Fractional Order Glucose Insulin System Using Fractional Back-Stepping Sliding Mode Control

Abstract

In this paper, based on a fractional order Bergman minimal model, a robust strategy for regulationof blood glucose in type 1 diabetic patients is presented. Glucose/insulin concentration in the patientbody is controlled through the injection under the patients skin by the pump. Many various con-trollers for this system have been proposed in the literature. However, most of them have considerthe system as an integer order system. Moreover, the majority of the presented methods suffer froman important disadvantage that is long settling time of the control system. Thus, the contribution ofthis paper in comparison with previous related works is presenting a fractional back-stepping slidingmode control that considerably reduces the required time for glucose to reach its desired level. Dueto the sliding mode design, the proposed controller is robust against external disturbances. Due tothe back-stepping design, convergence of each state variable of the system to its desired value canbe guaranteed separately. Simulation results verify the satisfactory performance of the proposedcontroller.