Effective control of insulin injections can result in better lives for diabetic persons. Automatically controlled insulin injection

Question:

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 blood-sugar level.
Figure E5.7
Blood-sugar level control.