proposed to stabilize the faulty WT. The controller and observer gain matrices are extracted employing the Lyapunov theory, where constraints are expressed as a set of linear matrix inequalities (LMIs). The Simulation results illustrate the best performances of the suggested strategy.

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