Stabilization of an X-Y inverted pendulum using adaptive gain scheduling PID controllers

An X − Y inverted pendulum, also known as a spherical or a two-dimensional inverted pendulum consists of a thin cylindrical rod attached to a base through a universal joint. The control objective is to place the pendulum in the upright position while keeping the base at some desired reference trajectory. This paper presents an adaptive gain scheduling method in designing PID controllers for the stabilization of an X − Y inverted pendulum. The variations in PID gains depend upon the transient and the steady-state part of the response. The performance of the proposed scheme has been compared with the conventional PID scheme given in the literature. The effectiveness of the proposed scheme under the effect of disturbance, noise and friction in the inverted pendulum system has also been studied. Simulation results show that the proposed controllers provide better performance than the conventional PID controllers in terms of various performance specifications.