Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 10 2 2019 12 01 Fractional Order Glucose Insulin System Using Fractional Back-Stepping Sliding Mode Control 1 10 4067 10.22075/ijnaa.2019.4067 EN S. Vakili Department of Electrical Engineering, Shahrood University of Technology, Shahrood, Iran H. Toosian Shandiz Department of Electrical Engineering, Ferdowsi University of Mashahd, Mashhad, Iran Journal Article 2019 06 15 In this paper, based on a fractional order Bergman minimal model, a robust strategy for regulation of blood glucose in type 1 diabetic patients is presented. Glucose/insulin concentration in the patient body is controlled through the injection under the patients skin by the pump. Many various controllers for this system have been proposed in the literature. However, most of them have consider the system as an integer order system. Moreover, the majority of the presented methods suffer from an important disadvantage that is long settling time of the control system. Thus, the contribution of<br />this paper in comparison with previous related works is presenting a fractional back-stepping sliding mode control that considerably reduces the required time for glucose to reach its desired level. Due to the sliding mode design, the proposed controller is robust against external disturbances. Due to the back-stepping design, convergence of each state variable of the system to its desired value can be guaranteed separately. Simulation results verify the satisfactory performance of the proposed controller. https://ijnaa.semnan.ac.ir/article_4067_75ffe41d631b8e5f13b5be7ce8523854.pdf