Proportional Multiple Integral Observer Research Articles

Estimation and fault diagnosis for non‐linear system with time‐varying faults and measurement noises: Application on two CSTRs in series

AbstractA continuously stirred tank reactor (CSTR) is largely used in water treatment and in chemical and biological processes. It is characterized by a complex non‐linear behaviour. Operating large reactors in industry can be expensive, so a common trick used to reduce costs is to operate multiple CSTRs in series. Consequently, the CSTR is usually exposed to faults and noises. This paper addresses the design of a robust observer for estimation and fault diagnosis strategy on two CSTRs in series. The considered system is affected simultaneously by time‐varying actuator and sensor faults with measurement noises. The Takagi‐Sugeno multimodel approach is proposed to transform the non‐linear model into an interpolation of several linear sub‐models with non‐measurable premise variables. The purpose of this brief is to provide the state and the fault estimation for the considered system using a proportional multiple integral (PMI) unknown input observer. The exponential stability conditions are studied with the Lyapunov theory and L2 optimization and formulated in terms of linear matrix inequalities. In addition, a comparative study with a PMI observer is conducted. Finally, the proposed observer is used for time‐varying fault detection and isolation.

Robust fault estimation for Takagi‐Sugeno fuzzy systems with state time‐varying delay

SummaryThis paper deals with the problem of H∞ robust fault estimation for a class of Takagi‐Sugeno (T‐S) fuzzy systems with state time‐varying delay, sensor, and actuator faults. The faults considered in this paper are time‐varying signals whose k‐order derivatives with respect to time are bounded. Then, we propose a proportional multiple integral observer to achieve simultaneous estimation of system states and time‐varying actuator and sensor faults. Furthermore, one less conservative delay‐dependent sufficient condition for the existence of fault estimation observer is given in terms of linear matrix inequality. The disturbance attenuation is constrained to a given level using H∞ performance index. Finally, simulation results of one numerical example is presented to show the effectiveness of the proposed method.

Trade‐offs on fault estimation via proportional multiple‐integral and multiple‐resonant observers for discrete‐time systems

The authors develop a fault estimation strategy which is based on a novel proportional multiple-integral (PMI) and multiple-resonant observer. This observer is an extension of the well-known PMI observer and it is able to estimate from low to high-frequency fault signals. The proposed estimation strategy is applied to discrete-time systems which are affected by faults and stochastic noises. We present a multi-objective design strategy of the observer that fixes the trade-offs between practical engineering parameters regarding the noise attenuation and the ability to track each kind of fault dynamics considered by the augmented observer. They study the influence of the order of the observer on the steady-state and transient performance of the estimation of different types of faults. Finally, a numerical example is given to illustrate the effectiveness of the proposed observer, design and characterisation.

State and unknown inputs estimation for Takagi–Sugeno systems with immeasurable premise variables: Proportional Multiple Integral observer design

In this work, we focus on the design of a Proportional Multiple Integral (PMI) observer for Takagi–Sugeno (T–S) fuzzy systems with immeasurable premise variables subjected to unknown inputs. The LMI-based stability conditions are significantly relaxed by the introduction of an output error injection in the premise variable of the PMI observer. The efficiency of the proposed observer is finally illustrated by a simulation example of a chaotic system.

Robust fuzzy fault tolerant control for induction motor subject to sensor fault

This study presents a strategy of fault tolerant control (FTC) to keep the vector controlled induction motor (IM). The aim is to minimise the effect of the sensor fault and the parametric uncertainties. Firstly, a fuzzy proportional multiple integral observer (PMIO) is used to estimate simultaneously the system state and the sensor fault. Secondly, a feedback robust state tracking control is synthesised to guarantee the control performances. The proposed controller is based on a T-S reference model to specify the desired trajectory. The performances of the trajectory tracking are analysed using the Lyapunov theory and the L2 optimisation. The gains of the observer and controller are obtained by solving a set of LMIs constraint. Finally, simulation results are given to show the effectiveness of the proposed control scheme.

Robust fuzzy fault tolerant control for induction motor subject to sensor fault

This study presents a strategy of fault tolerant control (FTC) to keep the vector controlled induction motor (IM). The aim is to minimise the effect of the sensor fault and the parametric uncertainties. Firstly, a fuzzy proportional multiple integral observer (PMIO) is used to estimate simultaneously the system state and the sensor fault. Secondly, a feedback robust state tracking control is synthesised to guarantee the control performances. The proposed controller is based on a T-S reference model to specify the desired trajectory. The performances of the trajectory tracking are analysed using the Lyapunov theory and the L2 optimisation. The gains of the observer and controller are obtained by solving a set of LMIs constraint. Finally, simulation results are given to show the effectiveness of the proposed control scheme.

Accelerometer error estimation and compensation for three-axis gyro-stabilized camera mount based on proportional multiple-integral observer

This paper deals with the problem of accelerometer error estimation and compensation for a three-axis gyro-stabilized camera mount. In a dynamic environment, the aircraft motion acceleration affects the accelerometer output and causes a degradation of attitude steady accuracy. In order to improve control accuracy, this paper proposes a proportional multiple-integral observer-based control strategy to estimate and compensate the accelerometer error. The basic idea of this paper is to approximate the error property by using a q-order polynomial function and extend the error and its derivatives as augmented states. Then a proportional multiple-integral observer is developed to estimate the error, with which the relationship between the error and the imbalance torque is formulated. The estimated value is compared to an angle threshold, the result of which is used to compensate the accelerometer output. Through static and vehicle-mounted experiments, it is demonstrated that compared with the traditional method, the proposed method can improve the attitude steady accuracy effectively.

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

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.

Chaos Synchronization Based on Unknown Input Proportional Multiple-Integral Fuzzy Observer

This paper presents an unknown input Proportional Multiple-Integral Observer (PIO) for synchronization of chaotic systems based on Takagi-Sugeno (TS) fuzzy chaotic models subject to unmeasurable decision variables and unknown input. In a secure communication configuration, this unknown input is regarded as a message encoded in the chaotic system and recovered by the proposed PIO. Both states and outputs of the fuzzy chaotic models are subject to polynomial unknown input withkth derivative zero. Using Lyapunov stability theory, sufficient design conditions for synchronization are proposed. The PIO gains matrices are obtained by resolving linear matrix inequalities (LMIs) constraints. Simulation results show through two TS fuzzy chaotic models the validity of the proposed method.

Proportional multiple-integral observer design for discrete-time descriptor linear systems

A type of proportional multiple-integral observers is proposed for discrete-time descriptor linear systems. First, some existence conditions of this type of observers are given. Then, a parametric design approach is proposed for proportional multiple-integral observers. Based on a general parametric solution to the generalised Sylvester-observer matrix equation, parameterisations for all the observer gains are given in terms of four parameter matrices. The proposed approach can offer all the degrees of design freedom and has great potential in applications. A numerical example is given to show the design procedure and the effectiveness of the proposed approach.

An FTC Approach to Wind Turbine Power Maximisation via T-S Fuzzy Modelling and Control

This paper presents a new strategy for offshore wind (OSW) turbine active sensor fault-tolerant control (FTC) to optimise the wind energy captured by a wind turbine operating at low wind speed via Takagi-Sugeno (T-S) multiple models with effective wind speed (EWS) estimation. The FTC strategy uses the proportional multiple integral observer (PMIO) as intermediate block between the system and the controller to provide (1) an estimation of the generator and/or rotor speed sensor(s) faults to compensate (hide) their effects from the T-S fuzzy dynamic output feedback controller (TSDOFC), and (2) robust estimation of the unknown aerodynamic torque component required to estimate the EWS. The Lyapunov stability condition and proof for the PMIO are derived and the TSDOFC stability with H∞ performance and D-stability constraints is formulated via a further Linear Matrix Inequality (LMI) problem. The strategy is illustrated using a non-linear benchmark system model of a wind turbine offered within a competition led by the companies Mathworks (USA) and KK-Electronic (Denmark).

Proportional multiple-integral observer design for descriptor systems with measurement output disturbances

A design approach for observers using multiple-integrals is presented for descriptor systems, which allows the authors to decouple or attenuate measurement output disturbances. Design schemes for both pure integral observers and proportional integral observers are investigated. Measurement noise and input disturbances are also simultaneously taken into account in the design. A systematic design procedure for a causal or normal multiple-integral observer is addressed, which can be implemented conveniently using Matlab software. The considered disturbance may be unbounded, which means that the presented design approach is suitable for more general cases. Moreover, the system state, together with the disturbance vector and its finite time derivatives can be simultaneously estimated. The proposed design has great potential for application to control problems, such as those in diagnosis or observer-based control. In addition, it also has good estimation robustness and can be directly applied to normal systems. Simulation results show a satisfactory tracking performance as compared to the results obtained for descriptor systems.