Diagnosis of delayed discrete-time singularly perturbed systems based on slow subsystem

Actuator fault tolerance based on continuous‐time fuzzy singularly perturbed model

“…From Equation ( 7), it can be seen that fuzzy fault detection and toleration control law are combined into a hybrid fuzzy controller to suppress actuator faults. The advantage of this structure is that the fault detection and toleration are finished by a controller (7), which can solve the time-delay problem between the FD and the FTC designed independently from the existing results.…”

“…We consider the abrupt faults on actuators (39), which is found in Figure 3. The state responses of the SDCM with the faults (39) are given in Figure 4, which shows that the HFFTC (7) with parameters (38) can stabilize the SDCM with the abrupt faults on actuators (39) under H ∞ index 𝛾 opt = 0.7071. The control inputs with abrupt faults are shown in Figure 5.…”

“…The first is that the fault detector and tolerant controller are designed after the SPSs with faults that are decomposed into slow subsystem model and fast subsystem model. For example, the fault diagnose (FD) based on linear discrete-time slow-fast submodels with time-delay and fault-tolerant control (FTC) methods based on linear and nonlinear slow-fast submodels was provided in Bougatef et al [7] and Ren et al [8], respectively. P. Mei [9] presented a delayed Luenberger observer and a FTC strategy for continuous-time time-delay SPSs with sensor faults.…”