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This study deals with a generalised version of lead/lag compensators known as fractional-order lead/lag compensators. Exact and simple formulas are found for designing this introduced type of fractional-order compensators in order to provide the required magnitude and phase at a given frequency. Also, the region in the phase-magnitude plane, which is accessible by these compensators, is analytically found. Moreover, numerical examples and experimental results are presented to show the applicability of the achievements of this study in control system design  

This paper deals with the problem of simultaneous compensation of the gain, phase, and phase-slope at an arbitrary frequency by using a fractional-order 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 fractional-order 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 fractional-order lead/lag compensators for simultaneously achieving desired phase margin, desired gain cross frequency,...