Higher order fuzzy control structure for higher order or time-delay systems

Attempts to develop new structures for higher order fuzzy logic control (FLC) systems, which could handle the higher order process and the time-delay system as well. Two different approaches are proposed to construct the higher order FLC, namely, the hierarchical structure and the distributed structure. Both structures can be designed via the theory of variable structure control (VSC). The complexity of the structure depends on the order of the process. The necessary and sufficient stability condition provided by the VSC theory facilitates the design of the nominal scaling gains. The difficulty of the design is to estimate the upper bound of the undesirable dynamics. Practically, this upper bound can be approximated by the peak value of the undesirable dynamics in the steady-state period. The simulation shows that this approximation is feasible and nominal scaling gains designed can lead to a stable and reasonably good performance. The fine tuning can be more easily carried out to provide a better performance from these nominal values instead of from scratch. The proposed higher order structure can also be used to control the time-delayed process if the delay time is known. The structure configuration depends on the approximation of the delay compensation factor. A first-order approximation is usually accurate enough when the delay is not very long. A partially known delay will result in either overcompensation or undercompensation. The overcompensation seems better than the undercompensation due to the former contribution to the PID effects. The simulation shows the effectiveness of the proposed structure to both the higher order process and the time-delay system.