Fault diagnosis for Takagi-Sugeno nonlinear systems

Abstract

This paper addresses a new scheme for fault diagnosis in nonlinear systems described by Takagi-Sugeno multiple models. Two cases are considered, the first one concerns the T-S models with known premise variables (the input or the output of the system). For the second case it is supposed that the weighting functions depend on unmeasurable premise variables (state of the system). The approach is based on the design of observer-based residual generator by minimization of the disturbances effect and maximizing the effects of the faults. The synthesis is based on the L 2 formalism developed for linear systems. The convergence conditions are given in LMI formulation.

Actuator fault diagnosis of singular delayed LPV systems with inexact measured parameters via PI unknown input observer

“…Thus, the goal is to design observer (6) robust against these uncertainties in addition to noise and disturbance. In order to consider the uncertainty induced by inexact measured parameters and facilitate the PI-UIO design, the method proposed in [28] is extended. This is done by means of some manipulations of system (3) that allow reformulating it as an uncertain system as follows:…”

Robust fault detection of singular LPV systems with multiple time–varying delays

“…The reference models with the condition (40) are suitable for fault detection because they have no fault attenuation in any frequency range (Ichalal et al, 2009 …”

“…In addition to robustness, the residual should present good sensitivity to faults. Various methods such as model matching the residual with a reference model (Frisk and Nielsen, 2006;Mazars et al, 2008;Ichalal et al, 2009;Habib et al, 2010;Ahmadizadeh et al, 2014) and using the H − index condition to directly formulate fault sensitivity (Wang et al, 2007;Aouaouda et al, 2015;Zhai et al, 2014) were proposed for ensuring fault sensitivity in observer-based methods.…”

Nonlinear observer based sensor fault tolerant control for nonlinear systems

“…In the purpose of sensor fault diagnosis, the approach given in (Ichalal et al, 2009b) is adopted. In order to isolate the sensor faults, a residual vector is generated such that its i th component is only sensitive to the i th fault.…”

“…Theorem 4. (Ichalal et al, 2009b) The robust residual generator (5) exists if there exists symmetric and positive definite matrices P 1 and P 2 , matrices K i and M and a positive scalar γ solving the following optimization problem min…”