# HW#2

```MEM 255/601
Introduction to Controls
HW #2
Problem #1:
Consider a system with transfer function
Y ( s)
 2n
G ( s) 

U ( s) s 2  2 n s   2n
(a) Let  n  1 rad / s ,   0.6 and the input be a unit step function. Then Y ( s) can be
written as
1
Y ( s) 
2
s( s  12
. s  1)
Find and plot y (t ) , the inverse Laplace transform of Y ( s) , using MATLAB.
(b) Repeat (a) for   1,   14
. , and   0 , and compare the rise time, overshoot, and
settling time of the four time responses.
(c) Repeat (a) for  n  2 rad / s and compare the rise time, overshoot, and settling time
of the two time responses.
Problem #2:
Consider a system with transfer function
 2n
Y ( s)
G ( s) 
 2
U ( s) s  2 n s   2n
(a) Let  n  1 rad / s ,   0.6 . Use the MATLAB command step to plot the step
response of the system.
(b) Repeat (a) for the system modified by adding a LHP zero at s  1 :
 2n ( s  1)
Y ( s)

G2 ( s) 
U ( s) s 2  2 n s   2n
Comment on how the adding LHP zero affects the rise time, overshoot, and settling
time.
(c) Repeat (a) for the system modified by adding a RHP zero at s  1:
 2n ( s  1)
Y ( s)
 2
G3 ( s) 
U ( s) s  2 n s   2n
Comment on how the adding RHP zero affects the rise time, overshoot, and settling
time.
```