161
dependent nature and guidance factors (K y,k ,K z,k ) dominate the control forces of the
maglev vehicle-guideway system. Next, the equations of motion of the 4-DOF rigid
maglev vehicle (see Fig. 9.1) are written as
M u
g t
G I
g t l
G d
lc
k
K
y k
Z
k
K
y k k
0
1
1
¨
,
¨
,
,
u
ª ¬
º ¼
¦
¦
T T
(9.11)
M u
p
G I
G d
vc
k
K
z k
y
k
K
z k k
0
0
1
1
¨
,
¨
,
,
ª ¬
º ¼
¦
¦
T T
(9.12)
in which M 0 = m v l + Km w = lumped mass of the vehicle, g(t) = control force to tune
the lateral response of the maglev vehicle, I T = total mass moment of inertia of the
rigid car, and p 0 = M 0 g = lumped weight of the maglev vehicle.
Though the vehicle will run by electromagnetic force, a wind turbine generator
is to be used for powering the vehicle as the additional source of energy to exit the
vehicle from road and park where maglev system is not available. Thus, the model
is developed by doubly fed induction generator (DFIG) for producing electricity for
transportation vehicles [11–13]. The fundamental equation governing the mechanical power of the wind turbine is
P
C
AV
w
p
,
1
2
3
O E U
(9.13)
where ρ is the air density (kg/m
3
), C p is the power coefficient, A is the intercepting
area of the rotor blades (m
2
), V is the average wind speed (m/s), and λ is the tip speed
ratio [14]. The theoretical maximum value of the power coefficient C p is 0.593; C p
is also known as Betz’s coefficient. Mathematically,
O
Z
R
V
(9.14)
R is the radius of the turbine (m), ω is the angular speed (rad/s), and V is the average wind speed (m/s). The energy generated by wind can be obtained by
Q
P
w
Time kWh
u
>
@
(9.15)
It is well known that wind velocity cannot be obtained by a direct measurement
from any particular motion [9, 15]. In data taken from any reference, the motion
needs to be determined for that particular motion; then, the velocity needs to be
measured at a lower motion:
v z
Z
Z
v Z
Z
Z
§
©
¨
·
¹
¸
§
©
¨
·
¹
¸
ln
ln
r
r
0
0
(9.16)
Methods and Materials
dependent nature and guidance factors (K y,k ,K z,k ) dominate the control forces of the
maglev vehicle-guideway system. Next, the equations of motion of the 4-DOF rigid
maglev vehicle (see Fig. 9.1) are written as
M u
g t
G I
g t l
G d
lc
k
K
y k
Z
k
K
y k k
0
1
1
¨
,
¨
,
,
u
ª ¬
º ¼
¦
¦
T T
(9.11)
M u
p
G I
G d
vc
k
K
z k
y
k
K
z k k
0
0
1
1
¨
,
¨
,
,
ª ¬
º ¼
¦
¦
T T
(9.12)
in which M 0 = m v l + Km w = lumped mass of the vehicle, g(t) = control force to tune
the lateral response of the maglev vehicle, I T = total mass moment of inertia of the
rigid car, and p 0 = M 0 g = lumped weight of the maglev vehicle.
Though the vehicle will run by electromagnetic force, a wind turbine generator
is to be used for powering the vehicle as the additional source of energy to exit the
vehicle from road and park where maglev system is not available. Thus, the model
is developed by doubly fed induction generator (DFIG) for producing electricity for
transportation vehicles [11–13]. The fundamental equation governing the mechanical power of the wind turbine is
P
C
AV
w
p
,
1
2
3
O E U
(9.13)
where ρ is the air density (kg/m
3
), C p is the power coefficient, A is the intercepting
area of the rotor blades (m
2
), V is the average wind speed (m/s), and λ is the tip speed
ratio [14]. The theoretical maximum value of the power coefficient C p is 0.593; C p
is also known as Betz’s coefficient. Mathematically,
O
Z
R
V
(9.14)
R is the radius of the turbine (m), ω is the angular speed (rad/s), and V is the average wind speed (m/s). The energy generated by wind can be obtained by
Q
P
w
Time kWh
u
>
@
(9.15)
It is well known that wind velocity cannot be obtained by a direct measurement
from any particular motion [9, 15]. In data taken from any reference, the motion
needs to be determined for that particular motion; then, the velocity needs to be
measured at a lower motion:
v z
Z
Z
v Z
Z
Z
§
©
¨
·
¹
¸
§
©
¨
·
¹
¸
ln
ln
r
r
0
0
(9.16)
Methods and Materials