MECH 3340, Section 1, Quiz 2
Name:
Matric No.:
2025.4.9
Figure 1 shows a BLDC motor system that is attached to a reducer. The
motor system is subjected to a voltage input, ea (t). Angular displacement,
ωm (t), and angular velocity, ω̇m (t), are the possible output of the system. The
transfer function is given in the figure. The system is linear, time-invariant
and at a zero state. Laplace table is provided on the next page.
Figure 1: A 300 Kv outrunner (BLDC) motor system attached to a reducer.
Note the transfer function given.
(a) Find the system’s response, ωm (t), at t = 0, t = 0.5, t = 1, and t = 4 if
the system is subjected to a unit step input, 1u(t).
(b) Find the system’s response equation, ω̇m (t), if the system is subjected
to a unit impulse input, 1ε(t).
1
(a)
0
=
1003
.
·
Om(s)
0
=
65178
.
(S + 0 1003)
Ga(s)
balt)
since
Fals)
.
get
K ,
multiply
I
=
crefer to tables provided)
**
-003)
To
⑯
1UC)
=
both sides with sand
set
k,
To
0
=
.
=
o
6578
oo3
get
set
s
- 0
.
5583
multiply both sides with
Ky ,
5 =
6
=
sto
.
1003
and
I
(b) Since d EOm)3
Response for
sOm(s)
=
ealt)
I
·
get
=
=
0
0
6578
.
.
0
.
1003) and
,
65178
.
4 , (s + 0
=
.
1003) + 42 S(S+ 0 1003) + kys
.
.
(6 5583) (s + 0 1003) + K25(s + 0 1003) +
.
=
.
.
65
.
38752-①
Differentiate & with respect to s
0
s+ 0 1003) + 42s(1) + 2(65 387)s
(6 5583)(1) + product rule
.
=
.
.
substitute
0
6
=
+
=
65583
12
Om(s)
.
8= 0
5583
k2(0
=
65
.
.
3.
03
=
Refer to the table provided for
the inverse Laplace transform .
Om()
Om 10)
=
=
Om (0 5)
.
Om (1)
Om (4)
1003) + 0 + 0
(6 15837
.
O
rad
=
0
=
=
.
-
65
0809 rad
bed
.
4 6239 rad
0
.
3182
.
.
387 + 64
.
3872000
J⑬
+
0
=
Eal)
Omit)
=
=
I⑪
I
LE(1)
/Where
18C)
S
"Esomi-
65.3 .
Ke
multiply both sides with 3 (s +
substitute 1 6 5583 and Kz 65 387
.
To
=
To get the response ;
I
=
I can get
Som
1003
=
67
43
sOm
froma
i
.
=
Keat
0
.
6578e-0
t
.
1003t
2