PD–PID controller for delayed systems with two unstable poles: a frequency domain approach

David Fernando Novella-Rodríguez; Basilio del Muro Cuéllar; Juan Francisco Márquez-Rubio; Miguel Ángel Hernández-Pérez; Martin Velasco-Villa

doi:10.1080/00207179.2017.1386326

PD–PID controller for delayed systems with two unstable poles: a frequency domain approach

David Fernando Novella-Rodríguez, Basilio del Muro Cuéllar, Juan Francisco Márquez-Rubio, Miguel Ángel Hernández-Pérez, Martin Velasco-Villa

Escuela Superior de Ingeniería Mecánica y Eléctrica (ESIME), Unidad Culhuacán

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

This paper deals with the stability problem of linear delayed systems containing two unstable real poles by means of PD controllers. The analysis presented is based on frequency domain techniques. Necessary and sufficient conditions for the existence of stabilising controllers are given in terms of the parameters of the system and the time delay size. The main result is extended to delayed systems with two unstable poles and n stable real poles. PID controllers are also considered in order to control the studied systems, obtaining similar stability conditions. Numerical examples are presented in order to illustrate the control performance.

Original language	English
Pages (from-to)	1196-1208
Number of pages	13
Journal	International Journal of Control
Volume	92
Issue number	5
DOIs	https://doi.org/10.1080/00207179.2017.1386326
State	Published - 4 May 2019

Keywords

PID controller
Time delays
high order system
unstable system

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10.1080/00207179.2017.1386326

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title = "PD–PID controller for delayed systems with two unstable poles: a frequency domain approach",

abstract = "This paper deals with the stability problem of linear delayed systems containing two unstable real poles by means of PD controllers. The analysis presented is based on frequency domain techniques. Necessary and sufficient conditions for the existence of stabilising controllers are given in terms of the parameters of the system and the time delay size. The main result is extended to delayed systems with two unstable poles and n stable real poles. PID controllers are also considered in order to control the studied systems, obtaining similar stability conditions. Numerical examples are presented in order to illustrate the control performance.",

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AU - Novella-Rodríguez, David Fernando

AU - Cuéllar, Basilio del Muro

AU - Márquez-Rubio, Juan Francisco

AU - Hernández-Pérez, Miguel Ángel

AU - Velasco-Villa, Martin

PY - 2019/5/4

Y1 - 2019/5/4

N2 - This paper deals with the stability problem of linear delayed systems containing two unstable real poles by means of PD controllers. The analysis presented is based on frequency domain techniques. Necessary and sufficient conditions for the existence of stabilising controllers are given in terms of the parameters of the system and the time delay size. The main result is extended to delayed systems with two unstable poles and n stable real poles. PID controllers are also considered in order to control the studied systems, obtaining similar stability conditions. Numerical examples are presented in order to illustrate the control performance.

AB - This paper deals with the stability problem of linear delayed systems containing two unstable real poles by means of PD controllers. The analysis presented is based on frequency domain techniques. Necessary and sufficient conditions for the existence of stabilising controllers are given in terms of the parameters of the system and the time delay size. The main result is extended to delayed systems with two unstable poles and n stable real poles. PID controllers are also considered in order to control the studied systems, obtaining similar stability conditions. Numerical examples are presented in order to illustrate the control performance.

KW - PID controller

KW - Time delays

KW - high order system

KW - unstable system

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SP - 1196

EP - 1208

JO - International Journal of Control

JF - International Journal of Control

IS - 5

ER -

PD–PID controller for delayed systems with two unstable poles: a frequency domain approach

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Keywords

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