Determination of the phase of a transfer function: theory versus practice

Pauline Sourdille; Aidan O'Dwyer

doi:10.21427/48q0-k657

Determination of the phase of a transfer function: theory versus practice

Pauline Sourdille, Aidan O'Dwyer

Technological University Dublin

Research output: Contribution to conference › Paper › peer-review

Abstract

In control systems, a way to evaluate the stability of a system is to determine the magnitude and phase of the open loop system transfer function in the frequency domain. But due to the nature of the phase expression, practice and theory are not aligned. Some problems arise when the phase is determined, caused by the properties of the arctan function. This paper analyses these phase problems for a third order lag system and a third order lag with time delay system. It also presents modifications to obtain the analytically correct phase values from the computed values.

Original language	English
DOIs	https://doi.org/10.21427/48q0-k657
Publication status	Published - 2004
Event	13th European Conference on Mathematics for Industry (ECMI 2004) - Eindhoven, Netherlands Duration: 1 Jun 2004 → 30 Jun 2004

Conference

Conference	13th European Conference on Mathematics for Industry (ECMI 2004)
Country/Territory	Netherlands
City	Eindhoven
Period	1/06/04 → 30/06/04

Keywords

control systems
stability
magnitude
phase
open loop system
frequency domain
arctan function
third order lag system
time delay system
analytically correct phase values

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10.21427/48q0-k657Licence: CC BY-NC-SA

Cite this

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title = "Determination of the phase of a transfer function: theory versus practice",

abstract = "In control systems, a way to evaluate the stability of a system is to determine the magnitude and phase of the open loop system transfer function in the frequency domain. But due to the nature of the phase expression, practice and theory are not aligned. Some problems arise when the phase is determined, caused by the properties of the arctan function. This paper analyses these phase problems for a third order lag system and a third order lag with time delay system. It also presents modifications to obtain the analytically correct phase values from the computed values.",

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T1 - Determination of the phase of a transfer function: theory versus practice

AU - Sourdille, Pauline

AU - O'Dwyer, Aidan

PY - 2004

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N2 - In control systems, a way to evaluate the stability of a system is to determine the magnitude and phase of the open loop system transfer function in the frequency domain. But due to the nature of the phase expression, practice and theory are not aligned. Some problems arise when the phase is determined, caused by the properties of the arctan function. This paper analyses these phase problems for a third order lag system and a third order lag with time delay system. It also presents modifications to obtain the analytically correct phase values from the computed values.

AB - In control systems, a way to evaluate the stability of a system is to determine the magnitude and phase of the open loop system transfer function in the frequency domain. But due to the nature of the phase expression, practice and theory are not aligned. Some problems arise when the phase is determined, caused by the properties of the arctan function. This paper analyses these phase problems for a third order lag system and a third order lag with time delay system. It also presents modifications to obtain the analytically correct phase values from the computed values.

KW - control systems

KW - stability

KW - magnitude

KW - phase

KW - open loop system

KW - frequency domain

KW - arctan function

KW - third order lag system

KW - time delay system

KW - analytically correct phase values

U2 - 10.21427/48q0-k657

DO - 10.21427/48q0-k657

M3 - Paper

T2 - 13th European Conference on Mathematics for Industry (ECMI 2004)

Y2 - 1 June 2004 through 30 June 2004

ER -

Determination of the phase of a transfer function: theory versus practice

Abstract

Conference

Keywords

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Cite this