MA 107
Modeling And Analysis of Dynamic Systems
S06
Professor TC. Tsao
HW 7
1. 9.5
The equation of motion and the transfer function are
()
1
I
tc
t
T
t
s
Ts
Is c
ω
=−
+
Ω
=
+
&
I=2,c=4.
Thus the steady state output for y(t) =30+5sin3t+2sin5t
is
11
1
1
1
30
5s
in
(3
)
2cos
(5
)
42
3
4
2
3
4
2
5
4
2
3
4
7.5 0.6935sin(3
0.9828)
0.1857cos(5
1.1903)
ss
tt
t
jj
j
j
=⋅ +
+
∠
+
+
∠
⋅+
=+
−
+
−
2. 9.9 (c)
yss(t)=5 G(j 0.7) sin(0.7t+ angle(G(j 0.7))=5*0.1118*sin(0.7t0.6719)
G(j 0.7) =
( 0.6719)
0.7
( 0.7)
0.0875 0.0696
0.1118
( 1.4 1)( 3.5 1)
j
j
Gj
i
e
−
==
−
=
++
3. 9.35 (See Example 9.4.1 for bandwidth).
Also show frequency domain input and out
put signal spectrum (line spectrum of Fourier coefficients) and system’s frequency
response at the Fourier harmonic frequencies.
4. 9.37 (Use the natural frequency as the bandwidth of 2
nd
order systems)
Also show frequency domain input and out put signal spectrum and system’s frequency
response at the Fourier harmonic frequencies.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentMA 107
Modeling And Analysis of Dynamic Systems
S06
Professor TC. Tsao
The bandwidth is somewhat larger than the natural frequency (70 rad/sec) because of the
numerator term.
From the Bode plot, we identify the bandwidth (3 dB or 0.707 from the
DC gain) to be about 140 rad/sec.
So the solution above should have calculated one more
term at 40
π
rad/sec.
The gains and phases may also be read from the Bode plot if the plot
gives sufficient resolution.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '06
 TSAO
 Signal Processing, Decibel, Modeling And Analysis of Dynamic Systems

Click to edit the document details