A simple modelling strategy for integer order and fractional order interval type-2 fuzzy PID controllers with their simulation and real-time implementation.

This paper presents a simple approach to the mathematical modelling of the Integer Order (IO) and Fractional Order (FO) Interval Type-2 Fuzzy Proportional Integral Derivative (IT2FPID) controllers. In this approach, the control effort produced by the IT2FPID controller is obtained by combining the individual control efforts generated by the Interval Type-2 Fuzzy Proportional (IT2FP), Interval Type-2 Fuzzy Integral (IT2FI), and Interval Type-2 Fuzzy Derivative (IT2FD) controllers. The analytical structures of each of the IT2FPID components are unveiled using one-dimensional (1D) input space and without using any AND or OR operator. To the best of the authors' knowledge, such a strategy was never used and is completely new for the modelling of the IT2FPID controllers. Properties, computational issues, and design guidelines of the newly obtained controllers are discussed, and their applicability is delineated using five simulation examples and one experimental case study. A chemical reactor plant, two fractional order plants, a nonlinear plant, and a Twin Rotor Multi Input Multi Output System (TRMS) are considered in the simulation study. The experimental study is conducted on an unstable nonlinear Magnetic Levitation System (MLS). Moreover, to exhibit the usefulness of the newly derived controllers, simulation and real-time results are also compared with the existing results available in the literature. As the proposed controllers are plant model-free, they can be used for other control applications also. • A simple strategy is proposed for the modelling of IT2 fuzzy PID controller. • The modelling is done using 1D input space and without any AND or OR operator. • The new modelling strategy is extended to fractional order IT2 fuzzy PID controller. • Applicability of the controllers is depicted through simulation and real-time. • Usefulness of the controllers is shown through system performance comparison. [ABSTRACT FROM AUTHOR]