Dalil Ichalal

Simultaneous state and unknown inputs estimation with PI and PMI observers for Takagi Sugeno model with unmeasurable premise variables

In this paper, a proportional integral (PI) and a proportional multiple integral observer (PMI) are proposed in order to estimate the state and the unknown inputs of nonlinear systems described by a Takagi-Sugeno model with unmeasurable premise variables. This work is an extension to nonlinear systems of the PI and PMI observers developed for linear systems. The state estimation error is written as a perturbed system. First, the convergence conditions of the state estimation errors between the system and each observer are given in LMI (Linear Matrix Inequality) formulation. Secondly, a comparison between the two observers is made through an academic example.

Design of observers for Takagi-Sugeno systems with immeasurable premise variables : an L2 approach

A new observer design method is proposed for Takagi-Sugeno systems with immeasurable premise variables. Since the state estimation error can be written as a perturbed system, then the proposed method is based on the L2 techniques to minimize the effect of the perturbations on the state estimation error. The convergence conditions of the observer are established by using the second method of Lyapunov and a quadratic function. These conditions are expressed in terms of Linear Matrix Inequalities (LMI). Finally, the performances of the proposed observer are improved by eigenvalues clustering in LMI region.

Fault detection, isolation and estimation for Takagi–Sugeno nonlinear systems

Abstract This article is dedicated to the problem of fault detection, isolation and estimation for nonlinear systems described by a Takagi–Sugeno (T–S) model. One of the interests of this type of models is the possibility to extend some tools and methods from the linear system case to the nonlinear one. The principle of the proposed strategy is to transform the problem of simultaneously minimizing the perturbation effect and maximizing the fault effect, on the residual vector, in a simple problem of L 2 - norm minimization. A linear system is used to define the ideal response of the residual signal to the fault. Then the aim is to synthesize a residual generator that both minimizes the difference between real and ideal responses and the influence of the disturbance. The minimization problem is formulated by the bounded real lemma (BRL) and linear matrix inequality (LMI) formalism. After studying the general framework, a special case of systems with actuator and sensor faults is considered where the fault incidence matrix is not full column rank. Simulation examples are given to illustrate the proposed method. Finally, Polyas theorem is used to reduce the conservatism of the proposed result. The obtained relaxation is also illustrated by a numerical example.

State and unknown input estimation for nonlinear systems described by Takagi-Sugeno models with unmeasurable premise variables

This paper presents a new method to synthesize observers for continuous time nonlinear systems described by Takagi-Sugeno (TS) model with unmeasurable premise variables. First, convergence conditions are established in order to guarantee the convergence of the state estimation error. These conditions are given in Linear Matrix Inequality (LMI) formulation. Secondly, a classical Proportional Integral Observer (PIO) is extended to the considered nonlinear systems in order to estimate the state and the unknown inputs (UI).

New fault tolerant control strategies for nonlinear Takagi-Sugeno systems

New fault tolerant control strategies for nonlinear Takagi-Sugeno systems New methodologies for Fault Tolerant Control (FTC) are proposed in order to compensate actuator faults in nonlinear systems. These approaches are based on the representation of the nonlinear system by a Takagi-Sugeno model. Two control laws are proposed requiring simultaneous estimation of the system states and of the occurring actuator faults. The first approach concerns the stabilization problem in the presence of actuator faults. In the second, the system state is forced to track a reference trajectory even in faulty situation. The control performance depends on the estimation quality; indeed, it is important to accurately and rapidly estimate the states and the faults. This task is then performed with an Adaptive Fast State and Fault Observer (AFSFO) for the first case, and a Proportional-Integral Observer (PIO) in the second. Stability conditions are established with Lyapunov theory and expressed in a Linear Matrix Inequality (LMI) formulation to ease the design of FTC. Furthermore, relaxed stability conditions are given with the use of Polyas theorem. Some simulation examples are given in order to illustrate the proposed approaches.

An approach for the state estimation of Takagi-Sugeno models and application to sensor fault diagnosis

In this paper, a new method to design an observer for nonlinear systems described by Takagi-Sugeno (TS) model, with unmeasurable premise variables, is proposed. Most of existing work on TS models consider models with measurable decision variables. As a consequence, these works cannot be applied when the decision variables are not available to measurement. The idea of the proposed approach is to rewrite the TS model with unmeasurable premise variable into an uncertain TS model by introducing the estimated state in the model. 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 academic example is given to illustrate the proposed approach, with an application to sensor fault detection and isolation using an observer bank.

Fault diagnosis for Takagi-Sugeno nonlinear systems

This paper addresses a new scheme for fault diagnosis in nonlinear systems described by Takagi-Sugeno multiple models. Two cases are considered, the first one concerns the T-S models with known premise variables (the input or the output of the system). For the second case it is supposed that the weighting functions depend on unmeasurable premise variables (state of the system). The approach is based on the design of observer-based residual generator by minimization of the disturbances effect and maximizing the effects of the faults. The synthesis is based on the L2 formalism developed for linear systems. The convergence conditions are given in LMI formulation.

Fault tolerant control for Takagi-Sugeno systems with unmeasurable premise variables by trajectory tracking

This paper presents a new method for fault tolerant control of nonlinear systems described by Takagi-Sugeno fuzzy systems with unmeasurable premise variables. The idea is to use a reference model and design a new control law to minimize the state deviation between a healthy reference model and the eventually faulty actual model. This scheme requires the knowledge of the system states and of the occurring faults. These signals are estimated from a Proportional-Integral Observer (PIO) or Proportional-Multi-Integral Observer (PMIO). The fault tolerant control law is designed by using the Lyapunov method to obtain conditions which are given in Linear Matrix Inequality formulation (LMI). Finally, an example is included.

On Unknown Input Observers for LPV Systems

This paper is dedicated to the design of unknown input (UI) observers for linear parameter-varying (LPV) systems using algebraic matrix manipulation. First, a discussion is provided concerning the classical design approach, which requires the matching condition. This condition is satisfied for a class of systems having relative degree 1. Second, for the same class of systems, a new generalized approach is proposed for simultaneous state and UI estimation. It is demonstrated that the proposed approach is more general than the classical approach. Finally, an extension of the approach is provided for LPV systems with arbitrary relative degree. Simulation examples are provided to illustrate the main results of the paper.

Observer design for two-wheeled vehicle: A Takagi-Sugeno approach with unmeasurable premise variables

This paper is dedicated to the problem of observer design for Takagi-Sugeno (T-S) nonlinear systems with unmeasurable premise variables (TSUPV) and application to autonomous bicycle system. The main idea is based on the use of differential mean value theorem combined to the sector nonlinearity transformation. The objective of this approach is to make the state estimation error dynamic on a T-S form which allows to apply the classical Lyapunov analysis to derive convergence conditions. The design algorithm is proposed in terms of linear matrix inequalities (LMI). To illustrate the proposed methodology, a nonlinear bicycle model is considered.