Page 703 - Mechatronics with Experiments

ELECTRIC ACTUATORS: MOTOR AND DRIVE TECHNOLOGY 689

m
T t0 t1
t0
a
T
t1 t0 m max
a
T
t2 t1 T e
a
a
T
t3 t3
a 1
t3

ti
e
FIGURE 8.65: Steady-state torque-speed characteristics of a DC motor.

Let us consider this equation for various constant terminal voltage values, V (Figure 8.65).
ti
The steady-state torque-speed curve has a negative slope of K T K e for a given constant
R a
terminal voltage. A given motor maximum torque at stall will saturate at the magnetic field
saturation point and the torque will not increase even if terminal voltage is increased beyond
̇
a certain voltage value. For a given constant terminal voltage, as the speed (Δ ) increases,
( )
̇
the torque capacity of the motor decreases by K T K e Δ .
R a
8.8.4 Steady-State Torque-Speed Characteristic of a DC
Motor Under Constant Commanded Current
Condition

When we consider a DC motor driven by a current amplifier, we need to consider the
following additional relation,
V (t) = K (i (t) − K i(t)); V (t) ≤ V
t 1 cmd 2 t tmax
when the amplifier saturates, V (t) > V
t tmax
V (t) = V r,t max
t
Substituting the above current feedback control to the motor dynamics, and letting
L ≈ 0.0,
a
di
̇
V (t) = L a + R i + K (t) (8.318)
t
e
a
dt
di
̇
K (i (t) − K i(t)) = L a + R i + K (t) (8.319)
a
2
1 cmd
e
dt
̇
Solve for i(t) in terms of i cmd (t) and (t), and substitute in the torque-current equation to
obtain the steady-state torque versus speed relationship under constant current condition,
T (t) = K i(t) (8.320)
T
m
K K K K
T e
T 1
T = i cmd − ̇ (8.321)
m
R + K K R + K K
a
1 2
1 2
a
When the amplifier is commanded a constant current, (i cmd ), the speed torque characteristic
is linear with negative slope. However, the slope is much flatter than the case of the DC