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 + τ₁s) / (1 + τ₂s), 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.