A Comparison Between PID and LQR Controllers for Stabilization of a Ball Balancing Robot

Abstract

Ball balancing robot (BBL) forms a dynamically stable system mounted on a ball which is in point contact with the ground surface. An omni-directional system for the BBL with maneuvering ability in the horizontal plane is attained as compared to two-wheeled robots, which can only move forward or backward. The stability of the BBL is defined by its capability to retain the upright position under all circumstances. Available literature [1, 2, 4, 5] includes the use of several single controllers to stabilize the BBL. This study performs a comparison of two popular controllers for stability analysis of the BBL, which included two model-based controllers, i.e., Proportional Integral Derivative (PID) and Linear Quadratic Regulator (LQR). A 2D planar model is considered for mathematical modeling at the two vertical planes as well as the horizontal plane. Furthermore, the steady state equations are derived using the Euler-Lagrangian method. PID and LQR controllers are used to provide stability to the BBL using a mathematical toolkit in MATLAB. The results from MATLAB are used to study the differences between PID and LQR for stability of the BBL based on time needed to balance the robot. The settling time for the PID and LQR controllers was 0.79 seconds and 2.25 seconds, respectively. The results illustrate that the PID controller stabilized the BBL in upright position efficiently and more swiftly as compared to the LQR controller.