Gaohua and Kimura (2006) derived an empirical patient model for the manipulation of ambient temperature u (^ˆ˜C) to influence the patient€™s brain intracranial pressure (ICP) y (mm Hg). The medical data support the following empirical values for a first-order-plus-time-delay model to describe the effect of cooling temperature (^ˆ˜C) on the ICP (mmHg) in time units of hours:

The nominal values for the process variables are: ICP = 20 mmHg; ambient temperature = 30 ^ˆ˜C.
(a) Using the IMC tuning rules, derive an appropriate PI controller for this medical experiment. (Begin with a value Ï„_c =1.0 h). What does that value of Ï„_c mean?
(b) Simulate the response of a 10-mmHg reduction in ICP. What is the overshoot? What is the minimum value of the temperature? What is the settling time?
(c) Comment on whether this is a reasonable controller design for a biomedical application. How might you improve the design?

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