Fuzzy Unknown Input Observer Research Articles

Robust fuzzy observer‐based fault‐tolerant control: A homogeneous polynomial Lyapunov function approach

In this paper, a homogeneous polynomial Lyapunov function (HPLF) is employed in robust observer-based Integrated Fault-Tolerant Control (IFTC) of nonlinear systems modelled by the polynomial fuzzy model (PFM). This makes the design problem benefit from the conservative reduction property of polynomial Lyapunov functions (PLFs) and simultaneously avoid the emergence of non-convex terms due to differentiation of the polynomial Lyapunov matrix. As a result, the less conservative sum of square (SOS) conditions are obtained in the form of polynomial matrix inequalities (PMI), which are solved via SOSTOOLS. For the first time, a non-quadratic Lyapunov function is used to design a polynomial fuzzy unknown-input observer that estimates the system's states and actuator faults in the presence of model uncertainties and external disturbances. The effectiveness of the proposed approach in providing more relaxed and less conservative results along with the better fault tolerance is illustrated through three simulating examples and compared with the quadratic Lyapunov function (QLF) approach.

Formula omitted] output feedback control for fractional-order T-S fuzzy model with time-delay

This paper addresses H∞ observer-based control issue for fractional-order uncertain Takagi-Sugeno (T-S) fuzzy model with unknown input and time-delay in the case of system order in (0,1). In order to construct the state estimation variables, reduced-order fuzzy observer is devised. By utilizing Lyapunov method of fractional-order derivative, the sufficient conditions are provided to ensure the effectiveness of proposed reduced-order unknown input observer and the stabilization of augmented T-S fuzzy model with an H∞-norm σ. The conditions are shown in terms of linear matrix inequalities (LMIs) and the matrices of unknown input fuzzy observer are computed by relevant LMIs. Furthermore, by solving LMIs, the T-S fuzzy output feedback control is realized. Finally, a numerical example and a single-link robot arm example are simulated to illustrate the validity of the addressed strategy.

Sensor and actuator fault-tolerant control based on fuzzy unknown input observer: A polynomial fuzzy approach

This paper studies sensor and actuator Fault-Tolerant Control (FTC) of nonlinear systems. The fault tolerance is necessary to have desired performance and prevent the system from instability. A Polynomial Fuzzy Unknown Input Observer (PFUIO) with immeasurable premise variable is proposed to estimate the states of the system, and sensor and actuator faults; and to use them in the controller to compensate the faults. The essence of the sensor fault necessitates considering the third class of Polynomial Fuzzy Model (PFM) with immeasurable premise variables. This makes the design procedure more complicated. Application of PFM reduces the conservatism and increases modeling accuracy. Moreover, the disturbance and model uncertainties are considered to realize more practical conditions. The polynomiality leads to Sum Of Squares (SOS), which can be solved using existing software. The proposed approach is evaluated by applying it to the inverted pendulum system. Simulating results show better performance of the proposed method as compared with the Linear Matrix Inequality (LMI) approach

Fuzzy FDI System for Flyback Converters

In this article, the design of a fault detection and isolation (FDI) system for a flyback converter, based on a fuzzy unknown input observer, is presented. The proposed FDI system aims to detect the saturation in the inductor core as a fault, considering the current increment can cause an avalanche effect provoking a failure in the system. A Takagi–Sugeno model of the flyback converter is used. The observer's convergence and the stability of the fault diagnosis system are guaranteed by Lyapunov's theory and the estimation error used to determine the necessary LMIs. A comparison of different FDI methods applied in fuzzy systems is performed in order to select the most robust system, capable of estimating the current in the system even in the presence of external disturbances. The system validation is performed in both, simulation and online implementation, using experimental data.

Vehicle lateral dynamics estimation using unknown input observer

This paper introduces an approach for estimating the parameters of the vehicle dynamics using a fuzzy Unknown Input Observer (UIO). The nonlinear model used has been deduced from the vehicle dynamics with a vision system is represented by a Takagi-Sugeno (T-S) fuzzy model in order to take into account the nonlinearities of the lateral forces. The convergence conditions of this observer are formulated as an optimization problem, subjected to constraints which are established using Lyapunov approach and expressed under Linear Matrix Inequalities (LMI). Thus, some simulations are performed on the nonlinear model of the vehicle lateral dynamics, with consideration of roll motion, that show a good efficiency of the proposed observer to estimate the system parameters, as well as the dynamic effect of the crosswind which is represented as an unknown input.

Fuzzy observer-based fault tolerant control against sensor faults for proton exchange membrane fuel cells

In this paper, robust fault diagnosis problem of Proton Exchange Membrane Fuel Cells (PEMFC) is presented based on Takagi-Sugeno (TS) Fuzzy Unknown Input Observer (FUIO). TS FUIO based on Linear Matrix Equalities (LMEs) and the Linear Matrix Inequalities (LMIs) are design. Firstly, the nonlinear PEMFC system with sensor faults and disturbance is represented by TS fuzzy model. Then, a FUIO and sensor fault estimation algorithm is developed and then a model based Fuzzy Fault Tolerant Controller design uses the concept of Parallel Distributed Compensation (PDC). Sufficient stability conditions are studied based on LMIs and LMEs. In order to verify the proposed approach, a PEMFC system with return manifold pressure and hydrogen mass sensors fault and disturbance was tested to illustrate the effectiveness of the proposed strategy.

Takagi–Sugeno Fuzzy Model Based Fault Estimation and Signal Compensation With Application to Wind Turbines

In response to the high demand of the operation reliability by implementing real-time monitoring and system health management, a robust fault estimation and fault-tolerant control approach is proposed for Takagi–Sugeno fuzzy systems in this study, by integrating the augmented system method, unknown input fuzzy observer design, linear matrix inequality optimization, and signal compensation techniques. Specifically, a fuzzy augmented system method is used to construct an augmented plant with the concerned faults and system states being the augmented states. An unknown input fuzzy observer technique is thus utilized to estimate the augmented states and decouple unknown inputs that can be decoupled. A linear matrix inequality approach is further addressed to ensure the global stability of the estimation error dynamics and attenuate the influences from the unknown inputs that cannot be decoupled. As a result, the robust estimates of the concerned faults and system states can be obtained simultaneously. Based on the fault estimates, a signal compensation scheme is developed to remove the effects of the faults on the system dynamics and outputs, leading to a stable dynamic satisfying the expected performance. Finally, the effectiveness of the proposed Takagi–Sugeno model based fault estimation and signal compensation algorithms is demonstrated by a case study on a 4.8-MW wind turbine benchmark system.

Fuzzy robust fault estimation scheme for a class of nonlinear systems based on an unknown input sliding mode observer

In this study, a novel fuzzy robust fault estimation scheme is developed for a class of nonlinear systems when both fault and disturbance are considered. The proposed scheme includes component fault with a nonlinear distribution matrix; as a result, the Takagi–Sugeno model is used to create multiple models. While the Takagi–Sugeno model is used for only the nonlinear distribution matrix of the fault signal, a larger category of nonlinear systems will be considered. This paper presents the problem of robust fault estimation based on fuzzy nonlinear observers, the first one is a fuzzy unknown input observer and the other one is a fuzzy sliding mode observer. The approach decoupled the faulty subsystem from the rest of the system through a series of transformations. Then, the objective is to design a fuzzy unknown input observer guaranteeing the asymptotic stability of the error dynamic using the Lyapunov method and completely removing disturbances; meanwhile, a fuzzy sliding mode observer is designed for a faulty subsystem to generate an estimation of fault based on a quadratic Lyapunov function and some matrices inequality convexification techniques. The sliding motion affects only the faulty subsystem through a novel reduced order fuzzy sliding mode observer; meanwhile, all disturbances are completely removed by fuzzy unknown input observer. Sufficient conditions are established in order to guarantee the convergence of the state estimation error and the results are formulated in the form of linear matrix inequalities. Thus, an exact fault estimator is determined on the basis of linear matrix inequality conditions while the estimation fault is completely insensitive to the disturbance. Finally, a simulation study on an electromagnetic suspension system is presented to demonstrate the g performance of the results compared with a pure sliding mode observer.

Fuzzy unknown input observer-based robust fault estimation design for discrete-time fuzzy systems

This paper investigates the problem of fuzzy unknown input observer (FUIO)-based fault estimation for discrete-time Takagi–Sugeno fuzzy systems. Firstly, an augmented system description is given. Then a FUIO is proposed to achieve fault estimation, which is robust against the effect of the external disturbance. Furthermore, a less conservative FUIO design method is proposed by using a finite-frequency range technique instead of an entire-frequency method. The gain matrices of the FUIO are obtained by solving linear matrix inequalities. Finally, simulation results of a discrete-time nonlinear system are presented to illustrate the effectiveness of the proposed strategy.

UIO-Based Fault Diagnosis Design in Finite-Frequency Domain for Discrete-Time T-S Fuzzy Systems

In this paper, the problem of fuzzy unknown input observer (FUIO)-based fault estimation in finite-frequency domain for discrete-time Takagi-Sugeno fuzzy systems is studied. Firstly, a FUIO is proposed to achieve fault estimation by using a finite frequency range technique instead of an entire frequency method, which is robust against the effect of the external disturbance. The gain matrices of the FUIO are obtained by solving linear matrix inequalities. Finally, simulation results of a discrete-time nonlinear system are presented to illustrate the effectiveness of the proposed strategy.

Vehicle dynamics and road curvature estimation for lane departure warning system using robust fuzzy observers: experimental validation

This paper describes a new approach to estimate vehicle dynamics and the road curvature in order to detect vehicle lane departures. This method has been evaluated through an experimental set-up using a real test vehicle equipped with the RT2500 inertial measurement unit. Based on a robust unknown input fuzzy observer, the road curvature is estimated and compared to the vehicle trajectory curvature. The difference between the two curvatures is used by the proposed lane departure detection algorithm as the first driving risk indicator. To reduce false alarms and take into account driver corrections, a second driving risk indicator based on the steering dynamics is considered. The vehicle nonlinear model is deduced from the vehicle lateral dynamics and road geometry and then represented by an uncertain Takagi–Sugeno fuzzy model. Taking into account the unmeasured variables, an unknown input fuzzy observer is proposed. Synthesis conditions of the proposed fuzzy observer are formulated in terms of linear matrix inequalities using the Lyapunov method.

Road curvature estimation for vehicle lane departure detection using a robust Takagi–Sugeno fuzzy observer

In this paper, a lane departure detection method is studied and evaluated via a professional vehicle dynamics software. Based on a robust fuzzy observer designed with unmeasurable premise variables with unknown inputs, the road curvature is estimated and compared with the vehicle trajectory curvature. The difference between the two curvatures is used by the proposed algorithm as the first driving risk indicator. To reduce false alarms and take into account the driver corrections, a second driving risk indicator is considered, which is based on the steering dynamics, and it gives the time to the lane keeping. The used nonlinear model deduced from the vehicle lateral dynamics and a vision system is represented by an uncertain Takagi–Sugeno fuzzy model. Taking into account the unmeasured variables, an unknown input fuzzy observer is then proposed. Synthesis conditions of the proposed fuzzy observer are formulated in terms of linear matrix inequalities using Lyapunov method. The proposed approach is evaluated under different driving scenarios using a software simulator. Simulation results show good efficiency of the proposed method.

Robust fault tolerant control of DFIG wind energy systems with unknown inputs

This paper proposes a Fuzzy Dedicated Observers (FDOS) method using a Nonlinear Unknown Input Fuzzy Observer (UIFO) with a Fuzzy Scheduler Fault Tolerant Control (FSFTC) algorithm for fuzzy Takagi-Sugeno (TS) systems subject to sensor faults, parametric uncertainties, and time varying unknown inputs. FDOS provide residuals for detection and isolation of sensor faults which can affect a TS model. The TS fuzzy model is adopted for fuzzy modeling of the uncertain nonlinear system and establishing fuzzy state observers. The concept of Parallel Distributed Compensation (PDC) is employed to design FSFTC and fuzzy observers from the TS fuzzy models. TS fuzzy systems are classified into three families based on the input matrices and a FSFTC synthesis procedure is given for each family. In each family, sufficient conditions are derived for robust stabilization, in the sense of Taylor series stability and Lyapunov method, for the TS fuzzy system with parametric uncertainties, sensor faults, and unknown inputs. The sufficient conditions are formulated in the format of Linear Matrix Inequalities (LMIs). The effectiveness of the proposed controller design methodology is finally demonstrated through a wind energy system with Doubly Fed Induction Generators (DFIG) to illustrate the effectiveness of the proposed method.

Unknown Input Observer with Fuzzy Fault Tolerant Control for Wind Energy System

This paper proposes a Fuzzy Dedicated Observers (FDOS) method using a Nonlinear Unknown Input Fuzzy Observer (UIFO) with a Fuzzy Fault Tolerant Control (FFTC) algorithm for fuzzy Takagi-Sugeno (TS) systems subject to sensor faults. FDOS provide residuals for detection and isolation of sensor faults which can affect a TS model. Parallel Distributed Compensation (PDC) is employed to design the fuzzy Fault Tolerant Controller from a TS fuzzy model. Sufficient stabilization conditions of the FFTC systems are given, which are formulated in terms of Linear Matrix Inequalities (LMIs). The LMIs can be efficiently solved using convex optimization techniques. Based on the derivation and simulation of the proposed FFTC approach, the stability of the closed-loop system in the event of sensor failures and unknown inputs is guaranteed. A wind Energy System (WES) with a Doubly-Fed Induction Generator (DFIG) example is illustrated to show the effectiveness of the proposed design method.

Design of observers for Takagi-Sugeno fuzzy models for Fault Detection and Isolation

This paper addresses the design of an unknown input fuzzy observer for Takagi-Sugeno (T-S) fuzzy model subject to unknown inputs. The main contribution of the paper is the development of a robust fuzzy observer in presence of disturbances. Based on Lyapunov function, it is shown how to determine observers gains in linear matrix inequalities (LMI). The proposed T-S observer is used for detection and isolation of faults which can affect a T-S model. The proposed methodology is illustrated by estimating the yaw rate and the fault of automatic steering vehicle.

On the design of observer for unknown inputs fuzzy models

In this paper, we consider the design of an fuzzy observer for a non-linear system with unknown inputs described by a fuzzy model. The main objective is to estimate state variables of the fuzzy model subject to unknown inputs which influence states and outputs of the system simultaneously. Using the Lyapunov method and Linear Matrix Inequalities (LMI), sufficient conditions are proposed to design the proposed unknown input fuzzy observer. The pole placement in an LMI region is also considered. The validity of the proposed methodology is illustrated by an academic example.