Control Performance Comparison between a Type-2 Fuzzy Controller and a Comparable Conventional Mamdani Fuzzy Controller

Control performance comparison between a type-1 fuzzy controller (Tl-FC) and a comparable type-2 fuzzy controller (T2-FC) was carried out using computer simulation. Our objective was to study whether T2 fuzzy control always had a control performance advantage over its Tl counterpart as claimed in some simulation-based reports. We used a genetic algorithm to optimize the Tl-FC and the T2-FCs that control process models of three different types (i.e., linear, linear with a time-delay, and nonlinear). Controllers' robustness against model parameter variation and capabilities of dealing with random noise were compared as well. The simulation results show that different settings result in different comparison outcomes: (1) the Tl-FC and the T2-FC performed (almost) identically, and (2) the T2-FC outperformed its Tl counterpart, and (3) the T1-FC was superior. These results are theoretically sensible because from the controllers' input-output mapping standpoint, their ability to produce continuous nonlinear control functions should be similar and no inherent advantage likely exists. Thus, one controller can appear to be better than, worse than, or equal to its counterpart depending on the specific configuration of the whole control system. Consequently, no one should claim that T2 fuzzy control is generally better than T1 fuzzy control.