A Nonlinear 2D Ball Balancing System with Robotic Arm Actuation and PID-Based Numerical Feedback Linearization

Abstract

This paper presents the modeling, simulation, and PID control of a nonlinear coupled two-dimensional ball balancing system actuated by two orthogonal planar robotic arms. The objective is to regulate and track the position of a ball on a movable plate by controlling the plate orientation through servo-driven mechanisms. Due to the nonlinear relationship between ball motion, plate inclination, and actuator angles, the control problem is formulated using a virtual acceleration-based approach. Within this framework, the PID controller generates desired ball accelerations, which are transformed into physically realizable actuator commands through a numerical feedback linearization procedure. Simulation results are presented to evaluate tracking accuracy, transient response, actuator effort, saturation behavior, and empirical frequency-domain characteristics. The study demonstrates that a classical PID controller can successfully control a nonlinear coupled mechatronic system when combined with numerical feedback linearization, robotic arm kinematics, and actuator constraint modeling.