Description

Question 1 (6 points)
Give an example of a closed loop control system. Using your example, explain the following terms associated with the control system represented by Figure 1: a) Plant
b) Sensors
c) Actuator
d) Desired State
e) Actual State
f) Feedback

Question 2 (9 points)
1 1− 1+
Given z= ( − )
2+2 2−2
a) Write z in the form +
b) Sketch z in the complex plane
c) Obtain the inverse of z in polar form
d) Given 3 = −8, find the complex values of that satisfy the equation.

Question 3 (5 points)
Consider the following differential equation:
̈()+5̇()+2() = 0. Find all values of such that () = satisfies the above differential equation.