7.3 Numeral Example
137
In order to prove the validity of the designed robust FDO, we suppose the timedelay τ to be 2 s. For t ∈ [0 20], the unknown disturbance ω(t) is the bounded noise
with the amplitude from −5 to 5. The fault signal f (t) is select as a square wave
signal with unit amplitude and the occurrence time is from 8s to 12s. The unknown
disturbance ω(t), the jumping mode r t and the residual signal r eo (t) are displayed in
Figs. 7.1, 7.2, 7.3.
Figure 7.4 displays the residual evolution function f (r eo ) in fault condition and
non-fault condition. Through the simulation results, we can determine that when the
fault will be detected. With a selected threshold J th = sup d∈L 2 , f =0 E{
20
0 r
T
eo (t)r eo (t)dt}
= 0.04, we calculate that f (r eo ) = E{
9
0 r eo
T
(t)r eo (t)dt} = 0.05 > J th . Therefore,
the occurred fault will be detected within 1.0 s after its appearance.
7.4 Conclusion
This paper applies the T-S fuzzy model to address the robust FDO problem of for
nonlinear multi-model jumping system with time-delays and uncertainties. By reconstructing the error dynamic multi-model jumping system, the robust FDO problem
is transformed into an optimization problem that can be resolved by using LMIs.
The devised robust FDO not only shows robustness to disturbances, but also detects
faults sensitively. A simulation result verifies the theoretical conclusions.