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

1. Considering only the insulin-glucose dynamics (i.e., ignore the meal for the moment), calculate an approximate second-order patient model by fitting the responses obtained from simulations of the equations given in the example.
2. Using the IMC tuning rules, design a PID controller for this process.
3. Simulate the closed-loop system response to a step set point change in blood glucose of -20 mg/dl. Try to tune your controller to improve the transient.
4. Simulate the closed-loop system response to the meal disturbance described in Example 23.4. Is your controller able to maintain the safety boundaries for blood glucose (54mg/dL < G < 144mg/dL)?
5. In practice, the sensors 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 delay, repeat your simulation from part (d) with a 10 minute sensor delay. How has the performance changed? What is the maximum time delay that your closed-loop design will tolerate before it becomes unstable?