Examples:
7
Examples: Write the transfer function of the electrical circuit including Op-Amp (Operational Amplifier). Write the Matlab program to calculate the eigenvalues of the system. + - V 2 (t) V 1 (t) L R 1 R 2 C 1 q 2 q dt dv 412 v 2500 v 7500 dt v d 120 2 1 2 2 2 2 1 2 2 2 v 2500 v 7500 v 412 v 120 ) s ( V 2500 ) s ( V 7500 ) s ( V s 412 ) s ( V s 120 1 2 2 2 2 7500 s 412 s 120 2500 ) s ( V ) s ( V ) s ( H 2 1 2 clc;clear a=[120 412 7500]; roots(a)
description
Examples:. R 2. R 1. L. C. -. +. V 1 (t). V 2 (t). Write the transfer function of the electrical circuit including Op-Amp ( Op erational Amp lifier). Write the Matlab program to calculate the eigenvalues of the system. clc;clear a=[120 412 7500]; roots(a). Examples:. f(t). - PowerPoint PPT Presentation
Transcript of Examples:
Examples:
Write the transfer function of the electrical circuit including Op-Amp (Operational Amplifier). Write the Matlab program to calculate the eigenvalues of the system.
+-
V2(t)V1(t)
L R1
R2
C
1q
2qdt
dv412v2500v7500
dtvd
120 2122
22
1222 v2500v7500v412v120
)s(V2500)s(V7500)s(Vs412)s(Vs120 12222
7500s412s1202500
)s(V)s(V
)s(H 21
2
clc;cleara=[120 412 7500];roots(a)
Examples:
The equation of motion of the system whose mass can be neglected is given as
x(t)k c
f(t)
k=4000 N/m, c=50 Ns/m
a) Find the transfer function. b) Find the response to the input in the form of f(t)=40e-4t .
c) Find the response to the input in the form of f(t)=40cos(3t-1).d) Find the response to the input in the form of f(t)=100e-2tcos(5t+1).e) Find the response to the input in the form of f(t)=10δ(t) (Impulse input with magnitude 10 Ns)
f) Find the response to the input in the form of f(t)=50u(t) (Step input with magnitude 50 N)
g) Write the form of the exponential input, for which the system works at resonance.
)t(fkxdtdx
c )t(fx4000dtdx
50
a)4000s50
1)s(F)s(X
)s(H
b) 4s 000263.03800
14000)4(50
1)4(H
t4
t4
e0105.0)t(x
e*40*000263.0)t(x
Examples:
c) f(t)=40cos(3t-1) s=3i
i10x3618.910x4965.2)i3(H
i16022500
15016022500
4000)i3(H
1504000i1504000
i15040001
4000)i3(501
)i3(H
64
22
)i1504000(
4
2624
10x4982.2)i3(H
10x3618.910x4965.2)i3(H
rad-0.0375)i10x3618.910x4965.2(angle
H
64H
)0375.1t3cos(01.0)t(x)0375.01t3cos(10x4982.2*40)t(x
)1t3cos()i3(H*40)t(x4
H
d) f(t)=100e-2tcos(5t+1) s=-2+5i
>>s=3i;
>>hs=1/(50*s+4000)
>>gen=abs(hs)
>>fi=angle(hs)
>>s=-2+5i;
>>hs=1/(50*s+4000)
>>gen=abs(hs)
>>fi=angle(hs)
i10x6369.110x5536.2)i52(H
i15272500
25015272500
3900)i52(H
2503900i2503900
i25039001
4000)i52(501
)i52(H
54
22
)i2503900(
-42.5589x10)i52(H
Re
Img
Re
Img
rad-0.0640)i10x6369.110x5536.2(angle
H
54H
)936.0t5cos(e025589.0)t(x
)064.01t5cos(e10x5589.2*100)t(xt2
t24
φH
φH
RegIm
atnH
Examples:
e) f(t)=10δ(t) 10)s(F
f) f(t)=50u(t)s
50)s(F
80sB
sA
)s(X
)80s(s1
)4000s50(s50
s50
*4000s50
1)s(F*)s(H)s(X
clc;clearnum=[1];den=[1 80 0];[r,p,k]=residue(num,den)
80s0125.0
0s0125.0
)s(X
t80e0125.00125.0)t(x
80s2.0
50/4000s50/10
)s(X
4000s5010
10*4000s50
1)s(F*)s(H)s(X
t80e2.0)t(x
0125.0801
)80s(s1
)80s(B
0125.0801
)80s(s1
)0s(A
80s
0s
Residue Theorem
Examples:
t80e0125.00125.0)t(x
0 0.02 0.04 0.06 0.08 0.1 0.120
0.002
0.004
0.006
0.008
0.01
0.012
0.014
Zaman [s]
x(t)
xss=0.0125Steady State Value 0125.0
801
)80s(s1
s)s(Xslim)t(xlimx0s
0stss
g) Exponential input for resonance;
The s value, which makes the denominator of the transfer function zero causes the system resonance. The s value for resonance is s=-80. So, the form of the exponential function for resonance condition is
t80Ae)t(f The resonance condition does not depend on the input amplitude A.
Examples:
Consider the electrical circuit including Op-Amp. Where v1 is the input and v2 is the output
1222 v2500v7500v412v120
a) Find the Laplace transform of the output V2(s) to a step input with magnitude 12 V. Calculate the steady-state value of the output v2ss .
7500s412s1202500
)s(V)s(V
)s(H 21
2
)7500s412s120(s
30000s
127500s412s120
2500)s(V 222
Volt47500
30000)7500s412s120(s
30000s)s(Vslimv
0s220sss2
b) Write the matlab code to calculate the |H(s)| and φHs for an exponential-harmonic input in the form of v1(t)=24e-0.2t cos(5t-0.2).
clc;clear
s=-0.2+5i;
hs=-2500/(120*s^2+412*s+7500);
hg=abs(hs)
hfi=angle(hs)
)hfi2.0t5(cose*hg*24)t(v t2.02
Examples:
In the calculation procedure of a system response, the result of the Matlab command [r,p,k]=residue(pay,payda) gives the r and p vectors as
r=-2+3i, -2-3i, 6, -2 ve p=-4+6i,-4-6i, -3, 0.
Find the system response x(t) using the given r and p. Find the steady-state response.
2111.7)3(2*2A 22 2e6)1588.2t6cos(e2111.7)t(x t3t4
xss=-2Steady-state value
-2
-3
rad4.124432
atn2
3
rad2.158832
atn2
Re
Img
or
t0t3t4 e2e6)t6cos(Ae)t(x
0s2
)3(s6
)i64(Si32
)i64(Si32
)s(X
