Zonotopic fault detection observer design for Takagi–Sugeno fuzzy systems

Abstract

This paper considers zonotopic fault detection observer design in the finite-frequency domain for discrete-time Takagi-Sugeno fuzzy systems with unknown-but-bounded disturbances and measurement noise. We present a novel fault detection observer structure, which is more general than the commonly used Luenberger form. To make the generated residual sensitive to faults and robust against disturbances, we develop a finite-frequency fault detection observer based on generalized Kalman-Yakubovich-Popov lemma and P-radius criterion. The design conditions are expressed in terms of linear matrix inequalities. The major merit of the proposed method is that residual evaluationa can be easily implemented via zonotopic approach. Numerical examples are conducted to demonstrate the proposed method.

Fault diagnosis by interval‐based adaptive thresholds and peak‐to‐peak observers

“…Thanks to their flexibility and high estimation accuracy, zonotopic methods have been widely studied. 32,33 Many optimization approaches such as P-radius minimization and F-radius minimization were used to reduce the conservatism of adaptive thresholds. Moreover, to obtain a trade-off between computational complexity and conservatism, ellipsoid-based approaches are equally adopted for threshold computation.…”

“…Since all the admissible residuals are bounded by some compact sets, the set‐based approaches can compute adaptive thresholds by representing and propagating the bounded uncertainties by geometric sets such as polytopes, zonotopes and ellipsoids. Thanks to their flexibility and high estimation accuracy, zonotopic methods have been widely studied 32,33 . Many optimization approaches such as $$$ P $$$‐radius minimization and $$$ F $$$‐radius minimization were used to reduce the conservatism of adaptive thresholds.…”

Sensor fault detection for dynamic point‐the‐bit rotary steerable system via finite‐frequency domain observer and zonotope residual evaluation

“…Since the tight estimations of admissible residual sets can be obtained by the zonotope set-membership approach [39], it becomes straightforward to evaluate residuals based on the residual sets. Recently, a number of zonotope-based residual evaluation methods have been proposed to detect faults, for instance, the actuator FD methods in [11,[40][41][42]. However, little attention has been paid to the residual evaluation for the sensor fault in the presence of drilling disturbances.…”

Zonotopic fault detection observer design for discrete‐time systems with adaptively adjusted event‐triggered mechanism

“…Recently, a zonotope-based fault detection approach has attracted much attention from researchers. Li et al [30] studied the zonotopic fault detection for a class of Takagi-Sugeno fuzzy systems. The problem of fault detection and isolation was investigated for a class of descriptor systems via a zonotopic residual evaluation method in [27].…”