Approach to fault detection of time‐delay systems using functional observers

Abstract

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:

Functional observers design for positive systems with delays and unknown inputs

“…In practical control systems, it is often the case that the entire state vector is not available for feedback and only some of the system states are required for control purposes. These factors necessitate the need for observer‐based control strategies [4, 5] and the study of functional observers [6, 7]. This paper addresses the design of functional observers for time‐delay positive systems with unknown inputs.…”

Unknown input fractional-order functional observer design for one-side Lipschitz time-delay fractional-order systems

“…Although the problem of the state observer design for integer-order systems has been intensively investigated in many aspects (Huong, 2018; Huong and Thuan, 2017; Huong and Trinh, 2015, 2016; Huong et al, 2014; Thuan et al, 2012; Trinh et al, 2004, 2006, 2016). The results accounted for fractional-order systems are very few in the literature since this problem is challenging due to the complexity of fractional-order calculus equations and the fact that integer-order algorithms cannot be directly applied to the fractional-order systems.…”

Functional interval observer for the linear systems with disturbances

“…The functional observer, as an outstanding contribution of Luenberger and compared with estimating all states of a system, only needs to observe for the linear functional of the state vectors, and so largely reduce the order and complexity in designing observers so that the physical implementation of the observer theory algorithm is applied easily. Furthermore, in fault detection, the generation of the residual signal needs only to estimate the output of the system, and as known widely, the output is also a linear functional of the system states [6, 7]. Apart from lower orders, the design of functional observer only needs to be functional observable than to be observable for the state observer and therefore reduce the design requirements of the observers [8].…”