Designing and implementing a Proportional Derivative-based Controllers for Ball and Beam Systems

Abstract: The Ball and Beam System (BBS) is considered as one of the most common used approaches on benchmark for evaluating control algorithms in control engineering laboratories. This system demonstrates significant instability and nonlinearity, finding practical relevance in scenarios like maintaining balance of a ball on a beam, akin to the horizontal stabilization required during airplane landings. The actual system contains a ball, a beam, and a motor, with the core principle involving motor-generated torque to govern ball position on the beam. This facilitates smooth ball movement along the beam. Several theoretical approaches are used to controller design exist for stabilizing the ball and beam system. This paper proposed a Proportional Derivative (PD) controllers design to regulate ball position on the beam. MATLAB environment is utilised for simulating the mathematical model of this system. The study showcases the efficacy of the control algorithm in effectively managing the inherent nonlinearity and instability of the system. The achieved results from the conducted simulation, approved the ability of the proposed PD controller for stabilising ball position tracking on ball and beam system.

Keywords: PD controller, Ball and Beam System, DC motor, Root locus.