Linear closed-loop control using Luenberger observer applied to insulin administration for type 1 diabetes

Abstract

In this work the design of a Luenberger observer is proposed to estimate the unmeasurable state space variables from Hovorka?s model. This model is linearized and evaluated in an operation point where Luenberger observer is designed using the Ackermann methodology. The observer is employed to estimate the unmeasurable variables of virtual patients which are generated by Bergman?s model. Once the unmeasurable state variables are obtained by the Luenberger observer using only the input-output information of the Bergman?s model, a control algorithm based on eigenvalues relocation trough Ackermann methodology for linear systems is applied. In this methodology, a constant feedback gain vector is obtained in order to compute the control signal (insulin) to be applied to virtual patient and keep on normoglycemia rank. The carbohydrates ingestion is considered as the main disturbances. In order to assess the proposed methodology, two tests are designed: the first one consists of changing the reference signal in order to evaluate the control sensitivity; and the second one includes different proportions of prandial insulin used in open-loop to try the controller response under distinct operation conditions. The results are obtained via simulation using Simulink of Matlab.