A Hybrid Fractional Order Fuzzy PID Controller Using Interval Type- 2 Fuzzy Neural Network

In this paper, a hybrid fractional order fuzzy PID controller structure has been studied for fractional order systems. In addition to the fractional order integral and derivative terms, this structure replaces the proportional part of the fractional order PID (FOPID) structure with an interval type-2 fuzzy neural network. In this structure, the fractional order derivative action is implemented on the process output to avoid sudden changes in the set-point. Moreover, the IT2-fuzzy neural network parameters are adapted online using the gradient descent algorithm. Hence, the structure can be more adaptable to system uncertainties, and it can give an observed improvement in the system's time response. By using two different fractional-order examples, simulation studies via five test cases are performed to assess the effectiveness of the controller structure. Moreover, the stabilization problem of the inverted pendulum system is performed to evaluate the developed structure. Furthermore, comparative results with conventional fractional-order PID controller and fractional order IT2- fuzzy controller structures are conducted.