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

This paper addresses a multi-loop interval Type-2 fuzzy logic proportional-integral-derivative (PID) control for a benchmark first order plus dead time system (FOPDT). In practice, Type-1 FLCs use crisp membership functions, which leads them less effective in modelling uncertainty in real-world systems where data and expert knowledge may be imprecise or noisy. In addition, this also Type-1 FLCs cannot explicitly handle uncertainties in the system dynamics, measurement noise, or modelling errors. This limits their robustness in highly dynamic or uncertain environments. Therefore, to mitigate these above mentioned draw backs of Type 1 FLC, Type 2 FLC is widely preferred. Basically, in Type 2 FLC normally incorporated an additional layer of uncertainty within the membership functions, to make more suitable for uncertain environments. In this work, the Takagi-Sugeno Fuzzy Inference System (FIS) is employed to construct the fuzzy logic system (FLS). This study comprehensively analyzes type-1 and type-2 FLS performances for a benchmark multivariable system. The simulation results reveal that the type-2 FLS outperforms the type-1 FLS and conventional PID controller. Also, to exhibit a concrete analysis, a performance analysis table has been incorporated by considering different performance indices to provide a clear visualization of output performances. The stability analysis of the system has also been described by considering the frequency domain analysis.