16.2 FEEDBACK CONTROL SYSTEMS 779
and
sinδ=
1500 × 746
3 ×( 6600 /
√
3 )× 144. 2
= 0. 6788
or the torque angleδ= 42 .75° electrical or 14.25° mechanical.
One-half of rated speed=600 r/min. With a constantV/fratio,Im′ is constant. Since
torqueT = ( 3 /ωs)V If′ sinδ = ( 3 Xs/ωs)Im′If′ sin δ,δis unchanged. Noting thatI ̄s =
I ̄m′ −I ̄f′,Is sinφ=−I ̄m′+I ̄f′ cosδ,andIs cosφ=I ̄f′ sinδ, then, for constant values
ofδandIm′, bothIsand the power factor remain the same, which is true for any speed. Therefore,
Is= 97 .9A; δ= 42 .75° electrical; power factor= 1. 0
V∠ 0 °
V
Vf
Vf∠−δ jXs
Is
I′m
I′f
I′f −(δ + ) =
δ
φ
δ δ +π 2
δ′
φ
Is jXs
IsXs
V∠ 0 °
Is
V
π
2
(a) (b)
I′m =jXVs
Vf
jXs
Figure E16.1.6
Applications for the Electronic Control of Motors
A wide range of variable-speed drive systems are now available, each having particular advantages
and disadvantages. The potential user needs to evaluate each application on its own merit, with
consideration given to both technical limitations of particular systems and long-term economics.
A number of possible applications of the electronic control of motors are listed in Table 16.1.4.
16.2 Feedback Control Systems
Anopen-loopsystem is one in which the control action is independent of the output or desired
result, whereas aclosed-loop(feedback) system is one in which the control action is dependent
upon the output. In the case of the open-loop system, the input command (actuating signal) is
the sole factor responsible for providing the control action, whereas for a closed-loop system the
control action is provided by the difference between the input command and the corresponding
output.
