[SOLVED] ECE486 Homework 0

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−𝑗 1+𝑗
Given z= ( − )
𝑗 2+2𝑗 2−2𝑗
a) Write z in the form 𝛼+𝛽𝑗
b) Sketch z in the complex plane
c) Obtain the inverse of z in polar form
d) Given 𝑥3 = −8, find the complex values of 𝑥 that satisfy the equation.

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