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Control
ch4
ch8
ch10
aem-ch4
aem-ch5
Control Systems
Interactive control systems using
Next.js
Resolution 20
K
G
(
s
)
H
(
s
)
=
K
(
s
+
1
)
(
s
+
2
)
(
s
−
1
)
(
s
−
2
)
KG(s)H(s) = \frac{K(s + 1)(s + 2)}{(s - 1)(s - 2) }
K
G
(
s
)
H
(
s
)
=
(
s
−
1
)
(
s
−
2
)
K
(
s
+
1
)
(
s
+
2
)
1
+
K
G
(
s
)
H
(
s
)
=
0
1 + KG(s)H(s) = 0
1
+
K
G
(
s
)
H
(
s
)
=
0
D
a
m
p
i
n
g
r
a
t
i
o
ζ
=
a
/
(
2
∗
b
)
Damping ratio \zeta = a / (2 * \sqrt{b})
D
a
m
p
i
n
g
r
a
t
i
o
ζ
=
a
/
(
2
∗
b
)
ω
n
=
b
\omega_n = \sqrt{b}
ω
n
=
b
Valid
numerator (s + 1)(s + 2)
denominator (s - 1)(s - 2)
zeros -1,-2
poles 1,2
Natural Frequency Omegan 1
Damping ratio 0.7
T
p
=
π
ω
n
1
−
ζ
2
=
Tp = \frac{\pi}{\omega_n \sqrt{1 - \zeta^2}} = \
T
p
=
ω
n
1
−
ζ
2
π
=
4
.
3
9
9
4.399
4
.
3
9
9
%
o
v
e
r
s
h
o
o
t
=
e
−
(
ζ
π
/
1
−
ζ
2
)
∗
1
0
0
=
\%overshoot = e^{-(\zeta\pi / \sqrt{1 - \zeta^2})} * 100 = \
%
o
v
e
r
s
h
o
o
t
=
e
−
(
ζ
π
/
1
−
ζ
2
)
∗
1
0
0
=
4
.
5
9
9
4.599
4
.
5
9
9
T
s
=
4
ζ
ω
n
=
Ts = \frac{4}{\zeta \omega_n} = \
T
s
=
ζ
ω
n
4
=
5
.
7
1
4
5.714
5
.
7
1
4
T
r
=
0
.
8
+
2
.
5
∗
ζ
ω
n
=
Tr = \frac{0.8 + 2.5 * \zeta} {\omega_n} = \
T
r
=
ω
n
0
.
8
+
2
.
5
∗
ζ
=
2
.
5
5
0
2.550
2
.
5
5
0
-10
-8
-6
-4
-2
0
2
4
6
8
10
-10
-8
-6
-4
-2
0
2
4
6
8
10
m
y
′
′
+
c
y
′
+
k
y
=
0
my'' + cy' + ky = 0
m
y
′
′
+
c
y
′
+
k
y
=
0