An Interval Type-2 Fractional Order Fuzzy Logic Controller Employed to Uncertain Nonlinear Inverted Pendulum

Inverted pendulum systems are extremely unstable, nonlinear, uncertain system wherein the load disturbance, random noise, and parameter variation adversely affect the performance of these systems. Therefore, controller's design, for controlling the pendulum angle, is an ambitious and fascinating task for control designer to handle such complexities present in the system. In this paper, the interval type-2 fuzzy proportional derivative plus integral $(\mathrm{IT}2\mathrm{FPD}+\mathrm{I})$ is incorporated with fractional order PID (FOPID) controller and resulting new interval type-2 fractional order fuzzy $\mathrm{PD}+\mathrm{I}(\mathrm{IT}2\mathrm{FO}-\mathrm{FPD}+\mathrm{I})$ controller is presented for inverted pendulum system to suspend pendulum in the vertical on cart. For the optimal controller design, the recent artificial bee colony (ABC) optimization technique is applied to achieve optimal controller parameters. Furthermore, to show the effectiveness of presented control approach, the inverted pendulum system is also tested in presence of disturbance, random noise rejection, and parameter variations. Eventually, the results clearly show that the performances of $\mathrm{IT}2\mathrm{FO}-\mathrm{FPD}+\mathrm{I}$ is superior to type-1 fractional order fuzzy $\mathrm{PD} +\mathrm{I}$ controller $(\mathrm{T}1\mathrm{FO}-\mathrm{FPD}+\mathrm{I}),\ \mathrm{T}1\mathrm{FPD}+\mathrm{I}$, and PID controllers.