Further results on the synthesis of PID controllers

This note focuses on a graphical approach to determine the stability region, in the parameter space, of PID-controlled second-order plants with dead time. This work is the extension of and further results on the same topic of the previous paper in the literature on first-order plants with dead time. The main characterization of the new method is the utilization of a graphical stability criterion in the parameter space, which releases a necessary and sufficient stability condition. Once the range of proportional gain is known, the complete stabilizing set in the plain of integral-derivative gains can be drawn and identified immediately, not to be computed mathematically. A practical algorithm of drawing the stabilizing boundaries in the integral-derivative space is proposed.