Fuzzy Logic Control of a Rotary Double Inverted Pendulum System

Abstract

This work presents a fuzzy logic control of a rotary double inverted pendulum (RDIP) system. The RDIP system consists of two inverted pendulums mounted on a rotating disc which is driven by a DC motor. The longer pendulum is hinged on the right side of the disc whereas the shorter pendulum is hinged on the left side of the disc. The RDIP is an extremely nonlinear, unstable and under-actuated system of high order. A mathematical model is built for the RDIP using the Lagrange-Euler equation. A Fuzzy Logic Controller is then designed for swing-up and stabilization control of the RDIP system and its stability analysis is presented. The fuzzy controller takes the angles and angular velocities of the two pendulums and the angle and angular velocity of the rotary disc as its inputs, and the driving force as its output. A PID controller is also developed for this system for the purpose of comparison. The simulation results of these two control schemes with their comparative analysis show that, although both of the classical PID and the fuzzy controllers can control the system properly, the latter performs better especially on the steady state behavior. The simulation results also show the capability of the fuzzy logic control strategy to control a highly nonlinear and unstable system such as the RDIP.

Keywords

• fuzzy logic control
• rotary inverted pendulum
• pid
• simulation