Design of dual PID-PD controller and gain tuning method using gain-scaling factors for a ball-beam system

In this paper, we propose a dual ϵ-PID/PD controller for the control of a ball position in a ball-and-beam system. The proposed controller has two parts: a ϵ₁-PID controller is for controlling the servo motor angle and a ϵ₂-PD controller is for controlling the position of the ball. The state equations of the ball-and-beam system are expressed separately into two parts by considering the servo motor angle (θ(u₁)) as a virtual input. The each separately controlled system is analyzed using the Routh-Hurwitz method. which provides the valid ranges of control gains. The output responses to changes in ϵ parameters are verified experimentally with selected gain values. Through the use of simulation and actual experiments, the usefulness of our proposed dual ϵ-PID/PD control method is clearly demonstrated.