If the transfer function of a plant contains one or more pairs of complex-conjugate poles, then a lead, lag,or lag–lead compensator may not give satisfactory results. In such a case, a network thathas two zeros and two poles may prove to be useful. If the zeros are chosen so as tocancel the undesirable complex-conjugate poles of the plant, then we can essentiallyreplace the undesirable poles by acceptable poles. That is, if the undesirable complexconjugate poles are in the left-half s plane and are in the form