PROBLEM SHEET 4.

Running head: PROBLEM SHEET 4 1
Problem Sheet 4
Name
Institution

PROBLEM SHEET 4 2
Part a
Motor output= y (t), motor input=x (t)
Gain , k=1 NM /V
Time Constant ,T =3 s
x (t ) unit step=0.25 V / s
Y ( s )
X ( s ) = k
1+Ts = 1
1+ 3 s
Y ( s ) = X ( s ) 1
1+ 3 s = 0.25
s ( 1
1+ 3 s )
Y ( s )= 0.25
s (1+3 s )
We split the equation using partial fractions technique to get:
0.25
s (1+3 s)= A
s + B
1+3 s
0.25= A
s × s(1+3 s)+ B
1+3 s × s (1+3 s )
0.25=A (1+3 s )+ Bs
When s=0
0.25=A (1+0)+0
A=0.25
When s=−1
3