Controlling the position of a ball on a beam is one of the conventional problems of control theory. Ball and Beam plant can be used for a wide range of control system design implementations from basic linear controllers to advance nonlinear methods. The ball and beam system consists of a long beam which can be tilted by a servo motor together with the ball rolling back and forth on top of the beam. The aim of this system is to change the position of the ball by operating the servo motor attached to the one corner of the beam. Please consider following tasks and prepare a report that answer all the questions related to the system given in Fig. 1.
A) Explain the dynamics of the system and how it works? Determine the components of the system needed to run a laboratory experiment. Give detailed explanations and justify your choice of component.
B) For the Ball and Beam system given in Fig 1. Obtain nonlinear mathematical model and construct its block diagram.
(Note that the angle of the beam is changed with the linear actuator connected to the beam not a rotational actuator!)
C) Obtain transfer function for this model (Linearize if needed, Choose the most appropriate values for the variables and indicate them in a table in your report.).