PRELIMINARY EXAM
Introduction to Feedback and Control Systems
1.) Differentiate closed-loop from open-loop systems. (5 pts)
2.) What are the steps in the design of a control system? (2 pts)
3.) Name the three major design criteria for control system. (3 pts)
Problem Solving:
A. Find the Laplace Transform of ℒ{𝑡𝑛𝑒−𝑎𝑡}= 𝑛!
(𝑠+𝑎)𝑛+1
a. 𝑓(𝑡)= 𝑡𝑐𝑜𝑠(𝑤𝑡)𝑢(𝑡)
b. 𝑓(𝑡)= 𝑒−0.4𝑡 cos(12𝑡)𝑢(𝑡)
B. Find the Inverse Laplace Transform of:
a. 𝐹(𝑠)= 𝑠+1
𝑠(𝑠2+𝑠+1)
b. 𝐹(𝑠)= 1
𝑠2(𝑠3−9)
C. Find the unit step response “c(t)” of the system if the transfer function
𝐺(𝑠)=𝐶(𝑠)
𝑅(𝑠)
where 𝑅(𝑠) is the input and 𝐶(𝑠) is the output:
a. 𝐺(𝑠)= 𝑠+3
(𝑠+1)(𝑠+2)
b. 𝐺(𝑠)= 2𝑠+12
𝑠2+2𝑠+5
D. Given the network shown below, find the transfer function, 𝑉𝑐(𝑠)
𝑉(𝑠)