Performance evaluation of interval type-2 and online rule weighing based Type-1 Fuzzy PID controllers on a pH process

In this paper, we will explore whether the efficiency of the Interval Type-2 Fuzzy PID (IT2-FPID) lies in its ability to handle the high level of uncertainties rather than only having an extra degree of freedom provided by the Footprint of Uncertainty (FOU) on a highly nonlinear pH neutralization process. In order to illustrate the effect of the FOU on the control performance, the control performance of an IT2-FPID controller composed of 3×3 rules will be compared with a Type-1 Fuzzy PID (T1-FPID) controller of 5×5 rules. Moreover, in order to provide more extra degree of freedom to the T1-FPID structure, we will employ two self-tuning mechanisms where the weights of the fuzzy rules are adjusted in an online manner. Thus, we will present detailed comparative studies on how the extra degrees of freedom provided by the FOU or the employed tuning mechanisms affect the control and robustness performance. The presented analysis confirm that by tuning the FOU the performance of the IT2-FPID is better in wide range of operating points in comparison with its type-1 and self-tuning type-1 fuzzy counterparts which is not merely for the IT2-FPID use of extra parameters, but rather its different way of dealing with the disturbance, nonlinearities uncertainties and noise.