This is the "Case Studies" from "CONTROL SYSTEMS ENGINEERING: Seventh Edition." testing "Antenna Control: Lag$-$Lead Compensation"

Do the challenge, but do PID configuration instead of the lag$-$lead configuration.

CHALLENGE: You are now given a problem to test your knowledge of this chapter's objectives. You are given the antenna azimuth position control system shown on the front endpapers, Configuration $2.$In the challenge in Chapter $8,$you were asked to design, via gain adjustment, an $8-$second settling time.

a$.$For your solution to the challenge in Chapter $8,$evaluate the percent overshoot and the value of the appropriate static error constant.

b$.$Design a cascade compensator to reduce the percent overshoot by a factor of $4$and the settling time by a factor of $2.$Also$,$improve the appropriate static error constant by a factor of $2.$

c$.$Repeat Part b using MATLAB $.$ Block Diagram