Modeling and simulation of dynamic systems is Pham Huy Hoang 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 opencircuited terminals.
Trang 1MODELING AND SIMULATION
OF DYNAMIC SYSTEMS
PHAM HUY HOANG
HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY
MIXED DISCIPLINE SYSTEMS
INTRODUCTION
MIXED DISCIPLINE SYSTEM:
MIXED DISCIPLINE SYSTEM – COUPLING SYSTEM OF
SINGLE-DISCIPLINE SYSTEMS
Trang 2Pham Huy Hoang
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):
electrons and ions) to flow;
to produce an electric potential difference across
two open-circuited terminals;
law)
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
ELECTROMECHANICAL SYSTEMS
Trang 3Pham Huy Hoang
ELECTROMECHANICAL SYSTEMS
The back emf voltage across a DC motor:
θ
e
The torque developed by the motor:
i K
: angular velocity of the rotor
T : torque applied to the rotor
ω
θ&=
Trang 4Pham Huy Hoang
) 1 (
0
a e
a a
a
a
e e
b
a b
a a
a
a
a b a
L
a
R
v K
dt
di L
i
R
K K
e
v e dt
di L
i
R
v e v
v
= +
+
=
=
= + +
=
− + +
θ
θ ω
&
&
a
V
a
a
i
b
d
B
L
T
ω θ
a
V
a
a
i
b
d
B
L
T
ω θ
) 2 (
θ θ
θ θ
&
&
&
&
J B
T
i
K
i
K
T
J B
T
T
J J
J
d L a
t
a t
d L
d r
=
− +
=
=
− +
+
=
ELECTROMECHANICAL SYSTEMS
Trang 5Pham Huy Hoang
a
V
a
a
i
b
d
B
L
T
ω θ
θ, &=
=
+
+
= +
+
=
−
+
a
L a
a
t a
a e
d a
a e
a a
a
a
L a t d
v
T i
R
K i
L K
B i
J
v K
i
R
dt
di
L
T i K
B
J
θ θ
θ
θ
θ
θ
0
0 0
0
0
0
&
&
&
&
&
ELECTROMECHANICAL SYSTEMS
B
K ,
a
V
a
a
i
b
d
B
L
T
ω θ
ELECTROMECHANICAL SYSTEMS
Trang 6Pham Huy Hoang
FIELD-CONTROLLED DC MOTOR
) 1 (
f
f f f
dt
di L i
f
v
f
R
f
L
const
0
=
b
e
r
J
d
J
d
B
L
T
ω θ
f
i
f
t i K
) 2 ( θ θ
θ θ
&
&
&
&
J B
T i
K
i K
T
J B
T
T
J J
J
d L f
t
f t
d L
d r
=
− +
=
=
− +
+
=
f
v
f
R
f
L
const
0
=
b
e
r
J
d
J
d
B
L
T
ω θ
f
i
f
t i K
ELECTROMECHANICAL SYSTEMS
Trang 7Pham Huy Hoang
f
v
f
R
f
L
const
0
=
b
e
r
J
d
J
d
B
L
T
ω θ
f
i
f
t i K
=
+
= +
=
− +
f v
L f
f R t K d B f f
L
J
f v f f R dt
f
di
f
L
L f t K d
B
J
θ θ
θ
θ
&
&
&
&
0 0
0
ELECTROMECHANICAL SYSTEMS
f
v
f
R
f
L
const
0
=
b
e
r
J
d
J
d
B
L
T
ω θ
f
i
f
t i K
ELECTROMECHANICAL SYSTEMS
Trang 8Pham Huy Hoang
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
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)
field)
ELECTROMECHANICAL SYSTEMS
Trang 9Pham Huy Hoang
-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
ELECTROMECHANICAL SYSTEMS
1
i
2
R C
2
i L
a y
1
k
2
k
1
c
2
c
1
x
2
x
1
m
2
m b
ELECTROMECHANICAL SYSTEMS
y K emf force ive
Electromot
i K force Magnetic
&
2
2 1
: ) ( :
Trang 10Pham Huy Hoang
0 1
1
1 1
1 2 0
2 2
2 2 0
1
0
2 0
1
1
1
=
−
∫ + +
+
∫
−
=
∫
−
∫
+
x a
b K dt i C i R dt
di L
dt
i
C
v dt i C dt
i
C
i
R
t t
t t
&
1
i
2
R C
2
i L
a y
0
) (
)
(
0 )
( )
(
)]
( ) (
[ ) (
2 2 1 2 2 2 1
2
2
2
2 2 1 2 2 1
2
2
2
2
2 1 2
2 2 1
2 2 1 2
2 2 1
2 2 1
1
1
1 2 1 1
2 2 1 2 2 1
1 1 1
2
1
= +
− +
−
=
−
−
−
−
= +
− +
+
− +
+
=
− +
− +
+
−
−
x k x k x c x
c
x
m
x m x x c x
x
k
x
m
F
abi K x b k x b k k x b c x b c
c
x
m
b
x b m b x x c x x k b x c x
k
a
i
K
J
M O O
&
&
&
&
&
&
&
&
&
&
&
&
&
&
α
1
k
2
k
1
c
2
c
1
x
2
x
1
m
2
m b
ELECTROMECHANICAL SYSTEMS
Trang 11Pham Huy Hoang
Trang 13Pham Huy Hoang