Robust μ-Controller for Automatic Glucose Regulation for Type I Diabetes Mellitus

Abstract

Type I diabetes mellitus is a serious autoimmune condition impacting a large population around the world that need a daily infusion of insulin substitutes to regulate blood glucose levels within healthy limits. The purpose of the study was to design a robust μ-controller based on an uncertain linear-time invariant (LTI) representation of the Hovorka model for glucose–insulin metabolism. The model set was obtained using linearization around an equilibrium point and adding parametric uncertainty to account for the time delay variation between plasma glucose concentration and its subcutaneous measurement. As a result, the robust stability and performance of the closed loop were proved using the structured singular value μ. The performance of the designed controller was also checked with a numerical simulation in connection with the nonlinear model.