Finite Frequency Performance Indexes Research Articles

Observer-based fault detection for continuous–discrete systems in T-S fuzzy model

The observer design problem for fault detection is considered for nonlinear continuous–discrete systems with Takagi–Sugeno fuzzy scheme and finite frequency specification in this paper. Two finite frequency performance indices H− and H∞ are introduced to evaluate the sensitivity to faults and the robustness against disturbances in finite frequency domains. Based on the H−/H∞ technique, this research is aimed to design a fault detection observer for the addressed system. Sufficient conditions are derived to guarantee the asymptotic stability, fault sensitivity and disturbance robustness of the residual error system. Simulation results further demonstrate effectiveness of the proposed approach.

Fault detection in wind turbine transmission systems via finite frequency observers

AbstractThis paper addresses fault detection for wind turbine transmission system (WTTS) subject to actuator stuck faults and wind disturbances. Taking into account the frequency domain characteristics of such faults and disturbances, a modified observer is designed in terms of finite frequency (FF) performance indices that have detection performances superior to some formerly proposed ones. With the generalized Kalman–Yakubovich–Popov (GKYP) lemma and the Lyapunov theory, the FF performance indices are related to linear matrix inequalities (LMIs), and parametrization of the corresponding FF modified observer is completed by convex optimization under LMI constraints. One typical advantage of the modified observer is that fault and disturbance signals in distinctive FF domains can be dealt with simultaneously. This makes the residual system sensitive to actuator stuck faults and robust against external wind disturbances. Simulations are included to show that the design method achieves fault detection performances better than those of the entire frequency observers.

Fault detection for fractional‐order linear systems in finite frequency domains

This study is concerned with the fault detection problem for fractional-order linear systems with disturbances. The H − and H ∞ performance indices of fractional-order systems in finite frequency domains are applied to measure the fault sensitivity and the disturbance robustness. A fractional-order fault detection observer is designed to satisfy the two finite frequency performance indices simultaneously. Based on the generalised Kalman–Yakubovich–Popov lemma and the projection lemma, the design conditions are obtained in terms of linear matrix inequalities. Compared with the existing full frequency approaches, the proposed finite frequency one can get better results when the frequency ranges of faults and disturbances are known. The effectiveness of the proposed method is validated by numerical examples.

Fault detection observer design for 2-D continuous nonlinear systems with finite frequency specifications

This research studies the problem of fault detection observer design for two-dimensional (2-D) continuous-time nonlinear systems in Takagi–Sugeno (T–S) form. Finite frequency (FF) specifications are used to design the observers, which makes observer designing different from previously proposed 2-D detection observers. Faults and disturbances are considered to be dominated in two different FF domain intervals. Fault sensitivity and disturbance robustness are measured by two FF performance indices, respectively. The aim of this paper is to design fault detection observers such that the residual error system has the sensitivity to faults and the desired robustness to disturbances. Sufficient conditions for the existence of a desired fault detection fuzzy observer are established in terms of linear matrix inequalities (LMIs). Simulation results indicate that faults can be detected effectively using the proposed method.

Multi-Objective H-/H∞ Fault Detection Filter Design For T-S Fuzzy Systems With Finite Frequency Specifications

This study aims to synthesize a fault detection filter for continuous-time T-S fuzzy systems. The proposed filter is designed in finite frequency domain in as much as the frequency ranges of the fault and unknown disturbances are assumed to be known beforehand and to belong in finite frequency bands. The generated residual is ensured to be as sensitive as possible to faults and as robust as possible against unknown disturbances by means of two finite frequency performance indices such as H_ and H∞ norms. By the use of the Generalised Kalman-Yakubovich-Popov (GKYP) lemma and the Lyapunov method, sufficient design conditions are derived in LMI terms. Finally, simulation study is introduced to validate the developed approach.

Fault Detection and Isolation Method Based on H−/H∞ Unknown Input Observer Design in Finite Frequency Domain

AbstractThis paper proposes an actuator fault detection and isolation strategy based on a bank of unknown input observers with finite frequency specifications. In order to deal with actuator fault diagnosis problem, a bank of H−/H∞ unknown input observers are designed to generate residuals, which are insensitive to the corresponding faults but sensitive to the other actuators faults, and meanwhile robust against the unknown disturbances. In this paper, the actuator faults and unknown disturbances are considered to belong to finite frequency domains, and two finite frequency performance indices are used to measure the fault sensitivity and the disturbance robustness of the residuals. Furthermore, some parameters for extra design of freedom are introduced in the H−/H∞ unknown input observers design. Based on the generalised Kalman‐Yakubovich‐Popov (GKYP) lemma, the design conditions of the H−/H∞ unknown input observer are derived and formulated as linear matrix inequalities (LMIs). Finally, a VTOL aircraft model is used to demonstrate the performance of the proposed fault diagnosis scheme.

Finite frequency fault detection for T-S fuzzy singular multiple timedelay systems

This paper focuses on the problem of fault detection (FD) for a class of nonlinear systems described by the T-S fuzzy singular model with multiple time delays and actuator faults. Two finite-frequency performance indices are introduced to measure fault sensitivity and disturbance robustness. To reduce the conservatism of the existing results, a finite frequency domain approach to fuzzy singular multiple time-delay systems is proposed. Then based on the approach, filter design conditions for the solvability of this problem are presented in terms of linear matrix inequalities (LMIs). Finally, simulation studies are provided to demonstrate the application of the proposed method.

Fault detection for singular switched linear systems with multiple time-varying delay in finite frequency domain

ABSTRACTThis paper deals with the problem of the fault detection (FD) for continuous-time singular switched linear systems with multiple time-varying delay. In this paper, the actuator fault is considered. Besides, the systems faults and unknown disturbances are assumed in known frequency domains. Some finite frequency performance indices are initially introduced to design the switched FD filters which ensure that the filtering augmented systems under switching signal with average dwell time are exponentially admissible and guarantee the fault input sensitivity and disturbance robustness. By developing generalised Kalman–Yakubovic–Popov lemma and using Parseval's theorem and Fourier transform, finite frequency delay-dependent sufficient conditions for the existence of such a filter which can guarantee the finite-frequency H− and H∞ performance are derived and formulated in terms of linear matrix inequalities. Four examples are provided to illustrate the effectiveness of the proposed finite frequency method.

A fault detection observer design for LPV systems in finite frequency domain

This paper addresses the fault detection observer design problem for linear parameter-varying systems. Two finite frequency performance indexes are introduced to measure the fault sensitivity and the disturbance robustness. First, the H− index fault sensitivity condition in finite frequency domain is obtained by generalised Kalman–Yakubovich–Popov lemma and new linearisation techniques. Then, with the aid of Kalman–Yakubovich–Popov lemma and projection lemma, the stability and robustness conditions are derived. It turns out that the non-convexity problem which is caused by dealing with the above three conditions can be translated into a bilinear matrix inequality optimisation problem by increasing the dimensions of slack variable matrix. An iterative linear matrix inequality algorithm is proposed to get the solution. The effectiveness of the filter is shown via three numerical examples.

Fault Detection in Finite Frequency Domain for Takagi-Sugeno Fuzzy Systems With Sensor Faults

This paper is concerned with the fault detection (FD) problem in finite frequency domain for continuous-time Takagi-Sugeno fuzzy systems with sensor faults. Some finite-frequency performance indices are initially introduced to measure the fault/reference input sensitivity and disturbance robustness. Based on these performance indices, an effective FD scheme is then presented such that the generated residual is designed to be sensitive to both fault and reference input for faulty cases, while robust against the reference input for fault-free case. As the additional reference input sensitivity for faulty cases is considered, it is shown that the proposed method improves the existing FD techniques and achieves a better FD performance. The theory is supported by simulation results related to the detection of sensor faults in a tunnel-diode circuit.

Fault Detection for T–S Fuzzy Discrete Systems in Finite-Frequency Domain

This paper investigates the problem of fault detection for Takagi-Sugeno (T-S) fuzzy discrete systems in finite-frequency domain. By means of the T-S fuzzy model, both a fuzzy fault detection filter system and the dynamics of filtering error generator are constructed. Two finite-frequency performance indices are introduced to measure fault sensitivity and disturbance robustness. Faults are considered in a middle frequency domain, while disturbances are considered in another certain finite-frequency domain interval. By using the generalized Kalman-Yakubovic-Popov Lemma in a local linear system model, the design methods are presented in terms of solutions to a set of linear matrix inequalities, which can be readily solved via standard numerical software. The design problem is formulated as a two-objective optimization algorithm. A numerical example is given to illustrate the effectiveness and potential of the developed techniques.

A finite frequency domain approach to fault detection observer design for linear continuous‐time systems

AbstractThis paper deals with the fault detection observer design problem in finite frequency domain for linear time‐invariant continuous‐time systems with bounded disturbances. Two finite frequency performance indexes are introduced to measure the fault sensitivity and the disturbance robustness. Faults are considered in the low frequency domain while disturbances are considered in certain finite frequency domain. With the aid of the Generalized Kalman‐Yakubovich‐Popov lemma, the design methods are presented in terms of solutions to a set of linear matrix inequalities. An example of the VTOL aircraft is studied to illustrate the effectiveness of the proposed method. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society