A fuzzy logic controller for nonlinear inverted pendulum systems: Design, simulation, and performance evaluation

The inverted pendulum on a cart is a classical benchmark used to evaluate control strategies for nonlinear and underactuated systems. Its inherent instability and strong coupling between the pendulum’s rotation and the cart’s translation make it a challenging system to stabilize. This paper proposes a fuzzy logic–based controller (FLC) designed to stabilize the pendulum in its upright position while maintaining the cart near its equilibrium point. Unlike traditional linear controllers that require precise modeling or system linearization, the FLC uses linguistic rules and triangular membership functions to manage nonlinearities and uncertainties. A nonlinear mathematical model of the pendulum–cart system is developed and implemented in MATLAB/Simulink, where the fuzzy controller computes the control force based on real-time feedback of angular and translational states. Simulation results demonstrate that the proposed FLC achieves fast stabilization with a settling time of less than 5 seconds, minimal overshoot, and smooth transient performance. The control input remains bounded and energy-efficient, and the system maintains stability under disturbances and parameter variations. Overall, the results confirm that the fuzzy logic controller provides a robust, adaptive, and interpretable solution for nonlinear dynamic systems, outperforming traditional PID and model-based controllers in terms of response speed, stability, and robustness.