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Insulin/Glucose dynamics are of fundamental importance for us to understand and develop a treatment for diabetes. 400 Glucose Insulin 200 Pancreas. (Stomach) Tissue 50 100 150 Liver -Stomach -Pancreas Large intestine Small intestine Liver Tissue 100 150 50 Timet [min] Let y(t) be the blood glucose concentration (mg/dL), and u(t) be the intraperitoneal insulin (U/h). Then from clinical data, the continuous transfer function from u to y is G(s) = -12000 (TDI) (247s+1)(17s+1)² where TDI is a positive constant representing the total daily insulin dose of the patient. (1) Assume y(t) starts from y(0) = 0. Describe the main features that we can expect from the response of y(t) when u(t) is a unit step input. (2) Explain how these features stated in (1) have resulted from the transfer function. (3) Now assume y(t) starts from y(0) = 10 and u (t) = cos(0.5t). Describe the main features that we expect from y (t) in this case. Glucose in blood [[p/Յա] soonq Insulin [µU/ml] 100 50 o