Data for a person with type 1 diabetes are available as both MATLAB and Excel data files on the book web site. 1 Glucose measurements (y) were recorded every five minutes using a wearable sensor that measures subcutaneous glucose concentration. The insulin infusion rate (u) from a wearable subcutaneous insulin pump was also recorded every five minutes. The data files consist of experimental data for two step changes in the insulin infusion rate. The data are reported as deviations from the initial values that are considered to be the nominal steady-state values. It is proposed that the relationship between the glucose concentration y and the insulin infusion rate u can be described by a discrete-time, dynamic model of the form:

y(k) = a₁y(kˆ’1) + a₂y(kˆ’2) + b₁u(kˆ’1) + b₂u(kˆ’2) 

(a) Use the least squares approach to estimate the model parameters from the basal1 data set. This data will be referred to as the calibration data. Graphically compare the model response and this data.
(b) In order to assess the accuracy of the model from part (a), calculate the model response y to the u step changes in the validation data (basal2). Then graphically compare the model response ŷ with the validation data y.

(c) Repeat Steps (a) and (b) using an alternative transfer function model.

Estimate the model parameters using graphical techniques and the basal1 data set. Then compare the model and experimental response data for both data sets.
(d) Which model is superior? Justify your answer by considering the least squares index for the one-step-ahead prediction errors,

where N is the number of data points.

Transcribed Image Text:

Y(s) U(s) K ts +1 TS - Σνω-9k)? [y(k) – ŷ(k)]? k=1