-
/, (r)s + R,fL,
3lfil,fr"## 111#:* gives the transrer function from the input
armarure vorrage to the
(2nd order system) (1.13)
The transfer function from the input armature voltage to the
resulting angurar positionchange is found by multiplying Equation (
I . 13) by ll s .
-
rrG) _
vf (s)0tL)
' +(n,14)
The transfer function from the inputcombining equations (l .2)
and(1.3).
(1't order system) ( 1.3)
(1.4)
voltage to the resulting motor torque is found by
T*(s) _T*(t) /r(s)
=Vr(s) t,(s) Vr(s)(x-,lrr)
s +(n,14) ( 1't order system)
So, a step input in field voltage results in an exponential rise
in the motor torque.
An equation that describes the rotational motion ofthe inertial
load is found by summing moments
\U - T* - cat * Ja (counterclockwise positive)0r
Jrh + c0) =T_
c&=cc9
Thus, the transfer function from the input motor torqueto
rotational speed changes is
o(s)T^(t) s+(clJ)
(U J) (1't order system)
Combining equations (1.4) and (1.5) gives thevoltage to the
resulting speed change
Free Body Diagramof the Inertial Load
(1.s)
transfer function from the input field
Finally, since to -
d?ldt, the transfer function from input field voltage to the
resultingrotational position changb is
o(s) =
g(s) T*(t)Vr(s) T^(s) Vr(s)
(x-r ltrt)
0(s) 0(s) ar(s)Vr(s) ar(s) I'r(s)
(x-, ltrt)s(s+clt)(s+RrlLr)
(2nd order system) (r.6)
(r.7)
2
(3'd order system)
-
Current Controlled:
In a armature'current controlled motor, the field current7 is
held constant, and the armature current is controlledthrough the
armature voltage vn. In this case, the motortorque increases
linearly with the armature current. wewrite
T* = K*o io
The transfer function from the input armature current to
theresulting motor torque is
L"T*el&
+- V. ---->+
DC MotorT-(t)ilt) = L*o
As before, the transfer function from
a{s) 0tr)4,(s) s +(cl J)
( 1.8)
where [u represents the "back EMF" induced by the rotation of
the armature windings in amagnetic field. The back EMF % is
proportional to the speed @, i.e. Vub)= qal(s).Taking Laplace
transforms of Equation ( I .9) gives
V,(s) -
Vub)= (& + z,s)d (s)
The voltage/current relationship for the armature side of the
motor is
V, =Vo +V, +Vu
V,(s)- Kua(s) = (& + f,s)f,(s)
(1.e)
(1.10)
(1.12)
or
(1.11)
the input motor torque to rotational speed changes is
( I't order system)
arnr( *uraI*
Tne,"*,bQ
-
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