Simultaneous Compensation of the Gain, Phase, and Phase Slope

Abstract

This paper deals with the problem of simultaneous compensation of the gain, phase, and phaseslope at an arbitrary frequency by using a fractionalorder lead/lag compensator. The necessary and sufficient conditions for feasibility of the problem are derived. Also, the number of existing solutions (i.e., the number of distinct fractionalorder lead/lag compensators satisfying the considered compensation requirements) is analytically found. Moreover, as a sample application, it is shown that the obtained results for the considered compensation problem are helpful in tuning fractionalorder lead/lag compensators for simultaneously achieving desired phase margin, desired gain cross frequency, and flatness of the Bode phase plot of the loop transfer function at this frequency.