Consider the diabetic patient in Example 23.3. Your goal is to design an automated device to administer insulin infusion in response to meal disturbances. 

(a) Considering only the insulin-glucose dynamics, calculate an approximate second-order patient model by fitting the responses (changes in insulin) obtained from simulations of the equations given in the example.
(b) Using the IMC tuning rules, design a PID controller for this process.
(c) Simulate the closed-loop system response to a step set point change in blood glucose of -20 mg/dl. Try to tune the controller to improve the transient response.
(d) Simulate the closed-loop system response to the meal disturbance described in Example 23.3. Is the controller able to maintain the safety boundaries for blood glucose (54 mg/dL < G < 144 mg/dL)? 

(e) In practice, sensors are available for measuring blood glucose sample from the subcutaneous tissue (the layer of fat under the skin, as opposed to directly from the blood stream). Assuming that such a procedure introduces a pure time delay, repeat the simulation from part (d) with a 10-min sensor delay. How has the performance changed? What is the maximum time delay that the closed-loop design will tolerate before it becomes unstable?