Fault Tolerant Controller Design for T–S Fuzzy Systems With Time-Varying Delay and Actuator Faults: A K-Step Fault-Estimation Approach

Abstract

This paper is concerned with the problem of robust fault estimation and fault-tolerant control for a class of Takagi-Sugeno (T-S) fuzzy systems with time-varying state delay and actuator faults. Based on the (k − 1)th fault estimation information, a novel k-step fault-estimation observer is proposed to construct the kth fault error dynamics. The obtained fault estimates via k-step fault-estimation can practically better depict the size and shape of the faults. Then, based on the information of online k-step fault-estimation, a dynamic output feedback fault tolerant controller is designed to compensate the fault effects on the closed-loop fuzzy system. Furthermore, some less conservative delay dependent sufficient conditions for the existence of fault estimation observers and fault tolerant controllers are given in terms of solution to a set of linear matrix inequalities. Finally, simulation results of two numerical examples are presented to show the effectiveness and merits of the proposed methods. Index Terms-Dynamic output feedback control, fault tolerant control (FTC), k-step-fault-estimation, linear matrix inequalities (LMIs), Takagi-Sugeno (T-S) fuzzy systems, time-varying delay.

Robust dynamic output feedback fault-tolerant control for Takagi-Sugeno fuzzy systems with interval time-varying delay via improved delay partitioning approach

“…It can be concluded that the obtained results in this paper are less conservative than those of [4,7], [34][35][36]. Moreover, if we assume timevarying delay .t/ satisfies (2), the delay-dependent fault estimation conditions proposed in [21][22][23][24][25], [27] fail to give a feasible solution. However, by using LMI toolbox in matlab, a feasible solution of Theorem 3.1 can be obtained for .t/ D 1 C 0:1si nt.…”

“…If there is no state delay, then (3) reduces to the existing one in [30]. Moreover, the lower bound of delay is not restricted to 0 as [23], which is even more applicable to networked control systems and other practical systems.…”

“…It is observed that, compared with CAFE, although there is initial estimation error, the n-steps estimation approach not only provides better rapidity of fault estimation but also achieves more accurate estimation of actuator fault by increasing steps N . Moreover, improved delay partitioning approach is employed to deal with interval time delay for increasing the maximum allowable delay bounds, while the approach in [21,23,27], [26] fail to give a feasible estimation. All of these make it meaningful for the approach to be implemented in practice.…”

Multiple-step fault estimation for interval type-II T-S fuzzy system of hypersonic vehicle with time-varying elevator faults

“…In this subsection, an MS-FE approach is developed according to the aforementioned work by Huang and Yang 25 and Zhang et al 26 With such fault estimation method, the estimation result can approximate the true value more precisely while the rapidity is guaranteed. The whole estimate scheme is shown in Figure 2.…”

“…The type-II T-S fuzzy sets can provide additional redundancy in modeling progress, which enhances the capability of the system to handle parameter uncertainties. An MS-FE algorithm is proposed in light of the works by Huang and Yang 25 and Zhang et al 26 Several conditions of fault value in Liu et al 27 such as f ðtÞ 2 L 2 ½0; 1Þ is not necessary, instead the assumption _ f ðtÞ 2 L 2 ð0; 1Þ is considered in this algorithm. And the estimation result from each step is used for the next estimation part, and such kind of "iteration" is helpful to enhance the estimation accuracy and ensure the speed.…”