By providing the generalisation of integration and differentiation, and incorporating the memory and hereditary effects, fractional-order modelling has gotten significant attention in the past few years. One of the extensively studied and utilised models to describe the glucose–insulin system of a human body is Bergman's minimal model. This non-linear model comprises of integer-order differential equations. However, comparison with the experimental data shows that the fractional-order version of Bergman's minimal model is a better representative of the glucose–insulin system than its original integer-order model. To design a control law for an artificial pancreas for a diabetic patient using a fractional-order model, different techniques, including feedback linearisation, have been applied in the literature. The authors’ previous work shows that the fractional-order version of Bergman's model describes the glucose–insulin system in a better way than the integer-order model. This study applies the sliding mode control technique and then compares the obtained simulation results with the ones obtained using feedback linearisation.

中文翻译：

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分数阶非线性葡萄糖-胰岛素系统的滑模控制

通过提供积分和微分的概括，并结合记忆和遗传效应，分数阶建模在过去几年中受到了极大的关注。描述人体葡萄糖-胰岛素系统的广泛研究和使用的模型之一是伯格曼的最小模型。该非线性模型由整数阶微分方程组成。然而，与实验数据的比较表明，伯格曼最小模型的分数阶版本比其原始整数阶模型更能代表葡萄糖-胰岛素系统。为了使用分数阶模型为糖尿病患者设计人工胰腺的控制律，文献中应用了不同的技术，包括反馈线性化。作者之前的工作表明，Bergman 模型的分数阶版本比整数阶模型更好地描述了葡萄糖-胰岛素系统。本研究应用滑模控制技术，然后将获得的仿真结果与使用反馈线性化获得的仿真结果进行比较。