Double-Input Interval Type-2 Fuzzy Logic Controllers: Analysis and Design

A significant number of investigations of type-1 and type-2 fuzzy logic controllers have revealed their exceptional ability to capture uncertainties in complex and nonlinear systems, particularly in real-time control applications. However, regardless of being type-1 or type-2, fuzzy logic controller design is still a complicated task due to the lack of a closed form solution of the output and an interpretable relationship between the control output and fuzzy logic controller design parameters, such as center or width of the membership functions. To simplify the design procedure further, we think every attempt to obtain such interpretable relationships is worthwhile. Accordingly, this paper aims to design a double-input interval type-2 fuzzy PID controller and obtain interpretable relationships between the input and the output of the controller. Thereafter, we deploy the novel design for the control of a Y6 coaxial tricopter unmanned aerial vehicle. Simulation results, which are realised in robot operating system (ROS) using C++ and Gazebo environment, are found to tally with the theoretical analysis and claims in the paper.