Self-tuning PID control of a plant with under-damped response with specifications on gain and phase margins

The effectiveness of the proportional-integral-derivative (PID) controller for plants with under-damped step response is not well understood. In practice, one may have to tune the PID controller manually through trial and error for such a plant. In this paper, a gain and phase margin tuning formula is derived for PID control of a second-order plus dead time plant with under-damped step response. A self-tuning controller incorporating this PID tuning formula has been implemented and tested on a pilot plant which consists of a hinged rectangular plate whose angular deflection from the vertical is controlled by an air stream generated by a variable speed fan. The results are given in the paper.