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 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.

scholarly journals Adaptive Proportional Integral Observer Design for Interval Type 2 Takagi–Sugeno Fuzzy Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Atef Khedher ◽  
Ilyes Elleuch ◽  
Kamal BenOthman
Keyword(s):  
Fuzzy Systems ◽  
Observer Design ◽  
Adaptive Observer ◽  
Fault Estimation ◽  
Sensor Faults ◽  
Proportional Integral ◽  
Augmented State ◽  
Interval Type ◽  
Takagi Sugeno

In this paper, the problem of fault estimation in systems described by Takagi–Sugeno fuzzy systems is studied. A proportional integral observer is conceived in order to reconstruct state and faults which can affect the studied system. Proportional integral observer can easily estimate actuator faults which are assimilated to be as unknown inputs. In order to estimate actuator and sensor faults, a mathematical transformation is used to conceive an augmented system, in which the initial sensor fault appears as an unknown input. Considering the augmented state, it is possible to conceive an adaptive observer which is able to estimate the whole state and faults. The noise effect on the state and fault estimation is also minimized in this study, which provides some robustness properties to the proposed observer. The proportional integral observer is conceived for nonlinear systems described by Takagi–Sugeno fuzzy models.

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.

Model predictive control of a CSTR: A hybrid modeling approach

2010 ◽  
Vol 64 (3) ◽  
Author(s):  
Michal Kvasnica ◽  
Martin Herceg ◽  
Ľuboš Čirka ◽  
Miroslav Fikar
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Linear Models ◽  
Nonlinear Behavior ◽  
Continuous Stirred Tank Reactor ◽  
Modeling Framework ◽  
Future Evolution ◽  
Continuous Stirred Tank ◽  
Traditional Approaches

AbstractThis paper presents a case study of model predictive control (MPC) applied to a continuous stirred tank reactor (CSTR). It is proposed to approximate nonlinear behavior of a plant by several local linear models, enabling a piecewise affine (PWA) description of the model used to predict and optimize future evolution of the reactor behavior. Main advantage of the PWA model over traditional approaches based on single linearization is a significant increase of model accuracy which leads to a better control quality. It is also illustrated that, by adopting the PWA modeling framework, MPC strategy can be implemented using significantly less computational power compared to nonlinear MPC setups.

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.

Robust fault tolerant control based on adaptive observer for Takagi-Sugeno fuzzy systems with sensor and actuator faults: Application to single-link manipulator

2020 ◽  
Vol 42 (12) ◽  
pp. 2308-2323
Author(s):  
Salama Makni ◽  
Maha Bouattour ◽  
Ahmed El Hajjaji ◽  
Mohamed Chaabane
Keyword(s):  
Controller Design ◽  
Fault Tolerant ◽  
Fault Tolerant Control ◽  
Single Step ◽  
Adaptive Observer ◽  
Linear Matrix ◽  
Actuator Faults ◽  
Single Link ◽  
Comparative Results ◽  
Takagi Sugeno

In this work, we investigate the problem of control for nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy models affected by both sensor and actuator faults subject to an unknown bounded disturbances (UBD). For this, we design an adaptive observer to estimate state, sensor and actuator fault vectors simultaneously despite the presence of external disturbances. Based on this observer, we develop a fault tolerant control (FTC) law not only to stabilize closed loop system, but also to compensate the fault effects. For the observer-based controller design, we propose less conservative conditions formulated in terms of linear matrix inequalities (LMIs). Moreover, both observer and controller gains are calculated via solving a set of LMIs only in single step. Finally, comparative results and an application to single-link flexible joint robot are afforded to prove the efficiency of the proposed design.

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.

New Nonlinear Takagi–Sugeno Vehicle Model for State and Road Curvature Estimation via a Nonlinear PMI Observer

2014 ◽  
Vol 23 (2) ◽  
pp. 155-170
Author(s):  
Zedjiga Yacine ◽  
Dalil Ichalal ◽  
Naima Ait Oufroukh ◽  
Said Mammar ◽  
Said Djennoune
Keyword(s):  
Estimation Error ◽  
Longitudinal Velocity ◽  
Multiple Integral ◽  
Lyapunov Theory ◽  
Observer Design ◽  
Force Model ◽  
Vehicle Model ◽  
Lateral Dynamics ◽  
Bounded Error ◽  
Takagi Sugeno

AbstractThe present article deals with an observer design for nonlinear vehicle lateral dynamics. The contributions of the article concern the nonconsideration of any force model and the consideration that the longitudinal velocity is time varying, which is more realistic than the assumption that it is constant. The vehicle model is then represented by an exact Takagi–Sugeno (TS) model via the sector nonlinearity transformation. A proportional multiple integral (PMI) observer based on the TS model is designed to estimate simultaneously the state vector and the unknown input (lateral forces and road curvature). The convergence conditions of the estimation error are expressed under LMI formulation using the Lyapunov theory, which guaranties a bounded error. Simulations are carried out for comparison between the conventional PI observer, the enhanced PI observer, and the PMI observer. Finally, experimental results are provided to illustrate the performances of the proposed PMI observer.

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.

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