Trabalho de Controle
31
Bode K = 6 GANHO clc; num1=[1 -3 1]; den1=[2 1 6]; tf(num1,den1) bode(num1,den1) title('F.T. SEM APLICAÇÃO DE GANHO') num2=[6]; den2=[1]; tf(num2,den2) num=conv(num1,num2); den=conv(den1,den2); tf(num,den) figure(2) bode(num,den) title('Bode K = 6 GANHO') -20 -10 0 10 20 M agnitude (dB) 10 -2 10 -1 10 0 10 1 10 2 0 90 180 270 360 Phase (deg) F.T.SEM A PLICA ÇÃ O DE G A NHO Frequency (rad/s)
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Transcript of Trabalho de Controle
Bode K = 6 GANHO
clc;num1=[1 -3 1];den1=[2 1 6];tf(num1,den1)bode(num1,den1)title('F.T. SEM APLICAÇÃO DE GANHO')num2=[6];den2=[1];tf(num2,den2)num=conv(num1,num2);den=conv(den1,den2);tf(num,den)figure(2)bode(num,den)title('Bode K = 6 GANHO')
-20
-10
0
10
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Mag
nitu
de (d
B)
10-2
10-1
100
101
102
0
90
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270
360
Phas
e (d
eg)
F.T. SEM APLICAÇÃO DE GANHO
Frequency (rad/s)
0
5
10
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20
25
30
Mag
nitu
de (d
B)
10-2
10-1
100
101
102
0
90
180
270
360
Phas
e (d
eg)
Bode K = 6 GANHO
Frequency (rad/s)
Transfer function:
s^2 - 3 s + 1
-------------
2 s^2 + s + 6
Transfer function:
6
Transfer function:
6 s^2 - 18 s + 6
----------------
2 s^2 + s + 6
Bode (1/s) integrativo
clc;num1=[1 -3 1];den1=[2 1 6];tf(num1,den1)figure(1)bode(num1,den1)num2=[6];den2=[1];tf(num2,den2)num=conv(num1,num2);den=conv(den1,den2);tf(num,den)figure(2)bode(num,den) title('Bode (1/s) integrativo')
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-10
0
10
20
Mag
nitu
de (d
B)
10-2
10-1
100
101
102
0
90
180
270
360
Phas
e (d
eg)
Bode Diagram
Frequency (rad/s)
0
5
10
15
20
25
30
Mag
nitu
de (d
B)
10-2
10-1
100
101
102
0
90
180
270
360
Phas
e (d
eg)
Bode (1/s) integrativo
Frequency (rad/s)
Transfer function:
s^2 - 3 s + 1
-------------
2 s^2 + s + 6
Transfer function:
6
Transfer function:
6 s^2 - 18 s + 6
----------------
2 s^2 + s + 6
Bode (s) derivativoclc;num1=[1 -3 1];den1=[2 1 6];tf(num1,den1)figure(1)bode(num1,den1)num2=[6];den2=[1];tf(num2,den2)num=conv(num1,num2);den=conv(den1,den2);tf(num,den)figure(2)bode(num,den)title('Bode (s) derivativo')
-20
-10
0
10
20
Mag
nitu
de (d
B)
10-2
10-1
100
101
102
0
90
180
270
360
Phas
e (d
eg)
Bode Diagram
Frequency (rad/s)
0
5
10
15
20
25
30
Mag
nitu
de (d
B)
10-2
10-1
100
101
102
0
90
180
270
360
Phas
e (d
eg)
Bode (s) derivativo
Frequency (rad/s)
Transfer function:
s^2 - 3 s + 1
-------------
2 s^2 + s + 6
Transfer function:
6
Transfer function:
6 s^2 - 18 s + 6
----------------
2 s^2 + s + 6
Bode (1/(s+1)) polos reaisclc;num1=[1 -3 1];den1=[2 1 6];tf(num1,den1)figure(1)bode(num1,den1)num2=[10];den2=[1];tf(num2,den2)num=conv(num1,num2);den=conv(den1,den2);tf(num,den)figure(2)bode(num,den)title('Bode (1/(s+1)) polos reais')
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-10
0
10
20
Mag
nitu
de (d
B)
10-2
10-1
100
101
102
0
90
180
270
360
Phas
e (d
eg)
Bode Diagram
Frequency (rad/s)
0
10
20
30
40
Mag
nitu
de (d
B)
10-2
10-1
100
101
102
0
90
180
270
360
Phas
e (d
eg)
Bode (1/(s+1)) polos reais
Frequency (rad/s)
Transfer function:
s^2 - 3 s + 1
-------------
2 s^2 + s + 6
Transfer function:
10
Transfer function:
10 s^2 - 30 s + 10
------------------
2 s^2 + s + 6
Bode (s+1) zeros reaisclc;num1=[1 -3 1];den1=[2 1 6];tf(num1,den1)figure(1)bode(num1,den1)num2=[4];den2=[1];tf(num2,den2)num=conv(num1,num2);den=conv(den1,den2);tf(num,den)figure(2)bode(num,den)title('Bode (s+1) zeros reais')
-20
-10
0
10
20
Mag
nitu
de (d
B)
10-2
10-1
100
101
102
0
90
180
270
360
Phas
e (d
eg)
Bode Diagram
Frequency (rad/s)
-5
0
5
10
15
20
25
Mag
nitu
de (d
B)
10-2
10-1
100
101
102
0
90
180
270
360
Phas
e (d
eg)
Bode (s+1) zeros reais
Frequency (rad/s)
Transfer function:
s^2 - 3 s + 1
-------------
2 s^2 + s + 6
Transfer function:
4
Transfer function:
4 s^2 - 12 s + 4
----------------
2 s^2 + s + 6
NICHOLS K = 8 GANHOclc;num1=[1 -3 1];den1=[2 1 6];tf(num1,den1)figure(1)nichols(num1,den1)title('F.T. SEM APLICAÇÃO DE GANHO')num2=[4];den2=[1];tf(num2,den2)num=conv(num1,num2);den=conv(den1,den2);tf(num,den)figure(2)nichols(num,den)title('NICHOLS K = 8 GANHO')
0 45 90 135 180 225 270 315 360-20
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-5
0
5
10
15F.T. SEM APLICAÇÃO DE GANHO
Open-Loop Phase (deg)
Ope
n-Lo
op G
ain
(dB)
0 45 90 135 180 225 270 315 360-5
0
5
10
15
20
25NICHOLS K = 8 GANHO
Open-Loop Phase (deg)
Ope
n-Lo
op G
ain
(dB)
Transfer function:
s^2 - 3 s + 1
-------------
2 s^2 + s + 6
Transfer function:
4
Transfer function:
4 s^2 - 12 s + 4
----------------
2 s^2 + s + 6
NICHOLS (1/s) integrativo
clc;num1=[1 -3 1];den1=[2 1 6];tf(num1,den1)figure(1)nichols(num1,den1)num2=[6];den2=[1];tf(num2,den2)num=conv(num1,num2);den=conv(den1,den2);tf(num,den)figure(2)nichols(num,den) title('NICHOLS (1/s) integrativo')
0 45 90 135 180 225 270 315 360-20
-15
-10
-5
0
5
10
15Nichols Chart
Open-Loop Phase (deg)
Ope
n-Lo
op G
ain
(dB)
0 45 90 135 180 225 270 315 360-5
0
5
10
15
20
25
30NICHOLS (1/s) integrativo
Open-Loop Phase (deg)
Ope
n-Lo
op G
ain
(dB)
Transfer function:
s^2 - 3 s + 1
-------------
2 s^2 + s + 6
Transfer function:
6
Transfer function:
6 s^2 - 18 s + 6
----------------
2 s^2 + s + 6
NICHOLS (s) derivativoclc;num1=[1 -3 1];den1=[2 1 6];tf(num1,den1)figure(1)nichols(num1,den1)num2=[6];den2=[1];tf(num2,den2)num=conv(num1,num2);den=conv(den1,den2);tf(num,den)figure(2)nichols(num,den)title('NICHOLS (s) derivativo')
0 45 90 135 180 225 270 315 360-20
-15
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-5
0
5
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15Nichols Chart
Open-Loop Phase (deg)
Ope
n-Lo
op G
ain
(dB)
0 45 90 135 180 225 270 315 360-5
0
5
10
15
20
25
30NICHOLS (s) derivativo
Open-Loop Phase (deg)
Ope
n-Lo
op G
ain
(dB)
Transfer function:
s^2 - 3 s + 1
-------------
2 s^2 + s + 6
Transfer function:
6
Transfer function:
6 s^2 - 18 s + 6
----------------
2 s^2 + s + 6
NICHOLS (1/s+1) polos reais
clc;num1=[1 -3 1];den1=[2 1 6];tf(num1,den1)figure(1)nichols(num1,den1)num2=[8];den2=[1];tf(num2,den2)num=conv(num1,num2);den=conv(den1,den2);tf(num,den)figure(2)nichols(num,den)title('NICHOLS (1/s+1) polos reais')
0 45 90 135 180 225 270 315 360-20
-15
-10
-5
0
5
10
15Nichols Chart
Open-Loop Phase (deg)
Ope
n-Lo
op G
ain
(dB)
0 45 90 135 180 225 270 315 3600
5
10
15
20
25
30NICHOLS (1/s+1) polos reais
Open-Loop Phase (deg)
Ope
n-Lo
op G
ain
(dB)
Transfer function:
s^2 - 3 s + 1
-------------
2 s^2 + s + 6
Transfer function:
8
Transfer function:
8 s^2 - 24 s + 8
----------------
2 s^2 + s + 6
NICHOLS (s+1) zeros reaisclc;num1=[1 -3 1];den1=[2 1 6];tf(num1,den1)figure(1)nichols(num1,den1)num2=[4 4];den2=[1 1];tf(num2,den2)num=conv(num1,num2);den=conv(den1,den2);tf(num,den)figure(2)nichols(num,den)title('NICHOLS (s+1) zeros reais')
0 45 90 135 180 225 270 315 360-20
-15
-10
-5
0
5
10
15Nichols Chart
Open-Loop Phase (deg)
Ope
n-Lo
op G
ain
(dB)
0 45 90 135 180 225 270 315 360-5
0
5
10
15
20
25NICHOLS (s+1) zeros reais
Open-Loop Phase (deg)
Ope
n-Lo
op G
ain
(dB)
Transfer function:
s^2 - 3 s + 1
-------------
2 s^2 + s + 6
Transfer function:
4 s + 4
-------
s + 1
Transfer function:
4 s^3 - 8 s^2 - 8 s + 4
-----------------------
2 s^3 + 3 s^2 + 7 s + 6
NYQUIST K = 8 GANHOclc;num1=[1 -3 1];den1=[2 1 6];tf(num1,den1)figure(1)nyquist(num1,den1)num2=[8];den2=[1];tf(num2,den2)num=conv(num1,num2);den=conv(den1,den2);tf(num,den)figure(2)nyquist(num,den)title('NYQUIST K = 8 GANHO')
-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5Nyquist Diagram
Real Axis
Imag
inar
y Ax
is
-25 -20 -15 -10 -5 0 5-20
-15
-10
-5
0
5
10
15
20NYQUIST K = ? GANHO
Real Axis
Imag
inar
y Ax
is
Transfer function:
s^2 - 3 s + 1
-------------
2 s^2 + s + 6
Transfer function:
8
Transfer function:
8 s^2 - 24 s + 8
----------------
2 s^2 + s + 6
NYQUIST (1/s) integrativoclc;num1=[1 -3 1];den1=[2 1 6];tf(num1,den1)figure(1)nyquist(num1,den1)num2=[10];den2=[1];tf(num2,den2)num=conv(num1,num2);den=conv(den1,den2);tf(num,den)figure(2)nyquist(num,den)title('NYQUIST (1/s) integrativo')
-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5Nyquist Diagram
Real Axis
Imag
inar
y Ax
is
-35 -30 -25 -20 -15 -10 -5 0 5 10-25
-20
-15
-10
-5
0
5
10
15
20
25NYQUIST (1/s) integrativo
Real Axis
Imag
inar
y Ax
is
Transfer function:
s^2 - 3 s + 1
-------------
2 s^2 + s + 6
Transfer function:
10
Transfer function:
10 s^2 - 30 s + 10
------------------
2 s^2 + s + 6
NYQUIST (s) derivativoclc;num1=[1 -3 1];den1=[2 1 6];tf(num1,den1)figure(1)nyquist(num1,den1)num2=[4];den2=[1];tf(num2,den2)num=conv(num1,num2);den=conv(den1,den2);tf(num,den)figure(2)nyquist(num,den)title('NYQUIST (s) derivativo')
-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5Nyquist Diagram
Real Axis
Imag
inar
y Ax
is
-14 -12 -10 -8 -6 -4 -2 0 2 4-10
-8
-6
-4
-2
0
2
4
6
8
10NYQUIST (s) derivativo
Real Axis
Imag
inar
y Ax
is
Transfer function:
s^2 - 3 s + 1
-------------
2 s^2 + s + 6
Transfer function:
4
Transfer function:
4 s^2 - 12 s + 4
----------------
2 s^2 + s + 6
NYQUIST (1/s+1) polos reaisclc;num1=[1 -3 1];den1=[2 1 6];tf(num1,den1)figure(1)nyquist(num1,den1)num2=[8];den2=[1];tf(num2,den2)num=conv(num1,num2);den=conv(den1,den2);tf(num,den)figure(2)nyquist(num,den)title('NYQUIST (1/s+1) polos reais')
-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5Nyquist Diagram
Real Axis
Imag
inar
y Ax
is
-25 -20 -15 -10 -5 0 5-20
-15
-10
-5
0
5
10
15
20NYQUIST (1/s+1) polos reais
Real Axis
Imag
inar
y Ax
is
Transfer function:
s^2 - 3 s + 1
-------------
2 s^2 + s + 6
Transfer function:
8
Transfer function:
8 s^2 - 24 s + 8
----------------
2 s^2 + s + 6
NYQUIST (s+1) zeros reaisclc;num1=[1 -3 1];den1=[2 1 6];tf(num1,den1)figure(1)nyquist(num1,den1)num2=[10];den2=[1];tf(num2,den2)num=conv(num1,num2);den=conv(den1,den2);tf(num,den)figure(2)nyquist(num,den)title('NYQUIST (s+1) zeros reais')
-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5Nyquist Diagram
Real Axis
Imag
inar
y Ax
is
-35 -30 -25 -20 -15 -10 -5 0 5 10-25
-20
-15
-10
-5
0
5
10
15
20
25NYQUIST (s+1) zeros reais
Real Axis
Imag
inar
y Ax
is
Transfer function:
s^2 - 3 s + 1
-------------
2 s^2 + s + 6
Transfer function:
10
Transfer function:
10 s^2 - 30 s + 10
------------------
2 s^2 + s + 6
