A new phase-lead design method using the root locus diagrams

A new phase-lead design method using the root locus diagrams is proposed. In the traditional phase-lead root locus design procedure, the designer has no direct control to the steady-state error constant of the resulting closed-loop system. In order to obtain a satisfactory steady-state error constant, the designer has to try different locations of the compensator's zero and the desired dominant roots. However, the procedure does not indicate to the designer how to alter the locations to obtain the desired steady-state error constant. With the new method presented in this note, the applicability of the phase lead compensation network is determined once the desired dominant roots are given, and the maximum "reachable" steady-state error constant can be directly determined. If the desired steady-state error constant rely within the "reachable" limit, the desired steady-state error constant together with the desired dominant roots are directly used to obtain the compensator. If the desired stead-state error constant exceeds the reachable limit, the note proposes a way to find out the proper locations of the desired dominant roots.