Matrix pencil design approach towards fractional-order PI, PD and PID regulators

Abstract

Synthesis method and its application leading to few derived network structures of the fractional-order PI controllers is proposed in this brief paper. It is based on algorithm originally developed for analysis of the linearized circuits widely known as matrix method of unknown nodal voltages (MMUNV); approach is only reversed. PI^α, PD^α regulators where α is a decimal-step fractions between zero and unity are discovered systematically by using prescribed voltage transfer function. Since MMUNV has significant degree of freedom derived networks are electronically reconfigurable. Approach leading to PI^αD, PID^α, PI^1−αD^α as well as PI^αD^1−α with single grounded constant phase element (CPE) is briefly discussed. Proposed concept is verified by considering few designed lumped analog circuits and verified by Orcad Pspice circuit simulations, both as time response to step signal and in the frequency domain. CPE as basic and required building block are implemented as two-terminal devices using known passive ladder topology. Frequency limitations of constructed controllers caused by valid approximation of CPE are mentioned; also in the context of parasitic properties of the active devices.