This paper is focused on feedback control of postprandial glucose levels for patients with type 1 Diabetes Mellitus. There are two important limitations that make this a challenging problem. First, the slow subcutaneous insulin pharmacokinetics that introduces a significant lag into the control loop. Second, the positivity constraint on the control action, meaning that it is not possible to remove insulin from the body. In this paper, both issues are explicitly considered in the design process using the internal model control framework, to derive a near-optimal feedback controller. Optimality is understood here as minimizing the blood glucose peak after a meal intake and, at the same time, preventing glucose values below a prescribed threshold. It is shown how the proposed controller approaches the optimal closed-loop performance as a limit case. The theoretical results are supported by a numerical example and the feasibility of the overall strategy under uncertainties is illustrated using an extended version UVa/Padova metabolic simulator.
Keywords: Artificial pancreas; Disturbance attenuation; Internal model control; Positive systems.
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