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, and flatness of the Bode phase plot of the loop transfer function at this frequency.
Simultaneous Compensation of the Gain, Phase, and Phase-Slope
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 6, 2015; final manuscript received June 21, 2016; published online August 11, 2016. Assoc. Editor: YangQuan Chen.
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Badri, V., and Saleh Tavazoei, M. (August 11, 2016). "Simultaneous Compensation of the Gain, Phase, and Phase-Slope." ASME. J. Dyn. Sys., Meas., Control. December 2016; 138(12): 121002. https://doi.org/10.1115/1.4034073
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