Repeat Problem 39 using MATLAB. The program will do the following in one program:

a. Display a root locus and pause.

b. Display a close-up of the root locus where the axes go from -2 to 0.5 on the real axis and -2 to 2 on the imaginary axis.

c. Overlay the 0.707 damping ratio line on the close-up root locus.

d. Allow you to select interactively the point where the root locus crosses the 0.707 damping ratio line, and respond by displaying the gain at that point as well as all of the closed-loop poles at that gain. The program will then allow you to select interactively the imaginary-axis crossing and respond with a display of the gain at that point as well as all of the closed-loop poles at that gain. Finally, the program will repeat the evaluation for critically damped dominant closed-loop poles.

e. Generate the step response for the critically damped case.

Data From Problem 39:

Sketch the root locus for the system of Figure P8.12 and find the following:

a. The range of gain to yield stability

b. The value of gain that will yield a damping ratio of 0.707 for the system’s dominant poles

c. The value of gain that will yield closed-loop poles that are critically damped

Transcribed Image Text:

R(s) + K C(s) s(s + 3)(s + 7)(s + 9) (s + 30) (s + 20s + 225) FIGURE P8.12