In the past, Type-1 diabetes patients had to inject themselves with insulin three to four times...

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In the past, Type-1 diabetes patients had to inject themselves with insulin three to four times a day. New delayed-action insulin analogues such as insulin Glargine require a single daily dose. A model for patients treated under a regimen of a single day of Glargine insulin (Tarín, 2005) is shown below. The model to find the response of a specific patient to medication can be expressed in state-variable form with -501.6 x 10-6 -128.8 x 10-3 -854 x 10-3. = 0; C= [0.78 x 10 41.4 x 10 0.01]; D = 0; u= external insulin flow (single input), and y = plasma insulin concentration (single output). a. Using pole-placement techniques (you can use direct substitution method and/or Matlab), obtain a state-feedback gain matrix so that the closed-loop system will have two of its poles placed at-1/15 and the third pole at -1/2. b. Use Matlab to verify the pole positions of the closed loop system. In the past, Type-1 diabetes patients had to inject themselves with insulin three to four times a day. New delayed-action insulin analogues such as insulin Glargine require a single daily dose. A model for patients treated under a regimen of a single day of Glargine insulin (Tarín, 2005) is shown below. The model to find the response of a specific patient to medication can be expressed in state-variable form with -501.6 x 10-6 -128.8 x 10-3 -854 x 10-3. = 0; C= [0.78 x 10 41.4 x 10 0.01]; D = 0; u= external insulin flow (single input), and y = plasma insulin concentration (single output). a. Using pole-placement techniques (you can use direct substitution method and/or Matlab), obtain a state-feedback gain matrix so that the closed-loop system will have two of its poles placed at-1/15 and the third pole at -1/2. b. Use Matlab to verify the pole positions of the closed loop system.