Publication detail

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

PETRŽELA, J.

Original Title

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

English Title

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

Type

conference paper

Language

en

Original 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. PIα, PDα 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 PID, PID, PI1-D as well as PID1- 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.

English 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. PIα, PDα 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 PID, PID, PI1-D as well as PID1- 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.

Keywords

circuit synthesis; constant phase element; feedback regulators; matrix method; transfer function

Released

19.04.2017

Location

Brno, Czech Republic

ISBN

978-1-5090-4591-4

Book

Proceedings of 27th International Conference Radioelektronika 2017

Pages from

1

Pages to

4

Pages count

4

BibTex

```
@inproceedings{BUT135854,
author="Jiří {Petržela}",
title="Matrix pencil design approach towards fractional-order PI, PD and PID regulators",
annote="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. PIα, PDα 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 PID, PID, PI1-D as well as PID1- 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.",
booktitle="Proceedings of 27th International Conference Radioelektronika 2017",
chapter="135854",
doi="10.1109/RADIOELEK.2017.7936653",
howpublished="electronic, physical medium",
year="2017",
month="april",
pages="1--4",
type="conference paper"
}
```