Stabilization of Mobile Inverted Pendulum System Using Conventional and Fuzzy PID Controllers

Abstract

An inverted pendulum is a pendulum that has its center of mass above its pivot point. It is often implemented with the pivot point mounted on a cart that can move horizontally and may be called a cart and pole. The ‘mobile inverted pendulum (MIP)’ is a special case of the fundamental inverted pendulum system where the cart is replaced with a two wheeled robotic system which can move two and forth in horizontal direction and can take U-turn about its axis. This work deals with the stabilization of mobile inverted pendulum using Proportional integral derivative (PID) controllers. A two loop controller scheme has been implemented to stabilize the MIP system. The tuning of the PID controllers has been done using three techniques: a) Trial and error: In this method PID parameters are tuned by hit and trial method. First tuning of controller1for angle control is done and then the second controller is tuned for position control. b) Pole placement technique: In this technique the PID parameters are given by placing the dominant closed loop poles at desired locations which are obtained by the LQR design of the system c) Fuzzy PID: In this method the PID parameters are auto tuned by fuzzy logic. For stabilizing the MIP two fuzzy based PID controllers are used. In one controller position error and its derivative is passed as inputs while in other controller angle error and its derivative is passed as inputs. The outputs in both the controllers are the PID gains proportional , integral and derivative . The simulation results of all the techniques are compared and it is shown that the performance parameters obtained using Fuzzy PID are better than the pole placement and trial and error technique.