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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
1
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
2
Pham Huy Hoang
ELECTROMECHANICAL SYSTEMS
The back emf voltage across a DC motor:
&
eb = K eω = K eθ
The torque developed by the motor:
T = Kt i
eb : back emf voltage.
θ : angular displacement of the rotor of the motor
& = ω : angular velocity of the rotor
θ
T : torque applied to the rotor
Ke : emf constant (Vs/rad)
Ki : torque constant (Nm/A)
Pham Huy Hoang
3
ELECTROMECHANICAL SYSTEMS
ia
Ra
La
&
θ ,θ = ω
Jr
eb
Va
TL
Jd
Bd
vRa + vLa + eb − va = 0
di
Raia + La a + eb = va
dt
&
eb = K eω = K eθ
Raia + La
dia
&
+ K eθ = va
dt
(1)
Pham Huy Hoang
ELECTROMECHANICAL SYSTEMS
ia
Ra
La
&
θ ,θ = ω
eb
Va
Jr
TL
Jd
Bd
J = Jr + Jd
&
&
T + TL − Bdθ = Jθ&
T = Kt ia
&
&
Kt ia + TL − Bdθ = Jθ& (2)
Pham Huy Hoang
4
ELECTROMECHANICAL SYSTEMS
ia
Ra
La
&
θ ,θ = ω
eb
Va
Jr
TL
Jd
Bd
&
&
Jθ& + Bdθ − Kt ia = TL
di
&
La a + Raia + K eθ = va
dt
&
&
θ&
θ
J 0 Bd 0 0 − Kt θ TL
0 0 .. + K L . + 0 R i = v
i e
a i
a a a
a
a
Pham Huy Hoang
ELECTROMECHANICAL SYSTEMS
ia
Va
Ra
La
&
θ ,θ = ω
eb
Jr
K, B
TL
Jd
Bd
Pham Huy Hoang
5
nguon tai.lieu . vn
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
1
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
2
Pham Huy Hoang
ELECTROMECHANICAL SYSTEMS
The back emf voltage across a DC motor:
&
eb = K eω = K eθ
The torque developed by the motor:
T = Kt i
eb : back emf voltage.
θ : angular displacement of the rotor of the motor
& = ω : angular velocity of the rotor
θ
T : torque applied to the rotor
Ke : emf constant (Vs/rad)
Ki : torque constant (Nm/A)
Pham Huy Hoang
3
ELECTROMECHANICAL SYSTEMS
ia
Ra
La
&
θ ,θ = ω
Jr
eb
Va
TL
Jd
Bd
vRa + vLa + eb − va = 0
di
Raia + La a + eb = va
dt
&
eb = K eω = K eθ
Raia + La
dia
&
+ K eθ = va
dt
(1)
Pham Huy Hoang
ELECTROMECHANICAL SYSTEMS
ia
Ra
La
&
θ ,θ = ω
eb
Va
Jr
TL
Jd
Bd
J = Jr + Jd
&
&
T + TL − Bdθ = Jθ&
T = Kt ia
&
&
Kt ia + TL − Bdθ = Jθ& (2)
Pham Huy Hoang
4
ELECTROMECHANICAL SYSTEMS
ia
Ra
La
&
θ ,θ = ω
eb
Va
Jr
TL
Jd
Bd
&
&
Jθ& + Bdθ − Kt ia = TL
di
&
La a + Raia + K eθ = va
dt
&
&
θ&
θ
J 0 Bd 0 0 − Kt θ TL
0 0 .. + K L . + 0 R i = v
i e
a i
a a a
a
a
Pham Huy Hoang
ELECTROMECHANICAL SYSTEMS
ia
Va
Ra
La
&
θ ,θ = ω
eb
Jr
K, B
TL
Jd
Bd
Pham Huy Hoang
5