Fault estimation based on observer for chaotic Lorenz system with bifurcation problem

Abstract

In this paper, the simultaneous estimation of the process and sensor fault of a chaotic Lorenz system in a noisy environment is investigated. The problem of the process fault leads to the occurrence of a bifurcation in the Lorenz system. The purpose of this article is to combine the concept of fault and bifurcation. Fault diagnosis of nonlinear systems becomes more practicable when it is managed over Takagi-Sugeno (TS) approximated fuzzy models. TS fuzzy model unknown input observer can estimate faults and states. In this respect, a TS fuzzy model augmented by a proportional plus integral, for fault modeling observer (FO) is lined up for the estimation of the unmeasured signal. The simulation conclusions hint that the observer runs well in estimating process fault, states, and sensor fault. Using these estimates, the deviation value of a parameter is determined from its actual value, which is the same as the low amount of deviation in this article because the bifurcation occurs in the system. In the first part of the simulation, the process fault occurs and drives system behavior into chaos, and the bifurcation diagram uses to explain it. In the second part, the system is influenced by actuator fault. The conclusion is validated through extensive simulations.