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 Relaxed State and Fault Estimation for Vehicle Lateral Dynamics Represented by T–S Fuzzy Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
N. El Youssfi ◽  
R. El Bachtiri ◽  
T. Zoulagh ◽  
H. El Aiss
Keyword(s):  
Fuzzy Systems ◽  
Sufficient Conditions ◽  
State Equation ◽  
Observer Design ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Vehicle Model ◽  
Lateral Dynamics ◽  
Takagi Sugeno ◽  
Vehicle Lateral Dynamics

This paper deals with the problem of observer design of the vehicle model which is represented by Takagi–Sugeno (T–S) fuzzy systems with the presence of uncertainties. A relaxed observer design is presented to estimate the unmeasurable states and the faults of the vehicle lateral dynamics model, simultaneously. The vehicle model is transformed into a system with unknown inputs. Then, it is rebuilt by adding the default to the system state equation. Based on the Lyapunov function approach and the introduction of some slack variables, sufficient conditions of unknown input observer design are formulated as Linear Matrix Inequalities (LMIs). Finally, the simulation section clearly shows the importance and effectiveness of the proposed strategy.

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 An interval observer design for uncertain nonlinear systems based on the T-S fuzzy model

2017 ◽  
Vol 27 (3) ◽  
pp. 397-407 ◽  
Author(s):  
Yamina Menasria ◽  
Hichem Bouras ◽  
Nasreddine Debbache
Keyword(s):  
Nonlinear Systems ◽  
Estimation Error ◽  
Fuzzy Model ◽  
Observer Design ◽  
Pole Placement ◽  
Dynamic State ◽  
New Approach ◽  
Dynamic State Estimation ◽  
Interval Observer ◽  
Takagi Sugeno

AbstractA new approach to build an interval observer for nonlinear uncertain systems is presented in this paper. Nonlinear systems modeled in the Takagi-Sugeno (T-S) form are studied. A T-S proportional observer is first issued by pole-placement and LMI tools. Secondly, time-varying change of coordinates for each dynamic state estimation error is used to design an interval observer. The system state bounds are then directly deduced.

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 Unknown Input Observer Design for a Class of Linear Descriptor Systems

2021 ◽  
Vol 229 ◽  
pp. 01019
Author(s):  
Karim Bouassem ◽  
Abdellatif El Assoudi ◽  
Jalal Soulami ◽  
El Hassane El Yaagoubi
Keyword(s):  
Estimation Error ◽  
Lyapunov Theory ◽  
Observer Design ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Simultaneous Estimation ◽  
Unknown Inputs ◽  
Pilot Model ◽  
The Stability ◽  
Differential Part

This paper addresses the problem of unknown inputs observer (UIO) design for a class of linear descriptor systems. The unknown inputs affect both state and output of the system. The basic idea of the proposed approach is based on the separation between dynamic and static relations in the descriptor model. Firstly, the method used to separate the differential part from the algebraic part is developed. Secondly, an observer design permitting the simultaneous estimation of the system state and the unknown inputs is proposed. The developed approach for the observer design is based on the synthesis of an augmented model which regroups the differential variables and unknown inputs. The exponential stability of the estimation error is studied using the Lyapunov theory and the stability condition is given in term of linear matrix inequality (LMI). Finally, to illustrate the efficiency of the proposed methodology, a heat exchanger pilot model is considered.

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 Performance and Observer Based Control for Periodic Discrete-Time Uncertain Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Natália A. Keles ◽  
Márcio J. Lacerda ◽  
Cristiano M. Agulhari
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Estimation Error ◽  
Performance Criterion ◽  
Lyapunov Theory ◽  
Observer Design ◽  
Control Technique ◽  
Duality Principle ◽  
Linear Matrix ◽  
Periodic Linear

This paper presents an approach for the synthesis of observer-based controllers for discrete-time periodic linear systems. The H2 performance criterion has been employed to design both the observer and the controller. For the periodic observer design, two conditions in the form of Linear Matrix Inequalities (LMIs) are proposed, which stem from the Lyapunov Theory applied over the dynamics of the estimation error. The LMI condition obtained for the periodic state-feedback controller results from the application of the duality principle over the periodic system, under the assumption that only the estimated states are available to be used in the state-feedback compensation. Numerical experiments illustrate the potential of the proposed observer-based control technique.

ON THE DIFFERENCE BETWEEN BOUNDED JACOBIAN AND LIPSCHITZ OBSERVERS FOR NONLINEAR ESTIMATION APPLICATIONS

2017 ◽  
Vol 41 (3) ◽  
pp. 395-415
Author(s):  
Gridsada Phanomchoeng ◽  
Rajesh Rajamani
Keyword(s):  
Convex Combination ◽  
Estimation Error ◽  
Lipschitz Constant ◽  
Longitudinal Velocity ◽  
Nonlinear Estimation ◽  
Velocity Estimation ◽  
Observer Design ◽  
Mean Value Theorem ◽  
Varying Coefficients ◽  
Time Varying Coefficients

This paper examines the performance of bounded Jacobian and Lipschitz observer design techniques for nonlinear estimation applications. The bounded Jacobian observer technique utilizes the mean value theorem to express the nonlinear estimation error dynamics as a convex combination of known matrices with time varying coefficients. The Lipschitz based observers are the most popular observer design technique used for nonlinear systems. But they are derived from more conservative Lipschitz conditions on the nonlinearity. Both observers are evaluated for longitudinal velocity estimation, vehicle roll angle estimation, and estimation in a polynomial nonlinear system with a large Lipschitz constant. The results show that the bounded Jacobian observer is the more appropriate observer for these problems.

Sign in / Sign up

Export Citation Format

Share Document