Robustness evaluation and robust design for proportional-integral-plus control. Issue 12 (2nd December 2019)

• Record Type: Journal Article
• Authors: Wilson, Emma D.; Clairon, Quentin; Henderson, Robin; Taylor, C. James
• Is Part Of: International journal of control. Volume 92:Issue 12(2019)
• Page Start: 2939
• Page End: 2951
• Publication Date: 2019-12-02
• Subjects: Proportional-integral-plus -- non-minimal state space -- robust control -- H∞ norm -- H2 norm -- hair dryer model -- forced ventilation chamber; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2018.1467042
• Languages: English
• ISSNs: 0020-7179

Abstract

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 ∞ 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.