Analytical formulae for designing PID controllers to give specified ga
in and phase margins have been proposed recently in the literature. Th
is approach is attractive as the gain margin and phase margin serve as
important measures of not only performance but also robustness. Anoth
er popular approach with similar emphasis is the internal model contro
l method. In this paper, a comparison study of these two approaches fo
r designing a PI and a PID controller is made. The comparison shows th
e differences and the similarities of the two approaches. Recommendati
ons on when and which method to apply are also given.