It is well known that when a person ingests a signifi-

Chapter 8, Problem 67

(choose chapter or problem)

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 pressurè 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

G(s) = \(\frac{b_p\left(1.759 s^3+2.318 s^2+2.173 \times 10^{-4}\right)}{3.362 s^3+11.34 s^2+7.803 s+0.00293}\)

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 \(b_p\)