136 • Chapter 10 Theory of Operation DMC-2X00

Motor-Amplifier

The motor amplifier may be configured in three modes:
1. Voltage Drive
2. Current Drive
3. Velocity Loop
The operation and modeling in the three modes is as follows:

Voltage Drive

The amplifier is a voltage source with a gain of Kv [V/V]. The transfer function relating the input
voltage, V, to the motor position, P, is

(

)

(

)

[]
PV K KS ST ST
Vt m e
=++11
where
TRJK
m
t
=2 [s]
and
T
L
R
e= [s]
and the motor parameters and units are
Kt Torque constant [Nm/A]
R Armature Resistance Ω
J Combined inertia of motor and load [kg.m2]
L Armature Inductance [H]
When the motor parameters are given in English units, it is necessary to convert the quantities to MKS
units. For example, consider a motor with the parameters:
K
t = 14.16 oz - in/A = 0.1 Nm/A
R = 2 Ω
J = 0.0283 oz-in-s2 = 2.10-4 kg . m2
L = 0.004 H
Then the corresponding time constants are
T
m = 0.04 sec
and
T
e = 0.002 sec
Assuming that the amplifier gain is Kv = 4, the resulting transfer function is
P/V = 40/[s(0.04s+1)(0.002s+1)]

Current Drive

The current drive generates a current I, which is proportional to the input voltage, V, with a gain of Ka.
The resulting transfer function in this case is
P/V = Ka Kt / Js2