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Robustness evaluation and robust design for proportional-integral-plus control

Lookup NU author(s): Dr Quentin Clairon, Professor Robin Henderson



This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).


© 2018 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group 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 (Formula presented.) 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 (Formula presented.) norm that encompass frequency weightings of generalised disturbance inputs are also determined. Novel analytical expressions to minimise the (Formula presented.) 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 (Formula presented.) norm. The (Formula presented.) norm is introduced in these cases to determine the controller that balances performance with robustness. Finally, the (Formula presented.) 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 (Formula presented.) controller is compared to previously developed PIP controllers based on pole placement and linear quadratic design.

Publication metadata

Author(s): Wilson ED, Clairon Q, Henderson R, Taylor CJ

Publication type: Article

Publication status: Published

Journal: International Journal of Control

Year: 2019

Volume: 92

Issue: 12

Pages: 2939-2951

Online publication date: 03/05/2018

Acceptance date: 09/04/2018

Date deposited: 31/05/2018

ISSN (print): 0020-7179

ISSN (electronic): 1366-5820

Publisher: Taylor and Francis Ltd


DOI: 10.1080/00207179.2018.1467042


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