Design and Implementation of a Multi-Loop Type 2 Fuzzy PID Control for an Inverted Two-Input-Two-Output System.

This article focuses on the design and performance evaluation of an interval type-2 fuzzy logic proportional-integral-derivative (IT2FLC PID) controller for a benchmark multi-loop first order plus dead time (FOPDT) system with two inputs and two outputs (TITO). It compares the IT2FLC PID controller with type-1 fuzzy logic controllers (T1FLC) and conventional PID controllers, demonstrating through simulations that the IT2FLC PID controller, especially with triangular membership functions, provides superior control accuracy, faster settling times, and better disturbance rejection under uncertain and nonlinear conditions. The study also includes a stability analysis of the plants using frequency response methods such as Bode and Nyquist plots, confirming system stability. The paper highlights the advantages of IT2FLC in handling uncertainties inherent in real-world systems, addressing limitations of T1FLCs, and discusses the effects of different membership function shapes and linguistic variable counts on control performance.