Blood Glucose Regulation via Double Loop Higher Order Sliding Mode Control and Multiple Sampling Rate

____________________________________________________________________________________ Abstract: Diabetes is a serious disease during which the body's production and use of insulin is impaired, causing glucose concentration level to increase in the bloodstream. The blood glucose dynamics is described using the Bergman minimal model. Higher order sliding mode control techniques, including the prescribed convergence law, the smooth second order, the quasi-continuous, and the super-twisting control algorithm, are studied for the double loop robust stabilization of the glucose concentration level of a diabetic patient in presence of the parameter variations and meal disturbance. In the inner loop supertwisting control stabilizes the glucose pump-actuator that yields a dynamical collapse of the loop. In the outer loop the higher order sliding mode controller generates a command to the pump-actuator in terms of insulin injection rate. The higher order sliding mode differentiator is employed to facilitate the controllers. The efficiency of the proposed controllers and observers/differentiators, i.e. robustness and high accuracy, in presence of physical disturbances like food intake and parametric uncertainties is confirmed via simulations. Two sampling rates are successfully employed in the simulations: a smaller one for the system and the controller and the larger one for the glucose sensor.