Stability analysis and control of the glucose insulin glucagon system in humans

The goal for the treatment of type-1 diabetes mellitus is the development of an artificial pancreas to regulate the blood glucose level in a closed loop design. A system of nonlinear differential equations having five variables (glucose, insulin, β-cell mass, α-cell mass, and glucagon) with seventeen parameters is considered. The Lyapunov function is used to check the stability analysis of the model. Controllability and observability of the linearized model are discussed under two different cases: in case 1 insulin is taken as an input, and in case 2 insulin and glucagon are taken as inputs for the system. This model played an important role in the development of a fully automatic artificial pancreas by stabilizing the control loop system for the glucose-insulin glucagon pump. A proportional integral derivative (PID) controller is designed for an artificial pancreas by using the transfer function. According to the desired value, the algorithm of an artificial pancreas measures the glucose level in the blood of a patient by using a glucose sensor that sends a signal to an insulin glucagon pump to adjust the basal insulin. A closed-loop system is tested in the Simulink environment, and the simulation results show the performance of the designed controller.