Linear Control Systems
–
Assignment #1
Due Tuesday, August 29, 2017
Problem 1
:
Prove that the quadratic formula for obtaining all solutions (possibly complex) of the second
order polynomial equation
?𝑥
2
+ ?𝑥 + ? = 0
is given by
𝑥 = −
? ± √?
2
− 4??
2?
Problem 2
:
Calculate and plot the variation of the closed-loop poles of the closed-loop system formed
cascading a controller
𝐶(𝑠) = ?
with the transfer function
?(𝑠) =
1
(𝑠 + 1)(𝑠 + 3)(𝑠 + 6)
and applying unity negative feedback around the cascade of the plant and the controller.
(Hint: Show that the closed loop transfer function for the system is given by
𝑇(𝑠) =
?
(𝑠 + 1)(𝑠 + 3)(𝑠 + 6) + ?
and calculate using any method you like (calculators or computer program) the

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