Robust control with stable proportional-integral-plus controllers

Liu, G. P.; Duan, Guang‐Ren; Dixon, Roger

doi:10.23919/ecc.2001.7076425

Cited by 2 publications

(1 citation statement)

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“…To our knowledge, there have been no previous attempts to evaluate overall PIP closed-loop performance using the H ∞ norm. The robustness of the control elements within the PIP closed-loop system were studied some years ago by Liu, Dixon, and Daley (2001) and Liu, Duan, and Dixon (2001), who used H ∞ methods to ensure that the designed controller was stable. However, these articles did not consider the overall closedloop performance, which is the focus of the present work.…”

Section: Introductionmentioning

confidence: 99%

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

Wilson

Clairon

Henderson

et al. 2018

International Journal of Control

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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 ∞ 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 ∞ norm that encompass frequency weightings of generalised disturbance inputs are also determined. Novel analytical expressions to minimise the H ∞ 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 ∞ norm. The H 2 norm is introduced in these cases to determine the controller that balances performance with robustness. Finally, the H ∞ 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 ∞ controller is compared to previously developed PIP controllers based on pole placement and linear quadratic design.

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Section: Introductionmentioning

confidence: 99%