First-order controllers design employing dominant pole placement

This paper presents two simple and effective methods to design problem of first- order controllers, having a transfer function of type G
_c
(s) = k(1 + τ
₁
s) / (1 + τ
₂
s), for a given linear plant possibly cascaded with a time-delay. These methods are based on dominant pole placement and use the root locus and Nyquist plot, respectively. Illustrative examples are given to demonstrate the effectiveness of the proposed methods.