Disturbance resilient fuzzy variable gain super twisting sliding mode control for underactuated Furuta pendulum systems

Abstract

The Furuta pendulum, also known as a rotary inverted pendulum, is a representative underactuated nonlinear system widely used for evaluating advanced control strategies. Its inherent instability, nonlinear dynamic coupling, and limited actuation make accurate stabilization particularly challenging, especially in the presence of model uncertainties and external disturbances. Conventional controllers, such as PID and fixed gain sliding mode controllers, may suffer from limited robustness, excessive control activity, or chattering when subjected to system uncertainties and disturbances. To address these limitations, this study proposes a disturbance resilient fuzzy Logic Based variable gain super twisting sliding mode controller (FLBVGSTA) for the stabilization of an underactuated Furuta pendulum. A state based sliding surface is formulated using the rotary-arm and pendulum states, while a fuzzy inference mechanism dynamically adjusts the super twisting gains according to the magnitude of the sliding variable. The nonlinear dynamics of the Furuta pendulum are derived using the Euler Lagrange formulation, and the finite time stability of the closed-loop system is investigated using Lyapunov based analysis under bounded disturbances. The proposed controller is evaluated through MATLAB/Simulink simulations and compared with FBSTSA and PID-STA controllers under identical simulation conditions. The results show that the proposed FLBVGSTA reduces the pendulum-angle RMSE by 5.0% compared with FBSTSA and by 78.05% compared with PID-STA. For the rotary-arm angle, the RMSE is reduced by 85.0% compared with FBSTSA and by 64.8% compared with PID-STA. In addition, the convergence time is reduced by 87.21% and 86.35% compared with FBSTSA and PID-STA, respectively. These results demonstrate that the proposed fuzzy variable gain super twisting strategy provides improved stabilization accuracy, faster convergence, and enhanced disturbance rejection while reducing unnecessary control activity.