Page 654 - Mechatronics with Experiments

640 MECHATRONICS
The complete electromechanical dynamic model of this actuator can be written as
( )
di(t) dL(x ) dx (t)
g
g
V(t) = L(x ) + R coil i(t) + ⋅ i(t) ⋅ (8.167)
g
dt dx g dt
2
1 N A x 2
o
F(x , i) =− ⋅ i (8.168)
g
2 ( ) 2
x + A x y g
g
2 A y
2
d x (t)
g
F(x , i) = m p + k spring ⋅ x (t) (8.169)
g
g
dt 2
where
N 2
L(x ) = ( ) A (8.170)
g o x
x + A x y g
g
2 A y
dL(x ) 2
g N
=− ⋅ ⋅ A (8.171)
dx 0 ( ) 2 x
g
x + A x y g
g
2A y
In order to simulate this solenoid, we need the following:
Parameters: , N, A , A , y , m , k spring , R coil .

p
g
y
0
x
Initial conditions: i(t ), x (t ), ̇ x (t ).

g 0
g 0
0
Variables of interest as simulation output: F(t), x (t), V(t), i(t).

g
8.4 DC SERVO MOTORS AND DRIVES
DC servo motors can be divided into two general categories in terms of their commutation
mechanism: (i) brush-type DC motors; (ii) brushless DC motors. The brush-type DC motor
has a mechanical brush pair on the motor frame and makes contact with a commutator
ring assembly on the rotor in order to commutate the current, that is to switch the current
from one winding to another, as a function of rotor position so that the magnetic fields of
the rotor and stator are always at a 90 degree angle relative to each other. In brush-type
permanent magnet DC motors, the rotor has the coil winding, the stator has the permanent
magnets.
The brushless DC motor is an inside-out version of the brush-type DC motor, that
is, the rotor has the permanent magnets and the stator has the winding. In order to achieve
the same functionality of the brush-type motor, the magnetic fields of the rotor and stator
must be perpendicular to each other at all rotor positions. As the rotor rotates, the magnetic
field rotates with it. In order to maintain a perpendicular relationship between the rotor
and stator magnetic fields, the current in the stator must be controlled as a vector quantity
(both magnitude and direction) relative to the rotor position. Control of current to maintain
this vector relationships is called commutation. Commutation is done by solid-state power
transistors based on a rotor position sensor. Notice that a rotor position sensor is necessary
to operate a brushless DC motor, whereas a brush-type DC motor can be operated without
any position or velocity sensor as a torque source. When a motor is controlled in conjunction
with a position or velocity sensor, it is considered a “servo” motor.
The field magnetics in a brush-type DC motor can be established either by permanent
magnets (hence the name permanent magnet DC motor) or electromagnets (hence the