H_/H_∞ fault detection observer design for a polytopic LPV system using the relative degree

Abstract

This paper proposes an H_/H∞ fault detection observer method by using generalized output for a class of polytopic linear parameter-varying (LPV) systems. As the main contribution, with the aid of the relative degree of output, a new output vector is generated by gathering the original output and its time derivative, and it is feasible to consider H_ actuator fault sensitivity in the entire frequency for the new system. In order to improve actuator and sensor fault sensitivity as well as guarantee robustness against disturbances, simultaneously, an H_/H∞ fault detection observer is designed for the new LPV polytopic system. Besides, the design conditions of the proposed observer are transformed into an optimization problem by solving a set of linear matrix inequalities (LMIs). Numerical simulations are provided to illustrate the effectiveness of the proposed method.

H−/L∞ fault detection observer for linear parameter‐varying systems with parametric uncertainty

“…Next, we prove inequality (29) is a sufficient condition of inequality (26). Using the Schur complement lemma, inequality (29) can be rewritten as…”

“…Besides, uncertainty was not considered in many existing H − ∕H ∞ fault detection methods. [23][24][25][26] Note that a finite-frequency approach for fault estimation has been considered recently in the work of Tian and Zhu. 27 However, the method in the aforementioned work 27 is only suitable for linear time-invariant systems not for LPV systems.…”

Design of H_/H∞ fault detection observer for closed-loop nonlinear system with disturbance

“…The methods can be divided into two categories, namely, one is to separate interference from residual, including eigenvalue assignment method and unknown input observer method, which, however, need to satisfy strict conditional constraints. The other is to construct an observer with robustness against unknown disturbances, including the H∞ observer method (Bai et al , 2006), the L∞ observer method (Tabarraie et al , 2016), the L2/L∞ observer method and the H_/L∞ observer method (Zhou et al , 2018a, 2018b). However, the methods of H∞ observer and the L2/L∞ observer are subject to bounded energy disturbances.…”

“…To weigh the fault sensitivity and the robustness against the disturbances, Qian et al (2012) proposed a hybrid method of H_/H∞ fault detection observer for the uncertainty of the system model and the unknown input disturbances. Zhou et al (2018a, 2018b) designed a method of generalized H_/H ∞ fault detection observer for a class of linear parameter variation systems.…”