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 -