Blood-Glucose Regulation Using Fractional-Order PID Control

This paper proposes a blood-glucose regulation approach employing a fractional-order proportional-integral-derivative (FOPID) controller, whose parameters are tuned using a numerical optimization methodology. The proposed technique is tested on 100 virtual patients using the Dalla Man model, an in silico type-1 diabetic patient model from the literature. The results are favorably compared with the ones obtained with a standard PID control. In a series of simulated tests, the FOPID approach leads to better results in terms of regulating the blood glucose levels between the specified limits, at the expense of requiring a higher, yet reasonable amount of insulin injected to the patient. Simulations were run for one day, and two different diets were considered. The quality of the regulation was measured in terms of the integral of blood glucose beyond the specified limits of 70 and 180 mg/dl. The values obtained with the PID controller were 17.5±18.9\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$17.5 \pm 18.9$$\end{document} and 13.1±16.8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$13.1 \pm 16.8$$\end{document} min g/dl, while the FOPID controller leads to values of 7.3±9.3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$7.3 \pm 9.3$$\end{document} and 7.0±8.0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$7.0 \pm 8.0$$\end{document} min g/dl, respectively. On the other hand, the FOPID increased the request amount of insulin, from 1.9±1.6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.9 \pm 1.6$$\end{document} and 1.7±1.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.7 \pm 1.5$$\end{document} nmol/kg to 3.0±2.2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3.0 \pm 2.2$$\end{document} and 2.7±2.0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2.7 \pm 2.0$$\end{document} nmol/kg (still within the expected daily range of 3–6 nmol/kg of insulin).