Fault Reconstruction for Lipschitz Nonlinear Systems Using Higher Terminal Sliding Mode Observer
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Fault Reconstruction for Lipschitz Nonlinear Systems Using Higher Terminal Sliding Mode Observer DAI Cong ∗ (
),
LIU Yongzhi (
ì),
SUN Haoshui (
)
(Aviation Engineering College, Air Force Engineering University, Xi’an 710038, China)
© Shanghai Jiao Tong University and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract: This paper considers the design of an adaptive second order terminal observer for robust fault reconstruction of nonlinear Lipschitz systems with unknown upper bound of derivative fault. Firstly, a linear transforming matrix is introduced, which transforms the system into two subsystems, and thus to reduce the dimension of the system. One of the subsystem is affected by fault and disturbances, while the other is free, which simplifies the design of observer. Then, the design method of the observer gain matrix is transformed into a convex optimization problem under linear matrix inequalities (LMIs). A second order non-singular terminal sliding mode observer is designed for the transformed system to realize the accurate estimation of state and fault. Considering the unknown upper bound of derivative fault, an adaptive algorithm is designed in the equivalent output error injection signal to ensure the sliding mode motion reach the sliding surface within limited time. Finally, an example demonstrates the effectiveness of the proposed method in the paper. Key words: second order terminal sliding mode observer, linear matrix inequalities, fault reconstruction, Lipschitz systems CLC number: TP 277 Document code: A
0 Introduction Fault detection and isolation (FDI) is a vital component of the active fault tolerant control (FTC) schemes. Among the techniques of model-based FDI, the observer-based techniques have obtained much attention. Compared with the techniques of FDI based on residual, where a residual signal is generated and flagged when an abnormal condition takes place in the system, the techniques of fault reconstruction can directly approximate the shape and magnitude of fault signals according to the state affected by the faults, and have a much wider application in the FDI especially in the active FTC. The sliding mode observer (SMO) has strong robustness to the matched uncertainties and high abilities to reconstruct unknown signals faults, and it has been successfully used for FDI in recent years[1-8] . One of the perceived drawbacks of first order SMO in physical systems is in dealing with the discontinuities which arise from the use of signum function. It can bring the case of producing a non-zero reconstruction when there are no faults, or even worse, the effect of a fault is masked. By producing a “zero” reconstrucReceived date: 2018-04-12 Foundation item: the National Natural Science Foundation of China (No. 61304120) ∗E-mail: [email protected]
tion in the presence of faults, furthermore the actual systems may be affected by non-linearity, disturbances and unknown faults, so it is necessary to research on a robust and precise fault reconstruction scheme based on improve
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