Balancing a ball on a beam / Nor Shamsi Ibrahim

The purpose of this project is to balance a ball on a beam. The control task is to position a steel ball, which rests on the beam (guided by two wires at both side) at the desired point along the length of the beam using a torque or force applied to the beam angle as the control input It is also required that the rotation of the beam and the rolling of the ball to occur without any slipping, which imposes a constraint on the rotational acceleration of the beam. The beam is made to rotate in a vertical plane by applying a torque at the centre rotation and the ball is free to roll (with one degree of freedom) on two nichrome support wires along the beam. The beam angle is adjusted and measured by a precision servo- potentiometer mounted on the pivot axis. The position of the steel ball along the beam is measured using a "Wheatstone Bridge" method, in which the small voltage is generated across the wires is proportional to the position of the ball. Using the approximated transfer function of the plant derived by Wellstead (1993), lead compensator, double lead compensator and proportional plus derivative continuous controller were designed using root locus approach. discrete-time equivalents of the analog controllers were obtained.