Brief paper: Nonlinear robust fault reconstruction and estimation using a sliding mode observer
Citations
327 citations
Cites background or methods from "Brief paper: Nonlinear robust fault..."
...The known nominal system model in (3) is similar to the model used in Yan and Edwards (2007)....
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...…considered for Lipschitz nonlinear systems in the fault diagnosis literature (e.g., Chen and Saif (2007), Vijayaraghavan et al. (2007), Yan and Edwards (2007)), which, to achieve robustness, additionally assumes that certain rank conditions are satisfied by the distribution matrix of the…...
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...For instance, Vijayaraghavan, Rajamani, and Bokor (2007) addressed the sensor fault diagnosis problem by assuming the absence of modeling uncertainty, and in Chen and Saif (2007), Yan and Edwards (2007) sliding mode 0005-1098/$ – see front matter© 2009 Elsevier Ltd....
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...By choosing x1 = q1, x2 = q̇1, x3 = q2, x4 = q̇2, and assuming that the motor position, motor velocity, and the sum of link position and link velocity are measured (see, e.g. Yan and Edwards (2007)), a state space model of the system can be obtained....
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...…2004; Garciá & Frank, 1997; Hammouri, Kinnaert, & El Yaagoubi, 1999; Krishnaswami & Rizzoni, 1997; Mhaskar, McFall, Gani, Christofides, & Davis, 2008; De Persis & Isidori, 2001; Wang, Huang, & Daley, 1997; Yan & Edwards, 2007; Zhang, Polycarpou, & Parisini, 2002, and the references cited therein)....
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293 citations
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Additional excerpts
..., [4], [6], [9], [14], [17] and the references therein....
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152 citations
Cites background from "Brief paper: Nonlinear robust fault..."
...To overcome this, Tan and Edwards [21] proposed an FDI scheme for a class of 1063-6536 © 2014 IEEE....
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...On the basis of the work by Edwards et al. [19], Tan and Edwards [20] proposed a sensor fault reconstruction method for well-modeled linear systems through the linear matrix inequality (LMI) technique....
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...Yan and Edwards [23] proposed a precise fault reconstruction scheme, using equivalent output error injection, for a class of nonlinear systems with uncertainty....
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...Edwards and Tan [13] and Alwi and Edwards [14] proposed fault reconstruction methods which estimate the magnitude and shape of faults in addition to detection and isolation....
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...This constraint was relaxed by Yan and Edwards [1], where the fault distribution vector and the structure matrix of the uncertainty are allowed to be functions of the system’s output and input....
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References
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"Brief paper: Nonlinear robust fault..." refers background in this paper
...where eq denotes the equivalent output error injection signal required to maintain the sliding motion (Edwards & Spurgeon, 1998; Utkin, 1992), and (·) is defined by (e1, z, ẑ, u) := A3e1 + G2(T −1z, u) − G2(T −1ẑ, u)....
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...This shows that a reachability condition is satisfied: see Utkin (1992) for example....
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...…(21) and (44): (e1, z, ẑ, u) + E2 (T −1z, u, t) + D2f (y, u, t) − eq = 0, (45) where eq denotes the equivalent output error injection signal required to maintain the sliding motion (Edwards & Spurgeon, 1998; Utkin, 1992), and (·) is defined by (e1, z, ẑ, u) := A3e1 + G2(T −1z, u) − G2(T −1ẑ, u)....
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...Sliding mode techniques, however, have good robustness and are completely insensitive to so-called matched uncertainty (Edwards & Spurgeon, 1998; Utkin, 1992)....
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3,826 citations
"Brief paper: Nonlinear robust fault..." refers background or methods in this paper
...In the last few decades, various modelbased approaches have been developed (Chen & Patton, 1999), and in particular observer-based techniques have obtained much attention....
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...The comprehensive survey paper (Frank, 1987) provides an overview of observer-based approaches, and many results have been established (see e.g. Chen & Patton, 1999; Frank & Ding, 1997; Shields, 2005; Xu & Zhang, 2004 and the references therein)....
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...All rights reserved. doi:10.1016/j.automatica.2007.02.008 a very effective method for FDI both in theory and practice (Chen & Patton, 1999)....
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3,355 citations
"Brief paper: Nonlinear robust fault..." refers background or methods in this paper
...By the same reasoning as used in Edwards and Spurgeon (1998), and employing further changes of coordinates, the system matrix can be made to have the structure in (7) whilst preserving the structures of the input and output distribution matrices....
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...1 of Edwards and Spurgeon (1998). From Edwards and Spurgeon (1998), it is easy to see that the nonnegative integer l in Lemma 1 above denotes the number of invariant zeros of the triple (A, [E D], C)....
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...Sliding mode techniques, however, have good robustness and are completely insensitive to so-called matched uncertainty (Edwards & Spurgeon, 1998; Utkin, 1992)....
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...From Edwards and Spurgeon (1998), it is easy to see that the nonnegative integer l in Lemma 1 above denotes the number of invariant zeros of the triple (A, [E D], C)....
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...Therefore, the conclusion in Lemma 1 above cannot be directly obtained from Lemma 6.1 of Edwards and Spurgeon (1998)....
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