Page 704 - Mechatronics with Experiments

690 MECHATRONICS

T e
a
1
T e
a
1

FIGURE 8.66: Speed-torque characteristics of a DC motor in steady state with current
controlled amplifier.

motor with a constant terminal voltage (Figure 8.66). In other words, the steady-state
torque produced by a DC motor under constant current conditions (i.e., controlled by a
current feedback amplifier) decreases with increasing speed at a much slower rate that the
case when the motor is controlled by a voltage amplifier under constant terminal voltage
condition.

Example Consider a DC motor with the following parameters, K Nm∕A = K V∕
T
E
2
−2
(rad∕s) = 6.7 × 10 , R = 0.5 Ω, L = 2mH, J = 4.8 × 10 −5 kg m , J = J . Determine
a a m l m
the mechanical and electrical time constant of the motor (consider the case that the motor
and the load inertia are rigidly connected). If the current loop control gains are K = 10.0 and
1
K = 1.0, determine the speed-torque slopes under constant voltage and constant current
2
control conditions.
The mechanical and electrical time constants of the motor with the load connected
J R 9.6 × 10 −5 ⋅ 0.5
T a
= = (8.322)
m 2 −4
K K 6.7 × 10
T E
= 0.010 s = 10 ms (8.323)
L a 2 × 10 −3 H
= = = 4 × 10 −3 s = 4 ms (8.324)
e
R a 0.5 Ω
The slope of the torque-speed curve in steady-state under constant voltage and constant
current conditions is,
K K
T E
slope = (8.325)
v
R a
2
6.7 × 10 −4
= (8.326)
0.5
= 89.7 × 10 −4 N ⋅ m∕(rad∕s) (8.327)
= 0.0857 N ⋅ m∕rpm (8.328)
K K
T E
slope = (8.329)
i
R + K K
a
1 2
2
6.7 × 10 −4
= (8.330)
0.5 + 10
= 4.27 × 10 −4 N ⋅ m∕(rad∕s) (8.331)