Blood-Glucose Regulation Using Fractional-Order PID Control
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Blood-Glucose Regulation Using Fractional-Order PID Control Henrique Mohallem Paiva1 · Wagner Souza Keller1 · Luísa Garcia Ribeiro da Cunha1 Received: 20 January 2019 / Revised: 19 October 2019 / Accepted: 25 November 2019 © Brazilian Society for Automatics–SBA 2019
Abstract 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 and 13.1±16.8 min g/dl, while the FOPID controller leads to values of 7.3 ± 9.3 and 7.0 ± 8.0 min g/dl, respectively. On the other hand, the FOPID increased the request amount of insulin, from 1.9 ± 1.6 and 1.7 ± 1.5 nmol/kg to 3.0 ± 2.2 and 2.7 ± 2.0 nmol/kg (still within the expected daily range of 3–6 nmol/kg of insulin). Keywords Automatic control · Fractional control · FOPID · Blood-glucose regulation
1 Introduction Designing an automatic glucose controller for a diabetic patient is a classic bioengineering problem which has been studied for almost six decades, since the seminal work of Arnold (Kadish 1963). This problem has gained attention in the last years, and much effort has been made toward the design of an artificial pancreas, which is the long-desired goal of this research (Haidar 2016). The reader is referred to the work of Cobelli et al. (2009) for a comprehensive review of the research in blood-glucose control until 2009, including a detailed description of the patient models and of the involved signals. A shorter literature survey, updated until 2013, has been published by Lunze et al. (2013).
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Henrique Mohallem Paiva [email protected] Wagner Souza Keller [email protected] Luísa Garcia Ribeiro da Cunha [email protected]
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UNIFESP - Universidade Federal de Sao Paulo (Federal University of Sao Paulo), Rua Talim, 330, Sao Jose dos Campos, SP 12231-280, Brazil
More recently, Boiroux et al. (2018) studied an overnight glucose control problem employing a model predictive control (MPC) approach. An internal model control approach, with both offline and online tuning, has been proposed by Bhattacharjee et al. (2018). Saleem et al. (2018) have studied the controllability and observability of the glucose–insulin– glucagon system. Linear Matrix Inequalities (LMI) were studied by
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