It is well known that when a person ingests a significant amount of water, the blood volume increases, causing an increase in arterial blood pressure until the kidneys are able to excrete the excess volume and the pressure returns to normal (Shahin, 2010). In order to describe mathematically this process, water-loading experiments are performed in various subjects while their mean arterial pressure is monitored. It was found that the open-loop transfer function of this process is

where b_p is an autonomous nervous activity parameter.

a. Make a sketch of the root locus of the system, indicating the breakaway points and the value of b_p for each point.

b. Indicate the range of b_p for which the system is overdamped.

c. Indicate the values of b_p for which the system is critically damped.

d. Indicate the range of b_p for which the system is underdamped.

e. Explain why the system will have a larger settling time for larger values of b_p

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b,(1.759s +2.3182 +2.173 x 104) G(s) = 3.362s3 +11.34s2 +7.803s +0.00293