Fundamentals of Control Systems - Nguyễn Trọng Tấn

Homework 04
Course: Fundamentals of Control Systems
Class: DD12KST1
Group 12:
	Student	Student’s Identification Number
Nguyen Trong Tuan	4120 4295
Nguyen Duy Vinh	4120 4579
Phan Trung Duong	4120 0648
Ho Dac Thuan	4120 3697
Part2: Computer exercise
2.1. Given the transfer functions:
a). Using Matlab to find the equivalent transfer function of the following systems:
>> G1=tf([3],[1 1])
Transfer function:
 3
-----
s + 1
>> G2=tf([5],[1 4 20])
Transfer function:
 5
--------------
s^2 + 4 s + 20
>> G3=tf([2],[1 -5])
 Transfer function:
 2
-----
s - 5
 >> G4=tf([1 1],[1 -2 2])
 Transfer function:
 s + 1
-------------
s^2 - 2 s + 2
>> Ga=tf(G1-G2)
 Transfer function:
 3 s^2 + 7 s + 55
-----------------------
s^3 + 5 s^2 + 24 s + 20
 >> Geq1=series(Ga,G3)
 Transfer function:
 6 s^2 + 14 s + 110
-----------------------
s^4 - s^2 - 100 s – 100
>> Gb=feedback(G3,G4)
 Transfer function:
 2 s^2 - 4 s + 4
----------------------
s^3 - 7 s^2 + 14 s - 8
>> Geq2=series(G1,Gb)
 Transfer function:
 6 s^2 - 12 s + 12
-----------------------------
s^4 - 6 s^3 + 7 s^2 + 6 s – 8
b). The step response of the systems:
¶ The step response of the system G1(s):
The response has value 3 when t goes to infinity and it doesn’t have any oscillation. The system is stable. Because G1 has a single pole p = -1 (the pole lies in the left-haft s-plane) and the gain K=3.
¶ The step response of the system G2(s):
The response has overshoot at t = 1.5 second then stable when t goes to infinity. The response has oscillation. Because G2 has two complex poles lie in the left-haft s-plane then the system is stable.
¶ The step response of the system G3(s):
The response is stable when t < 1 second then increases to infinity. Because G3 has pole p = 5 (the pole lies in the right-haft s-plane). The system is unstable.
¶ The step response of the system G4(s):
The response has oscillation and increases to infinity. Because G4 has two poles lie in the right-haft s-plane. The system is unstable.
2.2. Simulate the cascade tanks in the problem 1 using Simulink. Plot the output of the system when the input is u(t) =1(t) (unit step input).