First-order controllers design for second-order integrating systems with time delay

A new method is presented to design the firstorder controllers for second-order time-delay integrating systems that have an unstable pole at the origin and a stable pole in the left-half plane. In the first step the stable pole of the under controlled system is removed by the zero of the controller. Then by using the D-partition technique the entire stabilizing set is obtained in the plane of the remaining controller parameters. Finally some formulas and charts are derived for achieving the desired specifications. Simulation example is given to illustrate the usefulness and effectiveness of the proposed procedure.