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 regulation<br />of blood glucose in type 1 diabetic patients is presented. Glucose/insulin concentration in the patient<br />body is controlled through the injection under the patients skin by the pump. Many various con-<br />trollers for this system have been proposed in the literature. However, most of them have consider<br />the system as an integer order system. Moreover, the majority of the presented methods suffer from<br />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<br />mode control that considerably reduces the required time for glucose to reach its desired level. Due<br />to the sliding mode design, the proposed controller is robust against external disturbances. Due to<br />the back-stepping design, convergence of each state variable of the system to its desired value can<br />be guaranteed separately. Simulation results verify the satisfactory performance of the proposed<br />controller.