Effective T-S fuzzy model for decentralized control

In order to facilitate decentralized fuzzy controller designs for multi-input-multi-output (MIMO) processes, this paper presents a novel manner, called effective Takagi-Sugeno (T-S) fuzzy model (ETSM), to describe the interactions among the loops. For a certain control-loop of an MIMO process, in terms of relative normalized gain array (RNGA) based loop pairing criterion, simple calculating procedure is given to obtain an ETSM based on its individual open-loop T-S fuzzy model. With the ETSMs of control-loops, an MIMO process can be approximately regarded as multiple non-interacting single loops such that each local controller of a decentralized control system can be independently designed using linear single-input-single-output (SISO) control algorithms. Compared with the existing decentralized fuzzy control methods adding extra terms to individual open-loop models to characterize interactions, ETSM is a practical and low-cost way. While compared with the existing effective transfer function (ETF) methods, ETSM is an extension that can proceed without requiring exact process mathematical functions, and lays a basis to develop robust controller since fuzzy system is strong in handling uncertainties. In case study, a nonlinear MIMO process is used as an example to demonstrate the effectiveness of the proposed ETSM method.