Ball and beam: modeling and analysis / Zarina Che Amin

The condition of feedback linearization of a non-linear system had been a classical problem in control theory especially regarding the ball and beam equipment. Therefore many control engineers have tried to solve this problem using different approaches. This project explained the important of stability concept. The objective of this project is to position a stainless steel ball at the desired point along the length of the beam using a torque or force applied to the beam angle as the control input. The mathematical model of the equipment has been derived based on the concept of rotating mechanical system and free body (ball) rolling down a plane. This equipment is interfaced to a computer and the controller is written in C. The controller designed is a two loop controller to improve the stability of the system. The inner loop (slave loop) ensures that the servo angle 9 tracks a desired angle, 0d and the outer loop (master loop) controls the ball position. The important aspect of this design approach is that the inner loop response must be faster than the outer loop. This is done by implementing Proportional plus Derivative (PD) controller for the inner loop and Proportional plus Integral plus Derivative (PID) controller for the outer loop. The response of the output can be obtained using Matlab.