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Robustness evaluation and robust design for Proportional-Integral-Plus control

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Robustness evaluation and robust design for Proportional-Integral-Plus control. / Wilson, Emma Denise; Clairon, Quentin; Henderson, Robin; Taylor, C. James.

In: International Journal of Control, Vol. 92, No. 12, 01.09.2019, p. 2939-2951.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

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Wilson, ED, Clairon, Q, Henderson, R & Taylor, CJ 2019, 'Robustness evaluation and robust design for Proportional-Integral-Plus control', International Journal of Control, vol. 92, no. 12, pp. 2939-2951. https://doi.org/10.1080/00207179.2018.1467042

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Author

Wilson, Emma Denise ; Clairon, Quentin ; Henderson, Robin ; Taylor, C. James. / Robustness evaluation and robust design for Proportional-Integral-Plus control. In: International Journal of Control. 2019 ; Vol. 92, No. 12. pp. 2939-2951.

Bibtex

@article{615cb584483b4d3fade1924a99fa6130,
title = "Robustness evaluation and robust design for Proportional-Integral-Plus control",
abstract = "Proportional-integral-plus (PIP) control provides a logical extension to conventional two or three term (proportional-integral-derivative) industrial control, with additional dynamic feedback and input compensators introduced when the process has second order or higher dynamics, or time-delays. Although PIP control has been applied in a range of engineering applications, evaluation of closed-loop robustness has generally relied on empirical methods. In the present article, expressions for the H-infinity norm of two commonly used PIP control implementations, the feedback and forward path forms, are used, for the first time, to quantify closed-loop robustness. It is shown that the forward path form is not robust for unstable plants. Additional expressions for the H-infinity norm that encompass frequency weightings of generalised disturbance inputs are also determined. Novel analytical expressions to minimise the H-infinity norm are derived for the simplest plant, while simulation results based on numerical optimisation are provided for higher order examples. We show that, for certain plants, there are (non-unique) sets of PIP control gains that minimise the H-infinity norm. The H-2 norm is introduced in these cases to determine the controller that balances performance with robustness. Finally, the H-infinity norm is used as a design parameter for a practical example, namely control of airflow in a 2 m by 1 m by 1 m forced ventilation chamber. The performance of the new PIP H-infinity controller is compared to previously developed PIP controllers based on pole placement and linear quadratic design.",
keywords = "proportional-integral-plus, non-minimal state space, robust control, H-infinity norm, H-2 norm, hair dryer model, forced ventilation chamber",
author = "Wilson, {Emma Denise} and Quentin Clairon and Robin Henderson and Taylor, {C. James}",
year = "2019",
month = sep,
day = "1",
doi = "10.1080/00207179.2018.1467042",
language = "English",
volume = "92",
pages = "2939--2951",
journal = "International Journal of Control",
issn = "0020-7179",
publisher = "Taylor and Francis Ltd.",
number = "12",

}

RIS

TY - JOUR

T1 - Robustness evaluation and robust design for Proportional-Integral-Plus control

AU - Wilson, Emma Denise

AU - Clairon, Quentin

AU - Henderson, Robin

AU - Taylor, C. James

PY - 2019/9/1

Y1 - 2019/9/1

N2 - Proportional-integral-plus (PIP) control provides a logical extension to conventional two or three term (proportional-integral-derivative) industrial control, with additional dynamic feedback and input compensators introduced when the process has second order or higher dynamics, or time-delays. Although PIP control has been applied in a range of engineering applications, evaluation of closed-loop robustness has generally relied on empirical methods. In the present article, expressions for the H-infinity norm of two commonly used PIP control implementations, the feedback and forward path forms, are used, for the first time, to quantify closed-loop robustness. It is shown that the forward path form is not robust for unstable plants. Additional expressions for the H-infinity norm that encompass frequency weightings of generalised disturbance inputs are also determined. Novel analytical expressions to minimise the H-infinity norm are derived for the simplest plant, while simulation results based on numerical optimisation are provided for higher order examples. We show that, for certain plants, there are (non-unique) sets of PIP control gains that minimise the H-infinity norm. The H-2 norm is introduced in these cases to determine the controller that balances performance with robustness. Finally, the H-infinity norm is used as a design parameter for a practical example, namely control of airflow in a 2 m by 1 m by 1 m forced ventilation chamber. The performance of the new PIP H-infinity controller is compared to previously developed PIP controllers based on pole placement and linear quadratic design.

AB - Proportional-integral-plus (PIP) control provides a logical extension to conventional two or three term (proportional-integral-derivative) industrial control, with additional dynamic feedback and input compensators introduced when the process has second order or higher dynamics, or time-delays. Although PIP control has been applied in a range of engineering applications, evaluation of closed-loop robustness has generally relied on empirical methods. In the present article, expressions for the H-infinity norm of two commonly used PIP control implementations, the feedback and forward path forms, are used, for the first time, to quantify closed-loop robustness. It is shown that the forward path form is not robust for unstable plants. Additional expressions for the H-infinity norm that encompass frequency weightings of generalised disturbance inputs are also determined. Novel analytical expressions to minimise the H-infinity norm are derived for the simplest plant, while simulation results based on numerical optimisation are provided for higher order examples. We show that, for certain plants, there are (non-unique) sets of PIP control gains that minimise the H-infinity norm. The H-2 norm is introduced in these cases to determine the controller that balances performance with robustness. Finally, the H-infinity norm is used as a design parameter for a practical example, namely control of airflow in a 2 m by 1 m by 1 m forced ventilation chamber. The performance of the new PIP H-infinity controller is compared to previously developed PIP controllers based on pole placement and linear quadratic design.

KW - proportional-integral-plus

KW - non-minimal state space

KW - robust control

KW - H-infinity norm

KW - H-2 norm

KW - hair dryer model

KW - forced ventilation chamber

U2 - 10.1080/00207179.2018.1467042

DO - 10.1080/00207179.2018.1467042

M3 - Journal article

VL - 92

SP - 2939

EP - 2951

JO - International Journal of Control

JF - International Journal of Control

SN - 0020-7179

IS - 12

ER -