0195136047.pdf

824 BASIC CONTROL SYSTEMS

(e) For a step input ER, obtain the final steady-

state response ωm(∞), i.e., evaluate

ωm(∞)/ER.

(f) Evaluateωm(∞)/TLfor the step input

TLof a load torque.

16.2.24Consider the motor of Problem 16.2.3 to be used

as a field-controlled dc machine. Let the armature

be energized from a constant current source of 15

A. Assume no saturation.

(a) Develop a block diagram relating the motor

speed and the applied field voltage.

(b) Determine the steady-state speed for a step-

applied field voltage of 220 V.

(c) How long does the motor take to reach 0.95

of the steady-state speed of part (b)?

*16.2.25The output voltage of a 10-kW, 240-V dc generator
is regulated by means of the closed-loop system
shown in Figure P16.2.25. The generator parame-
ters areRf= 150 ,Ra= 0. 5 ,Lf=75 H, and
KE=150 V per field ampere at 1200 r/min. The
self-inductance of the armature is negligible. The
amplifier has an amplification factorA=10, and
the potentiometers are set such thatais unity and
the reference voltagevris 250 V. The generator is
driven by an induction motor, the speed of which
is almost 1200 r/min when the generator output is
zero, and 1140 r/min when the generator delivers
an armature current of 42 A.
(a) Compute the steady-state armature terminal
voltage at no load, and when the generator is
delivering 42 A.
(b) Calculate the time constant for part (a).
(c) With the value of the field current as in part
(a), for an armature current of 42 A, calculate
the steady-state armature voltage.
16.2.26(a) A common analog control element is thedc
tachometer, which is basically a permanent

magnet generator, as illustrated schematically

in Figure P16.2.26(a). Determine the transfer

function of this device, with speed as the input

and voltage as the output. See what happens

to the transfer function ifRL→∞.

(b) Adc servomotoris another common analog

element in control systems, shown schemat-

ically in Figure P16.2.26(b). Obtain an ex-

pression form(s)/Ei(s), assuming constant-

field configuration and linear elements.

(c) Add load torque to the load on the servomotor

of Figure P16.2.26(b). Develop a block dia-

gram with a voltage signal that will serve as a

speed reference and a load torque as a second

input (or load disturbance).

16.2.27(a) Consider a single loop system of the con-

figuration shown in Figure P16.2.27(a) with

positive feedback. Although positive feedback

generally results in instability, it is frequently

employed at low magnitudes or in portions of

a large control system, particularly in an inner

loop. Obtain an expression forC(s)/R(s).

(b) Figure P16.2.27(b) illustrates a multiple-loop

feedback control system, where the argument

sis omitted for simplicity. Reduce it to a

single-loop configuration.

16.2.28Loop topography that is relatively common in con-

trol systems is shown in Figure P16.2.28. Obtain

its single-loop representation.

*16.2.29A generalized two-input system is illustrated in

Figure P16.2.29. Treating multiple inputs by

means of the principle of superposition, which

holds in linear control systems, find the system

responseC.

16.2.30Simplify the loop topography shown in Figure

P16.2.30 to that of a single-loop configuration.

16.2.31Determine the steady-state error of a type 0 system

with a unit-step reference input function for the

Ward–Leonard system of Figure E16.2.3(a).

ve Gain A vf

Amplifier

+ ++

+

+

−

RL

iL

vt

avt

if

va

ava

Figure P16.2.25