A sliding mode observer for robust fault reconstruction in a class of nonlinear non-infinitely observable descriptor sys
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ORIGINAL PAPER
A sliding mode observer for robust fault reconstruction in a class of nonlinear non-infinitely observable descriptor systems Joseph Chang Lun Chan Chee Pin Tan
· Tae H. Lee
·
Received: 18 April 2020 / Accepted: 24 July 2020 © Springer Nature B.V. 2020
Abstract This paper presents a sliding mode observer (SMO) for robustly reconstructing faults affecting a class of nonlinear non-infinitely observable descriptor systems. Preliminary transformations are utilised to reexpress the system such that the design freedom in its structure is easier to exploit. An infinitely observable system is formed by treating some states as unknown inputs. The faults are then reconstructed from measurable inputs and outputs using a SMO. The structure of the SMO bounds the nonlinear components of its estimation errors. The effect of disturbances on the fault reconstruction is minimised using linear matrix inequality techniques. A summarised design procedure for the SMO scheme is presented. Finally, a simulated example is carried out to showcase the efficacy of the scheme. Keywords Nonlinear systems · Descriptor systems · Sliding mode observers · Fault reconstruction · Uncertain systems · Infinite observability
J. C. L. Chan · T. H. Lee (B) Division of Electronic Engineering, Jeonbuk National University, 567 Baekje-daero, Jeonju 54896, Republic of Korea e-mail: [email protected] C. P. Tan School of Engineering and Advanced Engineering Platform, Monash University Malaysia, Subang Jaya, Selangor, Malaysia
1 Introduction Systems often encounter faults during their operation, which if left unaddressed could lead to degradation in performance and costly downtime. Thus, it is essential that faults be detected and reconstructed when and as they occur so that timely intervention can be taken to improve system reliability [1,2]. Observers are commonly utilised for fault reconstruction [3–5], but numerous restrictive assumptions are made during their design process [6]. The sliding mode observer (SMO) is a special type of observer that incorporates a discontinuous switching term, which forces the output estimation error to zero in finite time. It is found that the switching term contains information on the fault and could be used to reconstruct the fault [7]. SMOs are able to reconstruct faults with more relaxed conditions compared to linear observers [8] and are therefore more widely applicable than conventional observers [9]. Descriptor systems (which are also referred to as singular systems [10,11]) contain algebraic equations representing links between subsystems of differential equations with dynamics evolving on different timescales. They are found in many different domains, such as in flexible-link robotic manipulators [3], chemical mixing tanks [12] and interconnected large-scale systems [13]. Descriptor systems have multiple measures of observability (unlike regular state-space systems which only have one: global observability)—one of which is infinite observability [14]. Many different
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