Design of complex fractional-order immittances for simple PID regulation

This brief paper is focused on the systematic design method towards active two-terminal circuit elements which itself allows four branch independent regulation type PI
^α
I
¹
I
^1+α
where mathematical order αε(0, 1), voltage is driving force and current being response. Synthesis is based on matrix method of unknown nodal voltages with prescribed form of admittance matrix. Few topologies have been derived and non-ideal behavior of controller caused by parasitic properties of used active devices is discussed. Proposed conception is proved by numerical analysis as well as circuit simulation using Orcad Pspice.