Single input interval type-3 fuzzy PID control of a magnetic levitation system

Single input fuzzy PID (SI-FPID) controllers combine a fuzzy controller with a PID controller, thereby enhancing performance while maintaining a simple and efficient design. In this structure, the fuzzy controller adds a nonlinear characteristic to the PID controller. Interval type-3 (IT3) fuzzy sets offer greater potential in handling disturbances, noise, and higher-order uncertainties than their type-1 and type-2 counterparts, they have not yet been applied in SI-FPID controllers. Therefore, for the first time in the literature, a single-input interval type-3 fuzzy PID (SIT3-FPID) control structure is proposed in this study, in which an interval type-3 fuzzy controller (IT3-FC) is integrated with a conventional PID controller. Three triangular IT3 fuzzy sets and three singletons are used for the input and output variables, resulting in only three rules. The SIT3-FPID controller introduces additional design parameters, such as apex points, alpha-cuts and fuzziness parameters, which enable performance improvements over type-2 controllers. To evaluate the effectiveness of the proposed SIT3-FPID controller, it is applied to a nonlinear magnetic levitation system and compared with SIT2-FPID and conventional PID controllers under a nominal condition, an external disturbance, and parameter uncertainties. The results demonstrate that the proposed SIT3-FPID controller exhibits robustness performance in all scenarios.