Design of T2FSMC controller with minimum gain scale factor by optimizing membership function using firefly algorithm on mobile inverted pendulum

The combination of FireFly and T2FSMC has succesfully not only in overcoming the chattering and robustness problems on mobile inverted pendulum robot, but also can effectively result optimal gain scale factor so that the controller can solve those problems more effectively and more robust against disturbances and parameter uncertainties compared with other artificial based optimization methods. This paper investigates more deeply the influence of membership functions on the effectiveness of gain scale factor as well as the robustness of resulted controller. It can be shown through the simulation that an optimal membership function can be found using firefly making the gain scale factor small enough which is very good from the hardware implementation point of view and in suppressing chattering- while still maintaining the robustness against the parameter uncertainties. The robustness comparison between controller based on the proposed optimal gain scale factor with other controllers are also shown in the simulation.