dynamics of electric systems-spania · microsoft powerpoint - dynamics of electric...
TRANSCRIPT
![Page 2: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/2.jpg)
The transfer functionThe transfer functionThe transfer functionThe transfer function
• A linear and invariant system is described by the equation:
• where:
• y is the output
• x is ithe input
( ) ( 1) ( )
0 1 1
( ) ( 1) ( )
0 1 1
* * * *
* * * * , ( )
n n
n n
m m
m m
a y a y a y a y
b x b x b x b x n m
− •
−
− •
−
+ + + + =
= + + + + ≥
K
K
![Page 3: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/3.jpg)
The transfer functionThe transfer functionThe transfer functionThe transfer function
• =L
L =
()
()=
⋯
⋯, ≥
( ) ( ) ( )zmzz
mmmssssssconstsbsbsb −−−=+++ −− *...***.... 2
2
2
1
10 1
( ) ( ) ( )n
nnnssssssconstsasasa −−−=+++ −− *...***.... 2
2
2
1
10 1
![Page 4: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/4.jpg)
The transfer functionThe transfer functionThe transfer functionThe transfer function
• Zeros.
• Poles.
( ) ( ) ( )( ) ( ) ( )
)(*...**
*...***)(
2
2
1
1 mnssssss
ssssssctsG
n
zmzz≥
−−−
−−−=
∞→poles
sG )(
0)( →zeros
sG
![Page 5: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/5.jpg)
)(*)(1
)(
)(
)(
sHsG
sG
sR
sC
+=
Block schematic
G(s)+
-
R(s) C(s)
G(s)+
-
R(s) C(s)
H(s)
Unity feed-back
Non-unity feed-back
)(1
)(
)(
)(
sG
sG
sR
sC
+=
![Page 6: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/6.jpg)
V = −R
RV
V = 1 +R
RV
V = V
Circuits with OA: basic structures
Inverting
Non-inverting
Repeating
![Page 7: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/7.jpg)
V = −R
RV +
R
RV +
R
R!V V =
R!
R
R + R
R + R!V −
R
RV
Sum
![Page 8: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/8.jpg)
V = −1
sCRV
V = −R
R
1
sCR + 1V
V = −sCRV
Derivation and integration
Derivation
Derivation
Integration
![Page 9: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/9.jpg)
Equivalent schematics
1
s+13
T ransfer Fcn
Subtract
Step
Scope2
Scope1
Scope
1
s
Integrator
13
Gain
G =1
+ 13=
1
1 + 13 ⋅1
![Page 10: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/10.jpg)
Equivalent schematics
1
s+13
T ransfer Fcn
Subtract
Step
Scope2
Scope1
Scope
1
s
Integrator
13
Gain
G =1
+ 13=
1
1 + 13 ⋅1
G =1
+ 13=
1
1 + 13 ⋅1
![Page 11: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/11.jpg)
Equivalent schematic with OA
1
s+13
T ransfer Fcn
Subtract
Step
Scope2
Scope1
Scope
1
s
In tegra tor
13
Gain
![Page 12: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/12.jpg)
Equivalent schematic with OA SI
1
s+13
T ransfer Fcn
Subtract
Step
Scope2
Scope1
Scope
1
s
Integrator
13
Gain
-1
![Page 13: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/13.jpg)
Equivalent schematic with OA SII
• =
'⋅!=
• =
(')'⋅(
!⋅
(')'⋅(
• =
'⋅=
⋅
=
• =
⋅
(
'
(
1
s +2s+42
T ransfer Fcn
Subtract
Step
Scope2
Scope1
Scope
1
s
Integrator1
1
s
Integrator
4
Gain1
2
Gain
![Page 14: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/14.jpg)
Equivalent schematic with OA
• =
'⋅!=
• =
(')'⋅(
!⋅
(')'⋅(
• =
'⋅=
⋅
=
• =
⋅
(
'
(
1
s +2s+42
T ransfer Fcn
Subtract
Step
Scope2
Scope1
Scope
1
s
Integrator1
1
s
Integrator
4
Gain1
2
Gain
![Page 15: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/15.jpg)
Equivalent schematic with OA
1
s +2s+42
T ransfer Fcn
Subtract
Step
Scope2
Scope1
Scope
1
s
Integrator1
1
s
Integrator
4
Gain1
2
Gain
![Page 16: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/16.jpg)
Equivalent schematic with OA
1
s +2s+42
T ransfer Fcn
Subtract
Step
Scope2
Scope1
Scope
1
s
Integrator1
1
s
Integrator
4
Gain1
2
Gain
![Page 17: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/17.jpg)
Equivalent schematic with OA
1
s +2s +4s+133 2
T ransfer Fcn
Subtract
Step
Scope2
Scope1
Scope
1
s
Integrator2
1
s
Integra tor1
1
s
Integrator
13
Gain2
4
Gain1
2
Gain
![Page 18: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/18.jpg)
Equivalent schematic with OA
• =
*⋅'!⋅=
(*)'⋅(')+⋅(
⋅
(*)'⋅(')+⋅(
•
• =
*⋅'!⋅=
⋅
'⋅!=
⋅
(')'⋅(
!⋅
(')'⋅(
• =
'⋅=
⋅
=
⋅
(
'
(
![Page 19: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/19.jpg)
Equivalent schematic with OA
![Page 20: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/20.jpg)
First order system S-I
1
1
C s
R s Ts
( )
( )=
+)(*)(1
)(
)(
)(
sHsG
sG
sR
sC
+=
![Page 21: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/21.jpg)
First order system S-I: step input
, - = 1 − ./
0
for t > 0
- = 1 →
, 1 = 1 − ./ =
= 0,632 = 63,20%
![Page 22: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/22.jpg)
Second order system SSecond order system SSecond order system SSecond order system S----IIIIIIII
8()
9()=
:;
+ 2ζ:; + :;
8()
9()=
:;
+ 2ζ:;
ζ – factor de amortizare
:;- pulsatie naturala de oscilatie
)(*)(1
)(
)(
)(
sHsG
sG
sR
sC
+=
![Page 23: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/23.jpg)
Second order system response: step inputSecond order system response: step inputSecond order system response: step inputSecond order system response: step input
0,-1
arctgsin1
1
sin1
cos1)(
2
2
2
≥
+
−−=
=
−+−= −
tt
ttetc
d
dd
tn
ξ
ξω
ξ
ξ
ωξ
ξωξω
![Page 24: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/24.jpg)
Second order system response: step inputSecond order system response: step inputSecond order system response: step inputSecond order system response: step input
![Page 25: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/25.jpg)
Transitory response: Transitory response: Transitory response: Transitory response:
step inputstep inputstep inputstep input
-=- delay time
->- rise time
-?- peak time
-- settling time
σ?- peak value
![Page 26: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/26.jpg)
Determination of transient parametersDetermination of transient parametersDetermination of transient parametersDetermination of transient parameters
Rising timettttrrrr :
0,-1
arctgsin1
1
sin1
cos1)(
2
2
2
≥
+
−−=
=
−+−= −
tt
ttetc
d
dd
tn
ξ
ξω
ξ
ξ
ωξ
ξωξω
1( )r
c t =
21
1( ) cos sinn rt
r d r d rc t e t t
−ξω ξ = − ω + ω − ξ
21 ξωω −= nd
![Page 27: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/27.jpg)
Determination of transient parametersDetermination of transient parametersDetermination of transient parametersDetermination of transient parameters
Rising timettttrrrr :
0n rte−ξω ≠
20
1cos sin
d r d rt t
ξω + ω =
− ξ
σ
ω
ξ
ξω d
rt −=−
−=2
d
1tg
dd
rtω
βπ
σ
ω
ω
−=
= darctg
1
21 ξωω −= nd
![Page 28: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/28.jpg)
Determination of transient parametersDetermination of transient parametersDetermination of transient parametersDetermination of transient parameters
Overshooting time ttttpppp :
0== pttdt
dc
0,-1
arctgsin1
1
sin1
cos1)(
2
2
2
≥
+
−−=
=
−+−= −
tt
ttetc
d
dd
tn
ξ
ξω
ξ
ξ
ωξ
ξωξω
![Page 29: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/29.jpg)
Determination of transient parametersDetermination of transient parametersDetermination of transient parametersDetermination of transient parameters
Overshooting time ttttpppp :
20 0
1sin sinn
p
tn
d p d p
t t
dce t t
dt
−ξω
=
ω= ω = => ω =
− ξ
0 2 3, , , , ...d ptω = π π π
d ptω = π
p
d
tπ
=ω
![Page 30: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/30.jpg)
Determination of transient parametersDetermination of transient parametersDetermination of transient parametersDetermination of transient parameters
Overshooting value σσσσpppp :
p
d
tπ
=ω
0,-1
arctgsin1
1
sin1
cos1)(
2
2
2
≥
+
−−=
=
−+−= −
tt
ttetc
d
dd
tn
ξ
ξω
ξ
ξ
ωξ
ξωξω
![Page 31: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/31.jpg)
Determination of transient parametersDetermination of transient parametersDetermination of transient parametersDetermination of transient parameters
Overshooting value σσσσpppp :
σ? = , -? − 1
= ./AB
CDE cos H +
ξ
1 − ξJsin H − 1
= ./
A
/A'J C
>> cos(pi)
ans =
-1
>> sin(pi)
ans =
1.2246e-016[ ]100* %d
pe
σ− π
ωσ =
21 ξωω −= nd
M = ζ:;
![Page 32: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/32.jpg)
Determination of transient parametersDetermination of transient parametersDetermination of transient parametersDetermination of transient parameters
Settling time ttttssss :
4 44
s
n
t T= = =σ ξω
3 33
s
n
t T= = =σ ξω
- ± 2%
- ± 5%
![Page 33: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/33.jpg)
DC motor model
−−=Ω
++=
sf
AAAAA
mmmdt
tdJ
tedt
tdiLtiRU
)(
)()(
)(
60
2 n
AnAAn
n
AnAAnn n
IRUIRUK
⋅
−=
Ω
−=Φ
π
−Ω⋅−⋅Φ⋅=Ω⋅⋅
Ω⋅Φ⋅+⋅⋅+⋅=
sA
AAAAA
msfsIKssJ
sKsIsLsIRU
)()()(
)()()(
![Page 34: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/34.jpg)
DC motor model
[ ]
[ ]
+⋅⋅−⋅Φ⋅=Ω
⋅+⋅Ω⋅Φ⋅−=
fJsmsIKs
LsRsKUsI
sA
AA
AA
1)()(
1)()(
1
sLA+ RA
KΦ1
sJ + f
KΦ
U A Ω
ms
+ +
-
-I A(s)
Ω
Ω (s)
![Page 35: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/35.jpg)
DC motor transfer function
( )( )( ) fsJ
m
sLRfsJ
sKsUK
fsJ
m
sLR
sKsU
fsJ
K
fsJ
msI
fsJ
Ks
s
AA
A
s
AA
A
sA
+−
++
ΩΦ−Φ=
=+
−+
ΦΩ−
+
Φ=
=+
−+
Φ=Ω
)()(...
...)()(
...
...)()(
2
( )( )( )AA
A
sLRfsJ
sKsUKs
++
ΩΦ−Φ=Ω
)()()(
2
( )( ) ( )
( ) ( )......
...)(
)(
22
2
=Φ++++
Φ=
=Φ+++
Φ=
Ω
KfRJRfLsJLs
K
KsLRfsJ
K
sU
s
AAAA
AAA
![Page 36: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/36.jpg)
DC motor transfer function
( )( ) ( )
( ) ( )......
...)(
)(
22
2
=Φ++++
Φ=
=Φ+++
Φ=
Ω
KfRJRfLsJLs
K
KsLRfsJ
K
sU
s
AAAA
AAA
( )
( )
( )
( )JL
KfR
JL
JRfLss
JL
KfR
JL
KfR
JL
K
JL
KfR
JL
JRfLss
JL
K
A
A
A
AA
A
A
A
A
A
A
A
A
AA
A
2
2
2
2
2
2
...
Φ++
++
Φ+
Φ+
Φ
=Φ+
++
+
Φ
=
2212
)(nn
n
ssKsG
ωζω
ω
++=
( )
( )
JL
JRfL
JL
KfR
JL
KfR
JL
K
K
A
AAn
A
An
A
A
A
+=
Φ+=
Φ+
Φ
=
ζω
ω
2
;
;
2
21
![Page 37: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/37.jpg)
DC motor dynamic parameters
( )
( )( )
−+
Φ−=
Φ+=
AAnAnA
AAn
nA
A
RLRL
KRLf
L
KfRJ
ξωω
ξω
ω
2
2222
2
2
2
( )
JL
JRfL
JL
KfR
A
AAn
A
An
+=
Φ+=
ζω
ω
2
;
2
![Page 38: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/38.jpg)
R-L circuit
• ω = 2πP
• QR = ωS = 9 tg φ
• WX = YX 9 + QRJ
• φ = ωΔ-[\
]
• Δ- – voltage and current delay
Δ-
9
S
W
Y
![Page 39: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/39.jpg)
Example:
![Page 40: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/40.jpg)
![Page 41: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/41.jpg)
DC motor nominal data
DC nominal data
Data Value []
1 UA 200 V
2 IA 2,0 A
3 nn 1500 rot/min
Measured data
Data Value []
1 RA 15,8 Ω2 LA 0,41 H
![Page 42: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/42.jpg)
Transient behavior of the DC motor
-? = 0,064
X = 1600,50 `a-/c
Xd= = 1371,01 `a-/c
-? = 0,064
σ? = 0,1674
![Page 43: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/43.jpg)
J and f determination
=−
=
=
+
=
9776,641
4945,0ln
1
ln
2
2
2
ζ
πω
π
σ
π
σ
ζ
p
n
p
p
t
( )
( )( )
=−+
Φ−=
=Φ+
=
0279,02
2
0011,0
222
2
2
2
AAnAnA
AAn
nA
A
RLRL
KRLf
L
KfRJ
ξωω
ξω
ω
-? = 0,064
σ? = 0,1674
![Page 44: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/44.jpg)
Experimental data
![Page 45: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/45.jpg)
DC motor block schematic
![Page 46: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/46.jpg)
DC motor block schematic - electric
![Page 47: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/47.jpg)
DC motor equivalent schematic
+−
−
−
![Page 48: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/48.jpg)
DC motor equivalent schematic
![Page 49: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/49.jpg)
DC motor block schematic - mechanic
![Page 50: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/50.jpg)
DC motor equivalent schematic
+
+
+
− −
−
![Page 51: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/51.jpg)
DC motor equivalent schematic
![Page 52: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/52.jpg)
DC motor equivalent schematic
![Page 53: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/53.jpg)
Experimental data
![Page 54: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/54.jpg)
Experimental
data
![Page 55: Dynamics of electric systems-Spania · Microsoft PowerPoint - Dynamics of electric systems-Spania.pptx Author: Robert Created Date: 9/29/2017 1:24:17 PM](https://reader034.vdocuments.us/reader034/viewer/2022050415/5f8b5903a49a653bbd0fca67/html5/thumbnails/55.jpg)
DC motor transient behavior