MODELING AND SIMULATION OF DYNAMIC SYSTEMS
MIXED DISCIPLINE SYSTEMS
PHAM HUY HOANG HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY
INTRODUCTION
MIXED DISCIPLINE SYSTEM:
MIXED DISCIPLINE SYSTEM – COUPLING SYSTEM OF
SINGLE-DISCIPLINE SYSTEMS
Pham Huy Hoang
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ELECTROMECHANICAL SYSTEMS
-
-
ARMATURE-CONTROLLED DC MOTOR Voltage is electric potential energy per unit charge (J/C = V) - referred to as "electric potential”. Electromotive force (emf) voltage (electromotance): is that which tends to cause current (actual - electrons and ions) to flow; is the external work expended per unit of charge to produce an electric potential difference across two open-circuited terminals; is generated by a magnetic force (Faraday’s law).
Pham Huy Hoang
ELECTROMECHANICAL SYSTEMS
Faraday's Law Any change in the magnetic environment* of a coil of wire will cause a voltage (emf) to be "induced" in the coil. * The change of magnetic field strength, relative displacement between the magnet field and the coil.
Pham Huy Hoang
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Pham Huy Hoang
ELECTROMECHANICAL SYSTEMS
The back emf voltage across a DC motor:
=
=
K
K
e b
w e
& q e
The torque developed by the motor:
= iKT t
q =&
: angular velocity of the rotor
eb : back emf voltage. q : angular displacement of the rotor of the motor w T : torque applied to the rotor Ke : emf constant (Vs/rad) Ki : torque constant (Nm/A)
Pham Huy Hoang
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ELECTROMECHANICAL SYSTEMS
aL
w
aR
ai
LT
rJ
dJ
be
aV
dB
+
+
=
v
v
0
e b
v a
aR
aL
-
+
+
=
iR aa
L a
e b
v a
=
di a dt = K
K
& q e
e b
w e
+
+
=
K
)1(
iR aa
L a
& q e
v a
di a dt
Pham Huy Hoang
ELECTROMECHANICAL SYSTEMS
aL
w
aR
ai
LT
rJ
dJ
be
aV
dB
r
d & q
= + J J J
= - && q J B d
& q = - && q J )2( + TT L = iKT at + T L iK at B d
Pham Huy Hoang
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ELECTROMECHANICAL SYSTEMS
aL
aR
ai
LT
rJ
dJ
be
aV
dB
w =&, qq
+ & q = - && q J B d iK at T L
+ + = K iR aa & q e v a L a di a dt
t
e
- 0 0 K + + = B d K 0 J 0 00 L a R a q i a T L v a && q .. i a & q . i a
Pham Huy Hoang
ELECTROMECHANICAL SYSTEMS
aL
w
aR
ai
LT
dJ
be
aV
rJ BK,
dB
Pham Huy Hoang
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ELECTROMECHANICAL SYSTEMS
FIELD-CONTROLLED DC MOTOR
w
fR
=
const
ia
LT
fi
rJ
fv
dJ
fL
dB
0=
be
ftiKT =
di
+
=
L
v
)1(
iR f
f
f
f
f dt
Pham Huy Hoang
ELECTROMECHANICAL SYSTEMS
w
fR
=
const
ia
LT
fi
rJ
fv
dJ
fL
dB
0=
be
ftiKT =
=
+
J
J
J
r
d & q
=
&& q J
B d
+ TT L = iKT ft +
& q
=
-
&& q J
)2(
iK ft
T L
B d
-
Pham Huy Hoang
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ELECTROMECHANICAL SYSTEMS
w
fR
=
const
ia
LT
fi
rJ
fv
dJ
fL
dB
0=
be
ftiKT =
+
=
& q
&& q J
fitK
LT
+
=
fv
fL
dB fdi dt
-
+
=
J 0
dB 0
tK fR
0 fL
LT fv
& q fi
fifR && q . fi
-
Pham Huy Hoang
ELECTROMECHANICAL SYSTEMS
w
fR
=
const
ia
LT
fi
rJ
fv
dJ
fL
dB
0=
be
ftiKT =
Pham Huy Hoang
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ELECTROMECHANICAL SYSTEMS
MAGNETO-ELECTRO-MECHANICAL SYSTEMS
Lenz’s law: increasing current in a coil will generate a counter emf which opposes the current. (The emf always opposes the change in current).
The relation of this counter emf to the current is the origin of the concept of inductance.
Pham Huy Hoang
ELECTROMECHANICAL SYSTEMS
Magnetic Force and Lorentz force law: - The force is perpendicular to both the velocity v of the charge q and the magnetic field B (N/A = Ns/C = Tesla). - The magnitude of the force is F = qvB sinθ (θ is the angle between the velocity and the magnetic field).
Pham Huy Hoang
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ELECTROMECHANICAL SYSTEMS
-The magnetic force on a stationary charge or a charge moving parallel to the magnetic field is zero. - The direction of the force is given by the right hand rule.
Pham Huy Hoang
ELECTROMECHANICAL SYSTEMS
2i
1i
2R
1R
L
v
C
1k
1c
b
1m
y
1x
a
2k
2c
Magnetic force :
2m
2x
Electromot ive iK 21 ( force emf :) &2 yK
Pham Huy Hoang
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ELECTROMECHANICAL SYSTEMS
2i
1i
2R
1R
v
L
C
y
a
+
=
dt
v
iR 11
i dt 1
i 2
1 C
1 C
t ∫ 0
t ∫ 0
+
+
+
=
-
L
Kdt
0
i dt 1
iR 22
i 2
2
& x 1
1 C
di 2 dt
1 C
b a
t ∫ 0
t ∫ 0
- -
Pham Huy Hoang
ELECTROMECHANICAL SYSTEMS
=
∑
M
J
O
a O
2
+
+
+
(
[
k
(
)
(
)]
aiK 21
xk 11
& bxc ) 11
x 2
2
x 1
c 2
& x 2
= & bmbx 1 1
&& x 1 b
2
2
+
+
+
=
+
- - - -
(
0
(
& xbc ) 1 2
2 & xbc 2 2
k 1
xbk ) 1 2
2 xbk 2 2
abiK 1 2
=
- -
& x 2
1k
1c
) +
) +
&& xm 22 =
- - - -
0
+ && xm c 11 1 ∑ = && xmF 22 ( k x x 2 1 2 && & xm xc 12 22
( c 2 & xc 22
& x 1 xk 12
xk 22
b
1m
1x
2k
2c
2m
2x
- -
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