Repeat Problem 32 using MATLAB. Use one program to do the following:

a. Display a root locus and pause.

b. Draw a close-up of the root locus where the axes go from -2 to 0 on the real axis and -2 to 2 on the imaginary axis.

c. Overlay the 10% overshoot line on the close-up root locus.

d. Select interactively the point where the root locus crosses the 10% overshoot line, and respond with the gain at that point as well as all of the closed-loop poles at that gain.

e. Generate the step response at the gain for 10% overshoot.

Data From Problem 32:

For the unity feedback system shown in Figure 8.3, where

do the following:

a. Sketch the root locus.

b. Find the value of K that will yield a 10% overshoot.

c. Locate all nondominant poles. What can you say about the second order approximation that led to your answer in Part b?

d. Find the range of K that yields a stable system.

K G(s) = %3D s(s + 3)(s + 4)(s + 8)