A new methodology is reported for designing functional observers to detect actuator faults of a class of time-delay systems where the matrix pair (A, C) is not observable. First, a generalised state transformation is used to transform the system into new coordinates where the delay term associated with the state vector is injected into the system's output and input. Then, a minimum-order functional observer is designed to construct a residual function that can trigger system faults. The finding is significant as it is now possible to detect faults of time-delay systems where the pair (A, C) is not required to be observable. A numerical example is given to illustrate the effectiveness of the proposed design approach.Introduction: Most of the state observer design methods reported in the literature for time-delay systems require that the matrix pair (A, C) be observable [1][2][3]. As a result, when this condition does not hold, any observer-based fault detection scheme that relies on such state observers cannot be realised. This Letter reports a new finding and a methodology for designing a minimum-order functional observer to detect actuator faults of a class of time-delay systems where the pair (A, C) is not observable. For ease of presenting our design methodology, let us consider a single-input time-delay system with an unpredictable fault signal f(t) entering from the system input defined as follows:
This paper examines the design of minimal-order residual generators for the purpose of detecting and isolating actuator and/or component faults in dynamical systems. We first derive existence conditions and design residual generators using only first-order observers to detect and identify the faults. When the first-order functional observers do not exist, then based on a parametric approach to the solution of a generalized Sylvester matrix equation, we develop systematic procedures for designing residual generators utilizing minimal-order functional observers. Our design approach gives lower-order residual generators than existing results in the literature. The advantages for having such lower-order residual generators are obvious from the economical and practical points of view as cost saving and simplicity in implementation can be achieved, particularly when dealing with high-order complex systems. Numerical examples are given to illustrate the proposed fault detection and isolation schemes. In all of the numerical examples, we design minimum-order residual generators to effectively detect and isolate actuator and/or component faults in the system.
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