Modeling, Fault Detection, and Fault-Tolerant Control for Nonlinear Singularly Perturbed Systems With Actuator Faults and External Disturbances

Abstract

A fuzzy singular perturbation model with additive faults on control inputs and external disturbances, a fuzzy <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> fault detector (FHFD), and a fuzzy <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> fault-tolerant controller (FHFTC) are constructed for nonlinear singularly perturbed systems (NSPSs) with actuator faults and external disturbances, respectively. The sufficient conditions for FHFD and FHFTC existence are derived, respectively, which are described by a set of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sigma$</tex-math></inline-formula> -independent linear matrix inequalities (LMIs), such that it can avoid the ill-conditioned problems caused by the tiny parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sigma$</tex-math></inline-formula> . An application to a CE150 helicopter with abrupt and intermittent faults is provided to verify the above approaches. The innovation of the article lies in the following points: i) The fault detection and fault-tolerant control for NSPSs are handled under the united model, which can avoid the incomplete decoupling problem caused by decomposing NSPSs as the slow and fast subsystems; ii) the estimate values for actuator faults are regarded as a state vector of the FHFD, and the output feedback control law is introduced into FHFD, which make the FHFD not only can accurately detect faults but also can stabilize the closed-loop system; iii) a new method to transform the nonlinear matrix inequalities into the LMIs is proposed; and iv) the presented FHFTC can avoid the problems of missing or inaccurate status information caused by the sensor faults because it adopts the state feedback of the FHFD.