An Adaptive Backstepping Based Nonlinear Controller for Patients with Type 1 Diabetes

Abstract

Automatic controllers for insulin infusion are used in arti cial pancreas for treatment of diabetes type 1 patients. Controllers are designed based on some models of blood glucose-insulin system. A physiologically veri ed model that governs the characteristics of human blood glucose is Bergman's nonlinear model. Using this model we have designed an adaptive backstepping based nonlinear controller for diabetes type 1 patients. For controller glucose e ectiveness factor of blood is treated as an unknown parameter and numerical values of controller gain and tuning function are selected to produce best possible results. A complete mathematical derivation of nonlinear controller is described and simulation results are discussed using MATLAB SIMULINK. Lyapunov stability theorems are used to analyze stability and convergence of blood glucose level to a desired concentration. Lyapunov theorems propose exponential stability of controlled glucose concentration. Simulation results also indicate faster convergence in tracking response and overshoot/undershoot characteristics as compared to some recently developed techniques in literature. In the end a simple backstepping based nonlinear controller is also proposed. Again its exponential stability is proved mathematically and shown in simulations also. Comparison of SIMULINK results with adaptive backstepping based controller is discussed in the last chapter.