Design and experimental validation of single input type-2 fuzzy PID controllers as applied to 3 DOF helicopter testbed

The aim of this paper is to present experimental validation results to show the design simplicity of single input interval type-2 (IT2) fuzzy PID (FPID) controllers by evaluating their performance on a real-time 3 DOF helicopter testbed. In this study, we briefly show that the presented analytical design approach gives the opportunity to construct the IT2 fuzzy mappings by tuning a single parameter which constructs the footprint of uncertainty (FOU) of the IT2 fuzzy sets. Then, by employing these theoretical analyses, various single input IT2 FPID (SIT2-FPID) controllers are designed to solve the control problem of the 3 DOF helicopter. Through extensive and comparative experimental analysis, we analyze the IT2 fuzzy control system performances and validate the effect of the FOU parameter on the controller characteristics. The experimental results show that, having neither a priori knowledge about the mathematical model of the system nor its parameters, the SIT2-FPID is able to achieve a satisfactory control performance over nonlinear working regions in the presence of noise and unmodelled disturbance dynamics. We believe that the experimental validation of the SIT2-FPID controllers' theoretical analyses will open the door to a wider deployment of SIT2-FPIDs to real world control engineering applications.