Bild
Name
Gleichung im Zeitbereich
Frequenzgangfunktion
Übertragungsfunktion
P-Glied
x
a
=
K
P
⋅
x
e
{\displaystyle x_{a}=K_{P}\cdot x_{e}\,}
F
(
p
)
=
x
a
(
p
)
x
e
(
p
)
=
K
P
{\displaystyle F(p)={\cfrac {x_{a}(p)}{x_{e}(p)}}=K_{P}\,}
G
(
s
)
=
x
a
(
s
)
x
e
(
s
)
=
K
P
{\displaystyle G(s)={\cfrac {x_{a}(s)}{x_{e}(s)}}=K_{P}\,}
PT1-Glied
T
1
⋅
d
x
a
d
t
+
x
a
=
K
P
⋅
x
e
{\displaystyle T_{1}\cdot {\cfrac {dx_{a}}{dt}}+x_{a}=K_{P}\cdot x_{e}}
F
(
p
)
=
K
P
1
+
T
1
p
{\displaystyle F(p)={\cfrac {K_{P}}{1+T_{1}p}}\,}
G
(
s
)
=
K
P
1
+
T
1
s
{\displaystyle G(s)={\cfrac {K_{P}}{1+T_{1}s}}\,}
PT2-Glied
1
ω
0
2
d
2
x
a
d
t
2
+
2
D
ω
0
d
x
a
d
t
+
x
a
=
K
P
⋅
x
e
{\displaystyle {\cfrac {1}{\omega _{0}^{2}}}{\cfrac {d^{2}x_{a}}{dt^{2}}}+{\cfrac {2D}{\omega _{0}}}{\cfrac {dx_{a}}{dt}}+x_{a}=K_{P}\cdot x_{e}}
F
(
p
)
=
K
P
1
+
2
D
ω
0
p
+
1
ω
0
2
p
2
{\displaystyle F(p)={\cfrac {K_{P}}{1+{\cfrac {2D}{\omega _{0}}}p+{\cfrac {1}{\omega _{0}^{2}}}p^{2}}}\,}
G
(
s
)
=
K
P
1
+
2
D
ω
0
s
+
1
ω
0
2
s
2
{\displaystyle G(s)={\cfrac {K_{P}}{1+{\cfrac {2D}{\omega _{0}}}s+{\cfrac {1}{\omega _{0}^{2}}}s^{2}}}\,}
PTt-Glied
x
a
=
K
P
⋅
x
e
(
t
−
T
t
)
{\displaystyle x_{a}=K_{P}\cdot x_{e}(t-T_{t})\,}
F
(
p
)
=
K
P
⋅
e
−
p
T
1
{\displaystyle F(p)=K_{P}\cdot e^{-pT_{1}}\,}
G
(
s
)
=
K
P
⋅
e
−
s
T
1
{\displaystyle G(s)=K_{P}\cdot e^{-sT_{1}}\,}
D-Glied
x
a
=
K
D
d
x
e
d
t
{\displaystyle x_{a}=K_{D}{\cfrac {dx_{e}}{dt}}\,}
[
x
a
=
T
D
d
x
e
d
t
]
{\displaystyle \left[x_{a}=T_{D}{\cfrac {dx_{e}}{dt}}\right]\,}
F
(
p
)
=
K
D
⋅
p
{\displaystyle F(p)=K_{D}\cdot p\,}
[
F
(
p
)
=
T
D
⋅
p
]
{\displaystyle \left[F(p)=T_{D}\cdot p\right]\,}
G
(
s
)
=
K
D
⋅
s
{\displaystyle G(s)=K_{D}\cdot s\,}
[
G
(
s
)
=
T
D
⋅
s
]
{\displaystyle \left[G(s)=T_{D}\cdot s\right]\,}
DT1-Glied
T
1
d
x
a
d
t
+
x
a
=
K
D
d
x
e
d
t
{\displaystyle T_{1}{\cfrac {dx_{a}}{dt}}+x_{a}=K_{D}{\cfrac {dx_{e}}{dt}}\,}
F
(
p
)
=
K
D
⋅
p
1
+
T
1
p
{\displaystyle F(p)={\cfrac {K_{D}\cdot p}{1+T_{1}p}}\,}
G
(
s
)
=
K
D
⋅
s
1
+
T
1
s
{\displaystyle G(s)={\cfrac {K_{D}\cdot s}{1+T_{1}s}}\,}
PD-Glied
x
a
=
K
P
[
T
V
d
x
e
d
t
+
x
e
]
{\displaystyle x_{a}=K_{P}\left[T_{V}{\cfrac {dx_{e}}{dt}}+x_{e}\right]\,}
F
(
p
)
=
K
P
(
1
+
T
V
p
)
{\displaystyle F(p)=K_{P}\left(1+T_{V}p\right)\,}
G
(
s
)
=
K
P
(
1
+
T
V
s
)
{\displaystyle G(s)=K_{P}\left(1+T_{V}s\right)\,}
PDT1-Glied
T
1
d
x
a
d
t
+
x
a
=
K
P
[
T
V
d
x
e
d
t
+
x
e
]
{\displaystyle T_{1}{\cfrac {dx_{a}}{dt}}+x_{a}=K_{P}\left[T_{V}{\cfrac {dx_{e}}{dt}}+x_{e}\right]\,}
T
V
>
T
1
{\displaystyle T_{V}>T_{1}\;}
F
(
p
)
=
K
P
1
+
T
V
p
1
+
T
1
p
{\displaystyle F(p)=K_{P}{\cfrac {1+T_{V}p}{1+T_{1}p}}\,}
T
V
>
T
1
{\displaystyle T_{V}>T_{1}\;}
G
(
s
)
=
K
P
1
+
T
V
s
1
+
T
1
s
{\displaystyle G(s)=K_{P}{\cfrac {1+T_{V}s}{1+T_{1}s}}\,}
T
V
>
T
1
{\displaystyle T_{V}>T_{1}\;}
PPT1-Glied
T
1
d
x
a
d
t
+
x
a
=
K
P
[
T
V
d
x
e
d
t
+
x
e
]
{\displaystyle T_{1}{\cfrac {dx_{a}}{dt}}+x_{a}=K_{P}\left[T_{V}{\cfrac {dx_{e}}{dt}}+x_{e}\right]\,}
T
V
<
T
1
{\displaystyle T_{V}<T_{1}\;}
F
(
p
)
=
K
P
1
+
T
V
p
1
+
T
1
p
{\displaystyle F(p)=K_{P}{\cfrac {1+T_{V}p}{1+T_{1}p}}\,}
T
V
<
T
1
{\displaystyle T_{V}<T_{1}\;}
G
(
s
)
=
K
P
1
+
T
V
s
1
+
T
1
s
{\displaystyle G(s)=K_{P}{\cfrac {1+T_{V}s}{1+T_{1}s}}\,}
T
V
<
T
1
{\displaystyle T_{V}<T_{1}\;}
I-Glied
x
a
=
K
I
∫
x
e
d
t
{\displaystyle x_{a}=K_{I}\int x_{e}dt\,}
[
x
a
=
1
T
I
∫
x
e
d
t
]
{\displaystyle \left[x_{a}={\cfrac {1}{T_{I}}}\int x_{e}dt\right]\,}
F
(
p
)
=
K
I
1
p
{\displaystyle F(p)=K_{I}{\cfrac {1}{p}}\,}
[
F
(
p
)
=
1
T
I
p
]
{\displaystyle \left[F(p)={\cfrac {1}{T_{I}p}}\right]\,}
G
(
s
)
=
K
I
1
s
{\displaystyle G(s)=K_{I}{\cfrac {1}{s}}\,}
[
G
(
s
)
=
1
T
I
s
]
{\displaystyle \left[G(s)={\cfrac {1}{T_{I}s}}\right]\,}
PI-Glied
x
a
=
K
P
[
x
e
+
1
T
N
∫
x
e
d
t
]
{\displaystyle x_{a}=K_{P}\left[x_{e}+{\cfrac {1}{T_{N}}}\int x_{e}dt\right]\,}
F
(
p
)
=
K
P
[
1
+
1
T
N
p
]
=
K
P
1
+
T
N
p
T
N
p
{\displaystyle F(p)=K_{P}\left[1+{\cfrac {1}{T_{N}p}}\right]=K_{P}{\cfrac {1+T_{N}p}{T_{N}p}}\,}
G
(
s
)
=
K
P
[
1
+
1
T
N
s
]
=
K
P
1
+
T
N
s
T
N
s
{\displaystyle G(s)=K_{P}\left[1+{\cfrac {1}{T_{N}s}}\right]=K_{P}{\cfrac {1+T_{N}s}{T_{N}s}}\,}
PID-Glied
x
a
=
K
P
[
x
e
+
1
T
N
∫
x
e
d
t
+
T
V
d
x
e
d
t
]
{\displaystyle x_{a}=K_{P}\left[x_{e}+{\cfrac {1}{T_{N}}}\int x_{e}dt+T_{V}{\cfrac {dx_{e}}{dt}}\right]\,}
F
(
p
)
=
K
P
[
1
+
1
T
N
p
+
T
V
p
]
{\displaystyle F(p)=K_{P}\left[1+{\cfrac {1}{T_{N}p}}+T_{V}p\right]\,}
G
(
s
)
=
K
P
[
1
+
1
T
N
s
+
T
V
s
]
{\displaystyle G(s)=K_{P}\left[1+{\cfrac {1}{T_{N}s}}+T_{V}s\right]\,}
PIDT1-Glied
T
1
x
a
d
t
+
x
a
=
{\displaystyle T_{1}{\cfrac {x_{a}}{dt}}+x_{a}=\,}
K
P
[
T
1
+
T
N
T
N
x
e
+
1
T
N
∫
x
e
d
t
+
(
T
1
+
T
V
)
d
x
e
d
t
]
{\displaystyle K_{P}\left[{\cfrac {T_{1}+T_{N}}{T_{N}}}x_{e}+{\cfrac {1}{T_{N}}}\int x_{e}dt+(T_{1}+T_{V}){\cfrac {dx_{e}}{dt}}\right]\,}
F
(
p
)
=
K
P
[
1
+
1
T
N
p
+
T
V
p
1
+
T
1
p
]
{\displaystyle F(p)=K_{P}\left[1+{\cfrac {1}{T_{N}p}}+{\cfrac {T_{V}p}{1+T_{1}p}}\right]\,}
G
(
s
)
=
K
P
[
1
+
1
T
N
s
+
T
V
s
1
+
T
1
s
]
{\displaystyle G(s)=K_{P}\left[1+{\cfrac {1}{T_{N}s}}+{\cfrac {T_{V}s}{1+T_{1}s}}\right]\,}
![{\displaystyle \left[x_{a}=T_{D}{\cfrac {dx_{e}}{dt}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/76f048c0cf0520fd35b16d4898a8ef7b1757c587)
![{\displaystyle \left[F(p)=T_{D}\cdot p\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7e07777dda292224638f7487240bb06fdb77eadd)
![{\displaystyle \left[G(s)=T_{D}\cdot s\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/04ebb759c13193cf23ca119d4609947c869b2d45)
![{\displaystyle x_{a}=K_{P}\left[T_{V}{\cfrac {dx_{e}}{dt}}+x_{e}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/71f23ec3aea98ff3850e3850f1f519f6ece7dbb3)
![{\displaystyle T_{1}{\cfrac {dx_{a}}{dt}}+x_{a}=K_{P}\left[T_{V}{\cfrac {dx_{e}}{dt}}+x_{e}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fd75fa1dd6bdc2d44ff4a8137d7c014be7dd8923)
![{\displaystyle \left[x_{a}={\cfrac {1}{T_{I}}}\int x_{e}dt\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/231dc84bff4020b492f06329f085fea87fb9bad7)
![{\displaystyle \left[F(p)={\cfrac {1}{T_{I}p}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3f42aab1bdf8befb805c77c043ae8c129609e183)
![{\displaystyle \left[G(s)={\cfrac {1}{T_{I}s}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/57b58983d939b417b3f881bc10af4d8d934d77cc)
![{\displaystyle x_{a}=K_{P}\left[x_{e}+{\cfrac {1}{T_{N}}}\int x_{e}dt\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b46eacbfa4ebebe7c9e2a0599c8428a718d8f8b7)
![{\displaystyle F(p)=K_{P}\left[1+{\cfrac {1}{T_{N}p}}\right]=K_{P}{\cfrac {1+T_{N}p}{T_{N}p}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/63292f186dba1ea98e78410d7fdb69b0f87368ba)
![{\displaystyle G(s)=K_{P}\left[1+{\cfrac {1}{T_{N}s}}\right]=K_{P}{\cfrac {1+T_{N}s}{T_{N}s}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e60e85ec03d9fd1d8abbad9b014d5f032f327dbc)
![{\displaystyle x_{a}=K_{P}\left[x_{e}+{\cfrac {1}{T_{N}}}\int x_{e}dt+T_{V}{\cfrac {dx_{e}}{dt}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5c771eb3587c6536b035cb83528bba4e28c3d095)
![{\displaystyle F(p)=K_{P}\left[1+{\cfrac {1}{T_{N}p}}+T_{V}p\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/510d95887b2e4dfc7a4052ca7dda054c995ab07f)
![{\displaystyle G(s)=K_{P}\left[1+{\cfrac {1}{T_{N}s}}+T_{V}s\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3177a3e55efcc0a2baed2f8515ccc20f89e27dba)
![{\displaystyle K_{P}\left[{\cfrac {T_{1}+T_{N}}{T_{N}}}x_{e}+{\cfrac {1}{T_{N}}}\int x_{e}dt+(T_{1}+T_{V}){\cfrac {dx_{e}}{dt}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/51c8a46f0881481e9e098aea8f3e72fd52e51af8)
![{\displaystyle F(p)=K_{P}\left[1+{\cfrac {1}{T_{N}p}}+{\cfrac {T_{V}p}{1+T_{1}p}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/49ed056bae1e90e2cca570209b8f1985d6478c16)
![{\displaystyle G(s)=K_{P}\left[1+{\cfrac {1}{T_{N}s}}+{\cfrac {T_{V}s}{1+T_{1}s}}\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f3bb32eca543ecf59a648b844c51083f9eb22f4c)
