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141_1_Final

# 141_1_Final - EE 141 Final Duration 3 hours The nal is...

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EE 141 – Final 03/18/10 Duration: 3 hours The final is closed book and closed lecture notes. No calculators. You can use a single page of handwritten notes. Please carefully justify all your answers. Problem 1: A simple model describing the concentration of insulin in patients with diabetes is given by: ˙ x 1 = - 0 . 4 x 1 + 0 . 2 x 2 + 0 . 02 x 3 + u ˙ x 2 = 0 . 2 x 1 - 0 . 4 x 2 ˙ x 3 = 0 . 2 x 1 - 0 . 02 x 3 where x 1 describes the concentration of insulin in the plasma, x 2 the concentration of insulin in the liver, and x 3 the concentration of insulin in the body tissues. The variable u represents the control input and describes the amount of insulin injected by the patients. 1. Derive the transfer function for this system by taking the concentration of insulin in the plasma as the output. 2. Is this system stable? 3. If we model an insulin injection as a step input of magnitude 0 . 5, what is the steady state concentration of insulin in the plasma upon an injection?

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