Abstract
This article introduces a nonlinear observer to reconstruct faults in a class of nonlinear descriptor systems affected by disturbances, in both the state and output equations. The fault enters the system through nonlinear functions in both its state and output equations. The original system is first transformed such that design freedom in its structure is easier to exploit, and then a nonlinear observer is designed based on the transformed system to reconstruct the fault. Linear matrix inequalities are used to determine the gains of the observer such that the effect of the disturbances on the fault reconstruction is bounded. Finally, three simulation examples are carried out to verify the effectiveness of the scheme.
Highlights
Practical systems are often affected by faults [1], which can cause costly downtime
Remark 1: Assumption 1 implies that the root-mean square (RMS) values of f, f, ξxo, ξyo, ξxo, ξyo, and dg(Toxo) dt are finite, which means these signals are energy-bounded, and is required to reconstruct faults entering the nonlinear functions in system (1)–(2)
The following definition quantifies the performance of the proposed observer: Definition 1 (Definition 1, [37]): Consider the two signals ci : [0, ∞) → R and co : [0, ∞) → R, and let Z be the set of all admissible signals ci
Summary
Practical systems are often affected by faults [1], which can cause costly downtime. it is important to reconstruct faults as they occur to mitigate their effects. L. Chan et al.: Nonlinear Observer for Robust Fault Reconstruction in OSL and QIB Nonlinear Descriptor Systems be positive, negative, or even zero [32], [33]. Chan et al.: Nonlinear Observer for Robust Fault Reconstruction in OSL and QIB Nonlinear Descriptor Systems be positive, negative, or even zero [32], [33] These two conditions could reduce conservativeness when designing observers using linear matrix inequalities (LMIs) [34]. This article proposes a robust fault reconstruction scheme for OSL and QIB nonlinear descriptor systems to address these limitations. The proposed work considers systems with faults and disturbances affecting the outputs, as well as faults entering nonlinear functions in both the state and output equations, which make the problem much more challenging. ∗ denotes the transposed term in the symmetric positions of a matrix, and r(·) is the unit ramp function
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