Minimum ISE Fractional-order PID (FOPID) Controller for Ball and Beam Mechanism

In this paper, fractional-order PID controller (FOPID) for ball and beam is being considered. Ball and beam system is one of the control engineering prototypes used to illustrate balancing mechanism of dynamical systems. The challenge in this system is to make the ball to stay on a beam at a desired position while it is naturally unstable during open-loop. This paper demonstrates the results obtained for this application using fractional-order PID (FOPID). FOPID is an improvement of PID controller with more degree of freedom. This paper also presents the effect of different fractional-orders on the closed-loop response. For comparison, FOPID controller that was tuned using FOMCON toolbox integrated in MATLAB software was also presented. The results also demonstrated the comparison between FOPID and PID controller to see the improvement gains from FOPID controller. In overall, FOPID can reduce overshoot in the output response significantly and improved the response speed if the gains are optimally tuned. This research also presented the optimal FOPID gain that was obtained through minimum ISE of output response which is better compared to the one tuned using FOMCON.