Unmeasurable Premise Variables Research Articles

Sensor Faults Observer Design with H∞ Performance for Non-linear T-S systems

This paper deals with the problem of the state estimation and the sensor faults detection for nonlinear perturbed systems described by Takagi-Sugeno (T-S) fuzzy models with unmeasurable premise variables. Indeed, a T-S observer is synthesized, in descriptor form, to estimate both the system states and the sensor faults simultaneously. The idea of the proposed approach is to introduce the sensor fault as an auxiliary variable in the state vector. Besides, the T-S model with unmeasurable premise variables is reduced to a perturbed model with measurable variables. Convergence conditions are established with Lyapunov theory and the H ? performance in order to guarantee the best robustness to disturbances. These conditions are expressed in terms of linear matrix inequalities (LMIs). The parameters of the observer are computed using the solution of the LMI conditions. Finally, a numerical example is given to illustrate the design procedures. Simulation results show the satisfactory performances.

Vehicle dynamic estimation with road bank angle consideration for rollover detection: theoretical and experimental studies

This article describes a method of vehicle dynamics estimation for impending rollover detection. This method is evaluated via a professional vehicle dynamics software and then through experimental results using a real test vehicle equipped with an inertial measurement unit. The vehicle dynamic states are estimated in the presence of the road bank angle (as a disturbance in the vehicle model) using a robust observer. The estimated roll angle and roll rate are used to compute the rollover index which is based on the prediction of the lateral load transfer. In order to anticipate the rollover detection, a new method is proposed in order to compute the time-to-rollover using the load transfer ratio. The used nonlinear model is deduced from the vehicle lateral dynamics and is represented by a Takagi–Sugeno (TS) fuzzy model. This representation is used in order to take into account the nonlinearities of lateral cornering forces. The proposed TS observer is designed with unmeasurable premise variables in order to consider the non-availability of the slip angles measurement. Simulation results show that the proposed observer and rollover detection method exhibit good efficiency.

Discrete‐time H − ∕ H ∞ sensor fault detection observer design for nonlinear systems with parameter uncertainty

SUMMARYThis work concerns robust sensor fault detection observer (SFDO) design for uncertain and disturbed discrete‐time Takagi–Sugeno (T–S) systems using H − ∕ H ∞ criterion. The principle of the proposed approach is based on simultaneously minimizing the perturbation effect and maximizing the fault effect on the residual vector. Furthermore, by introducing slack decision matrices and taking advantage of the descriptor formulation, less conservative sufficient conditions are proposed leading to easier linear matrix inequalities (LMIs). Moreover, the proposed (SFDO) design conditions allow dealing with unmeasurable premise variables. Finally, a numerical example and a truck–trailer system model are proposed to illustrate the efficiency of the SFDO design methodology. Copyright © 2013 John Wiley & Sons, Ltd.

Nonlinear joint state and parameter estimation: Application to a wastewater treatment plant

A systematic approach to joint state and time-varying parameter estimation for nonlinear systems is proposed in this paper. Applying the sector nonlinearity transformation to both the system nonlinearities and the time-varying parameters, the original system is equivalently rewritten as a Takagi–Sugeno system with unmeasurable premise variables. A joint state and parameter observer whose parameters are designed by solving an LMI optimization problem is then proposed. The target application is a realistic model of an activated sludge wastewater treatment plant, being an uncertain nonlinear system affected by a time-varying parameter.

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.

Multi‐objective H − ∕ H ∞ fault detection observer design for Takagi–Sugeno fuzzy systems with unmeasurable premise variables: descriptor approach

SUMMARYThis paper investigates the problem of robust fault detection observer design for nonlinear Takagi–Sugeno models with unmeasurable premise variables subject to sensor faults and unknown bounded disturbance. The main idea is to synthesize a robust fault detection observer by means of a mixed H − ∕ H ∞ performance index. The considered observer is used to estimate jointly states and faults. Using the technique of descriptor system representation, we proposed a new less‐conservative approach in term of a linear matrix inequality (LMI) by considering the sensor fault as an auxiliary state variable. A solution of the problem is obtained by using an iterative LMI procedure. Copyright © 2012 John Wiley & Sons, Ltd.

Robust non-quadratic static output feedback controller design for Takagi–Sugeno systems using descriptor redundancy

This work concerns robust static output feedback controller (SOFC) design for uncertain and disturbed Takagi–Sugeno (TS) systems using an H-infinity criterion. The main result is based on a descriptor formulation of the closed-loop dynamics. The proposed approach allows avoiding appearance of crossing terms between the controller’s and the TS system’s input matrices leading to easier LMI formulation than existing studies in the literature. Moreover, the proposed SOFC design conditions do not require any restrictions on the output equation and allow dealing with unmeasurable premise variables. Indeed, taking advantage of the uncertain TS modeling, nonlinearities associated to unmeasurable premises variables can be reported from the nominal part to the uncertainties. To provide LMIs of less conservatism, the results are conducted in the non-quadratic framework. Finally, two numerical examples and a benchmark of a crane system are proposed to illustrate the efficiency of the SOFC design methodology.

Observer-Based Piecewise Affine Output Feedback Controller Synthesis of Continuous-Time T–S Fuzzy Affine Dynamic Systems Using Quantized Measurements

This paper is concerned with the problem of robust <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\mathscr H}_{\infty }$</tex></formula> output feedback control for a class of continuous-time Takagi–Sugeno (T–S) fuzzy affine dynamic systems using quantized measurements. The objective is to design a suitable observer-based dynamic output feedback controller that guarantees the global stability of the resulting closed-loop fuzzy system with a prescribed <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\mathscr H}_{\infty }$</tex></formula> disturbance attenuation level. Based on common/piecewise quadratic Lyapunov functions combined with S-procedure and some matrix inequality convexification techniques, some new results are developed to the controller synthesis for the underlying continuous-time T–S fuzzy affine systems with unmeasurable premise variables. All the solutions to the problem are formulated in the form of linear matrix inequalities (LMIs). Finally, two simulation examples are provided to illustrate the advantages of the proposed approaches.

A robust [formula omitted] observer-based controller design for uncertain T–S fuzzy systems with unknown premise variables via LMI

This paper addresses the problem of robust H∞ fuzzy observer-based controller design for the Takagi–Sugeno (T–S) fuzzy systems with unmeasurable premise variables. The proposed design method considers uncertainty for such a problem for the first time. Using some linear transformations for the output matrices of each local model of the T–S fuzzy system, and employing Finsler's lemma, the robust stability conditions in the form of linear matrix inequalities (LMIs) are derived. Two numerical simulations are provided to show the validity of the proposed method.

Robust fault tolerant tracking controller design for unknown inputs T–S models with unmeasurable premise variables

This work concerns the tracking problem of uncertain Takagi–Sugeno fuzzy continuous systems with unmeasurable premise variables and affected by unknown inputs. The aim is to synthesize a fault tolerant controller (FTC) ensuring trajectory tracking of a desired reference model. To emit the original plant system, a norm bounded parametric uncertainty is employed in building the T–S model. The control scheme is based on a fuzzy observer to estimate both faults and faulty system states; a proportional integer (PI) observer to estimate constant faults is then adopted. Using descriptor redundancy property and L2 optimization to attenuate the unknown inputs effect, a solution is proposed in terms of bilinear matrix inequalities (BMIs). The performances of the proposed approach are pointed out by accentuating on a model of wastewater treatment plant (WWTP) through numerical results.

Takagi-Sugeno Sliding Mode Observer Design for Fault Diagnosis in Pitch Control Systems of Wind Turbines1

The performance and reliability of the pitch control systems significantly influences the functional safety of wind turbines. In this paper an observer-based fault detection approach for a class of nonlinear systems, which can be modeled by Takagi-Sugeno (TS) fuzzy models, is presented and applied to electro mechanical pitch drive systems of wind turbines. To achieve robustness we propose a TS fuzzy observers combined with sliding mode that deals with unmeasurable premise variables, bounded uncertainties in the plant and allows fault estimation based on an equivalent output error injection approach. The stability of the error dynamics is ensured by linear matrix inequality (LMI) conditions. Based on a derived physical model of the pitch drive system and the unknown but bounded wind loads the robust observer is systematically designed using the TS system form of the plant. Simulation results demonstrate the effectiveness of the proposed scheme.

Observer synthesis for uncertain nonlinear systems. Application to waste-water treatment plants

The paper proposes an observer synthesis for uncertain nonlinear systems, described by multimodels with unmeasurable premise variables, affected by unknown inputs. A proportional multi-integral observer is considered in order to estimate the system states and the unknown inputs and minimize the influence of the model uncertainties. The stability analysis and the observer synthesis are expressed through linear matrix inequalities based on the Lyapunov method. The performances of the proposed observer synthesis method are highlighted through the application to a waste-water treatment plant model, which is an uncertain nonlinear system affected by unknown inputs.

State estimation of two-time scale multiple models. Application to wastewater treatment plant

This paper addresses the state estimation of two-time scale nonlinear systems with an unknown input multi-observer (UIMO). In order to design such an observer, the nonlinear system presented in a singular perturbed form is transformed into an equivalent multiple model with unmeasurable premise variables (UPV) affected by unknown inputs (UI). Then an observer is built and the stability analysis of the state reconstruction error is performed by using the Lyapunov method that leads to the resolution of linear matrix inequalities (LMIs). The performances of the proposed estimation method are highlighted through the application to a wastewater treatment plant (WWTP) model.

Observers design for uncertain Takagi–Sugeno systems with unmeasurable premise variables and unknown inputs. Application to a wastewater treatment plant

Abstract This article aims the observer synthesis for uncertain nonlinear systems and affected by unknown inputs, represented under the multiple model (MM) formulation with unmeasurable premise variables. A proportional integral observer (PIO) is considered. In order to design such an observer, the nonlinear system is transformed into an equivalent MM form. The Lyapunov method, expressed through linear matrix inequality (LMI) formulation, is used to describe the stability analysis and for the observer synthesis. An application to a model of wastewater treatment plant (WWTP) is considered and the performances of the proposed approach are illustrated through numerical results.

Driver attention warning system based on a fuzzy representation of the vehicle model

AbstractIn this paper a lane departure detection method is studied and evaluated using the full vehicle dynamics software CarSim. The road curvature is estimated and compared to the vehicle trajectory curvature. The proposed algorithm takes account of the steering dynamics and uses the Time to the Lane Keeping (TLK) as a second risk indicator in order to reduce false alarms and integrate the driver corrections. The used nonlinear model deduced from the vehicle lateral dynamics and a vision system is represented by a T-S fuzzy model. Stability conditions of the fuzzy observer are expressed in terms of linear matrix inequalities (LMI)using unmeasurable premise variables. Simulation results show good efficiency of the method under different driving scenarios.

State estimation of Takagi–Sugeno systems with unmeasurable premise variables

This study is dedicated to the design of observers for non-linear systems described by Takagi–Sugeno (T–S) multiple models with unmeasurable premise variables. Furthermore, this T–S structure can represent a larger class of non-linear systems compared to the T–S systems with measurable premise variables. Considering the state of the system as a premise variable allows one to exactly represent the non-linear systems described by the general form x=f(x, u). Unfortunately, the developed methods for estimating the state of T–S systems with measured premise variable are not directly applicable for the systems that use the state as a premise variable. In the present paper, firstly, the design of observers for T–S systems with unmeasurable premise variable is proposed and sufficient convergence conditions are established by Lyapunov stability analysis. The linear matrix inequality (LMI) formalism is used in order to express the convergence conditions of the state estimation error in terms of LMI and to obtain the gains of the observer. Secondly, the proposed method is extended in order to attenuate energy-bounded unknown inputs such as disturbances. An academic example is proposed to compare some existing methods and the proposed one.

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.

Discussion on ‘Optimal Control of Disturbed Linear-Quadratic Differential Games’ by G. Jank and G. Kun

In this paper, an active Fault Tolerant Tracking Controller (FTTC) scheme dedicated to vehicle dynamics system is proposed. To address the challenging problem, an uncertain dynamic model of the vehicle is firstly developed, by considering the lateral forces nonlinearities as a Takagi–Sugeno (TS) representation, the sideslip angle as unmeasurable premise variables and the road bank angle as an unknown input. Subsequently, the vehicle dynamic states with the sensor faults are jointly estimated by a descriptor observer on the basis of the roll rate and the steering angle measures. Then a fault tolerant tracking controller is synthesized and solutions are proposed in terms of Linear Matrix Inequalities (LMIs). Simulation results show that the proposed FT control approach can effectively improve tracking performance of the vehicle motion.