A one to three input mapping IT2-FLC PID design strategy

In this study, a single input interval type-2 fuzzy PID controller with a one to three inference mapping has been developed. Since it consists of a single input variable (the feedback error), a closed form formulation of the type-2 fuzzy controller output is possible. The closed form solution is derived in terms of the tuning parameters which are chosen as the heights of lower membership functions of the antecedent interval type-2 fuzzy sets. Then, a simple strategy is proposed for a process independent type-2 fuzzy PID controller design. The developed single input type-2 fuzzy controller structure preserves the most preferred features of the PID such as simplicity, independent gain tuning and easy implementation. The one to three input mapping type-2 fuzzy controller structure has been implemented on an experimental ball and beam system. The results illustrated that the proposed type-2 fuzzy controller produces superior control performance than a one-to-one inference mapping type-2 fuzzy and conventional controllers.