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Single Vs. Double Input Interval Type-2 Fuzzy PID Controllers: Which One is Better?

In this paper, we will analyze and present systematic design approaches for the most commonly employed Interval Type-2 (IT2) Fuzzy PID (FPID) controllers which are the Single input IT2 (SIT2) and Double IT2 (DIT2) FPID controllers. We will firstly start with presenting the general structure of the IT2-FPID controllers and then present internal model control based tuning approaches to calculate the scaling factors of the IT2-FPID controllers. It will be shown that, by simply tuning the Footprint of Uncertainty parameters, how to construct aggressive and smooth control curves for SIT2-FPID controllers while aggressive and smooth control surfaces for DIT2-FPID controllers. Finally, we will present real world experiments using a tricycle that will act as a platform to validate the control systems. The comparative experimental results will show that the real-time tracking control performance of both the SIT2-FPID and DIT2-FPID control structure is better in the presence of noise and unmodelled dynamics in comparison with their Type-1 fuzzy and conventional counterparts. We will also try to address the question "Which IT2-FPID controller is better?" by taking account the design simplicity and control system performance.