Effective control of insulin injections can result in better lives for diabetic persons

Chapter 0, Problem E5.7

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Effective control of insulin injections can result in better lives for diabetic persons. Automatically controlled insulin injection by means of a pump and a sensor that measures blood sugar can be very effective. A pump and injection system has a feedback control as shown in Figure E5.7. Calculate the suitable gain K so that the overshoot of the step response due to the drug injection is approximately 7%. R(s) is the desired blood-sugar level and Y(s) is the actual bloodsugar level. (Hint: Use Figure 5.13a.)

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