Fault diagnosis for hybrid systems based on a bank of linear observers and a discrete automaton
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Fault diagnosis for hybrid systems based on a bank of linear observers and a discrete automaton Héla Gara1 · Kamel Ben Saad1 Received: 17 October 2019 / Accepted: 22 September 2020 © Springer Nature Switzerland AG 2020
Abstract This paper presents a fault diagnosis approach for a four-tank system considered as a hybrid dynamical system. The proposed diagnosis approach is based on a hybrid observer composed of a discrete automaton and a bank of linear observers. An automaton is used to improve the performance of the proposed method. For this study, we considered sensor, parametric and discrete faults. Simulation results showed the efficiency of the proposed diagnosis approach to detect and to localize the considered faults, despite the hybrid behaviors of the studied system. Keywords Hybrid dynamical system · Four tank system · Fault diagnosis · Hybrid observer · Linear observers · Discrete automaton
1 Introduction Nowadays, the modern production tools of some industrial systems are becoming more complex. So, the modeling of these systems has always been an issue. In fact, the system model is an abstraction of the real one. However, some complex systems combine continuous and discrete behaviors. These kinds of systems are called hybrid dynamical systems (HDS). HDS can be classified into several classes. Among them, we can cite switched linear systems, composed of a set of linear subsystems, called modes of functioning and controlled by a discrete events algorithm [1–4]. Reliability, availability, and safety have also become real issues for some industrial applications. Therefore, many fault diagnosis techniques have been proposed. They were used to detect and to localize the faults which can occur and generate damage in systems at any time. These techniques can be divided into two classes. The first one is based on mathematical models such as the parity space, observer and parametric estimation [5–7]. The second one
is based on artificial intelligence, artificial neural network or fuzzy logic and is called qualitative approaches [8]. Studying observability for the fault diagnosis of HDS has been the subject of several studies. The authors in [9] developed a diagnosis technique based on a bank of Luenberger observers ensuring the detection of sensor and parameter faults. In [10] a faults signature is generated by a switched robust observer to detect only single sensor fault. The convergence of the proposed observer by using the LMI conditions. Based on higher-order sliding mode observer, authors in [11] proposed an approach to detect the kind of faults that affect the continuous part of the switched linear systems. In [12], there are two designed observer methods for switched systems in the presence of sensor and actuator faults were proposed. Indeed, a few works focused on the modeling of HDS for fault diagnosis that takes into account the interaction of the two parts: continuous and discrete. Authors in [13] presented a quantitative method based on the hybrid bond graph that describes the hybrid system behavi
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