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 bp 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 bp for each point.
b. Indicate the range of bp for which the system is overdamped.
c. Indicate the values of bp for which the system is critically damped.
d. Indicate the range of bp for which the system is underdamped.
e. Explain why the system will have a larger settling time for larger values of bp
