An optimal fuzzy logic controller design for a single-linked inverted pendulum system

Abstract

Inverted pendulum (IP) is an underactuated systems, since the input of the system is the force applied to the cart and the outputs are the cart position and pendulum angle (single input multi output - SIMO) system, which makes this system is highly nonlinear and unstable. Inverted pendulum considered as the one the most famous classical systems in the field of control and mechatronics. This work focuses on the design of an optimized fuzzy controller to stabilize an inverted pendulum in a vertical position. A continuous correction mechanism is required to move the cart in a certain way in order to balance the pendulum to prevent it from falling down. This project started by a derivation of the mathematical model of the single linked inverted pendulum system by using Euler-Lagrange method. After that, a fuzzy logic controller (FLC) based on Sugeno inference system was designed, and genetic algorithm was used to tune the parameters of the controller using MATLAB software. Both controllers were tested using real time inverted pendulum. Experimental results showed that in T-K Sugeno FLC, the pendulum stabilized after 4.5 s with overshoot equal to 0.029 rad. On the other hand, the cart reached steady state at 4.3 s and steady state error was 0.04 m. Optimized FLC achieved better results with the Sugeno, since the pendulum stabilized after 1.6 s, and the cart took only 1.34 s to reach the steady state.