A FEEDBACK CCNTROL SYSTEM ER
VOLTAGE REGULATECN

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This is to eel-tug that the
thesis entitled

"A Feedback Control System For
Koltage Regulation"

presented by

Wilbur Carroll Peterson

has been accepted towards fulfillment
of the requirements for

 

M.S. degree in Electrical Engineering

 

 

U Major profelsor

(

-'-—

 

 

. 1‘ _._,.

A FEEDBACK CONTROL SYSTIM FOR VOLTAGE REGULATION

BY

WILBUB CARROLL PETERSW

A THESIS

Submitted to the School of Graduate Studies of nichigm
State College of Agriculture and Applied Science
in partial fulfillment of the requirmnents

for the degree ‘0:

EASTER OF SSIENGE

Department of Electrical Engineering

1951

THESIS

ACHTO'WDGEEEWT

The author wishes to thank Doctor .1. A. Strelzoff for his helpful
critici- of the first draft of this thesis; and both Doctor Strelzoff
and Professor I. B. Baccus for encouraging the author to carry on

graduate studies at Michigan State College.

W. (3. Peterson

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A w
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id
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I.

II.

III.

IV.

V.

VII.

VIII.

I.

TABLE OF OON’TSNTS
Purpose...............
Introduction ............
TheDOGenerator ..........
The Amplidyne Generator . . . . . . .
Direct Coupled Electronic uplifier .

Composite Open Locp Transfer Emotion
syatmmw51.eeeeeeeeeee

Frequency Response of the Closed Leap

and

Steady State

Syotan.....

Stabilization of the Systan . . . . . . . . . . . . . .

Transient Response of the Syetan . . . . . . . . . . .

Wmdpiaoualionooesseesseeeesee

Page
. . 1
. . 1
s s 2
e 10
o 16
. 21
. 22
. 29
e 40
e 49

WIS.
The primary purpose of this thesis is the design and analysis of a

control system intended to maintain the output voltage of a no generator
at a fixed value, or any arbitrary fixed value within the voltage rating
of the machine. It is required that the deviation from the desired
fixed value mu not exceed 0.1% under steady state conditions.
W

a feedback control system is best suited to accomplish the above
stated requirements. As the name implies, such a system is character-
ised by a circuit arrangement in whieh the output quantity. in this case
the output voltage of the generator, is fed back to the input. to obtain
a continuous comparison with a fixed reference quantity. The control
elements respond to the magnitude of difference between reference and
output quantities and in turn supply field current to the generator so
as to tend to maintain the output at a fixed value.

Since the purpose of the systm to be described is to maintain an
output quantity at a fixed level. it is called a regulating systul. The
systan is incidentally also capable of responding to arbitrary changes
in the level of the reference quantity, but such performance is not or-
dinarily required. Since it is capable of such performance, the system
may be properly designated a servo system.

a system designed to maintain the rotary or translatory position of
an output member in correspondence with the arbitrary position of some
input member is called a servunechanian. In this case the output ma-

ber might be a gun turret, and the input member a hand wheel, as an

ample.

- 2 -

The above discussion is intended to bring out the close relations
existing between regulating systems and servonechanians; each systan
is in fact a type of feedback control system.

The methods for synthesis and analysis of all types of feedback
control systems are much the same, differing only in detail having to
do with the end result desired.

Figure 1 shows a simple block diagram of a feedback control sys-

tem having unity feedback from output to input.

 

 

 

 

ERRoR
INF”. \ CoNTRoL Our-par
y a
ELEMBNTS
choBAcK
4

 

 

 

Simplified 'Block Diagram of Feedback Control Systan

Pig. 1

III. The Dc Generator

The output device in this system is a m generator. The rating is
3 m, 250 volts, 12 amperes. The specific machine used had the serial
number 2426655. manufactured by the General Electric company. The gen-
erator was driven by a synchronous motor at the constant speed of 1800
m.

This machine was used as a separately excited generator, the field

current being supplied by an amplidyne generator. The generator was

- 3 .-
equipped with interpoles for improvement of camnutation. Field poles
were of laminated steel, but part of the magnetic circuit of the machine.
namely the generator frame, was made of solid rolled steel.

Figure 2 is an elementary diagram of the generator as used in this

system.

Elanentary Diagram of 13.0. Generator

Fig. 2

a test made at steady state on any no generator shows a definite
correspondence between field current, I: and generated, or no load
output voltage Es, neglecting hysteresis effects in the core steel.
Figure 3 shows positive field current resulting in positive generated
volts; the relations for minus values of If and 33 are identical but

in the third quadrant.

a /

Es

 

 

 

Typical Magnetization Curve of D.c. Generator

Pig. 3

.. 4 ..

The curve is observed to be quite linear at the lower values of
voltage and current. The bend at higher values is the result of core
material approaching magnetic saturation.

For pm-poses of control system analysis, a linear relation between
E8 and If is desired. The whine used was tested at steady state and
found to have a saturation characteristic similar to that shown in Fig-
ure 3. The straight (dotted) line was then dram through the rated vol-

tage point to establish an optimm linear relation. This gave the re-

 

lation
Ea
.._..... - 3608
If steady state
no load

or since field resistance was 36% ohms

__.... II 1.554

E: steady state
- no load

 

Since we are minly interested in the transfer characteristic under
load, the machine was loaded to full load and a similar relationship was
found between output voltage under load and field voltage, giving

Eo

 

E: steady state
full load

In order to predict the performance of a feedback control oyster,
under conditions of arbitrary input quantities or disturbances, it is

desirable to know the frequency response of each elanent in the system.

.. 5 ..
We must then establish a relationship for the generator, between a sinu-
soidal field current and the corresponding generated voltage. We have I
seen above that generated voltage may be expressed as 38 - K11, assas-
ing linearity, for the case of steady as Operation. In addition the

field current at steady state may be expressed as

E:
If. n:
Under conditions of sinusoidal input, most writers 1'2'3 assume

that a constant correspondence between I: and flux, and therefcre
betwoen I: and fig exists Just as in the steady state no case. It is
however recognised that the field circuit contains inductance which
must be considered under sinusoidal conditions. The relation for field

current is given as,

_ 3: (Jen)
3: + M:

where L: is a constant field inductance.

It (366)

The assumed relation for generated volts is

Eg ”a” " 311(30)-

1 James, Nichols and Phillips. Theory of Servanechsnians. First Ed. 1947,
p106 , low York: ncGraw-Hi ll .

2 Chestnut and Mayer. Servomechanisms an! Regulating Systae Design
Vol. 1, 1951, p174, New York: John Wiley and Sons.

3 Brown and Catnpbell. Principles of Servanechanians. 1948, p127
New York: John Wiley and Sons.

- 6 .—

There is reason to doubt that the last relation given is correct,
since the generator core is of steel, resulting in hysteresis and eddy
current losses under sinusoidal conditions. Therefore the field current
is not entirely a metising current, but must contain a loss compon-
out.

In order to test this relation experimentally, oscillograns were
taloen of sinusoidal field current and the resulting sinusoidal genera-
ted voltage. The result showed a phase shift betwoen If and Be, vary-
ing with frequency. Specific values were

21.8 degrees at 4.95 cycles per second

29.4 degrees at 9.55 cycles per second

31.6 degrees at 19.4 cycles per second.

The field circuit had a no resistance of 364 ohms. However, tests
made on the field circuit at varying frequencies up to 20 cps indicated
that the effective resistance increased to' approximately 2000 ohns at
the upper frequency. In addition the effective inductance decreased
with frequency. has this result it is evident that the field circuit
cannot be exactly represented as a fixed resistance in series with a
fixed inductance. It was found that Figure 4 is a more accurate equiv-
alent circuit for the field. Here 31 is the no resistance and fig and I.

are fixed values determined from sinusoidal tests.

5:” ”rt“ A

M
v

 

Equivalent Circuit for Field of D.C. Generator

Pig. 4

 

.. 7 ..
In Figure 4, If is total field current. Im is magetising current,

and 12 a loss current, 32 may be considered the resistance of the eddy

current paths in the core steel, referred to the field *circuit, in the

same sense that core losses in a transformer4

are referred to the pri-
mary circuit as an equivalent shunt resistance. However. in the present
case, the representation, to be accurate, must hold for a range of fre-
quencies.

Fran the power standpoint it is seen that for a constant In (JG).
the voltage across 1.. and therefore across 32 must equal Jlmmia - Else.
The dissipation in Hz is equal to

2 2
2 2

Therefore the loss in kg is proportional to frequency squared. It
is known that ecu current loss is proportional to frequency squared,
therefore this equivalent circuit should be reasonably correct fru this
standpoint if losses are predominantly due to eddy currents. mysteresis
losses vary directly with frequnicy and cannot be represented in the same
fashion.

The total field impedance for Figure 4 is

a- 31+ 23.12%.— .. 3132+Jfl-(Bitfiz)
32’1“- 320'st

4 Bryant Ind Johnson. Alternating Current machinery. First Ed. 1935,
p108, New York: licGraw-Hill.

Field current will be

.31.

I
f a

Magnetizing current is

Ila-J3— II: I“ L I E...
Rz+Jflo thdml i
3132

 

1132 4- Jet. (31 + 32)

._____.¥.L
31 + gas. (Bi/£2 + 1)

 

low if 32 >> 31. the denominator is simply R1 + Job. This condition
could be approached by making the core losses wall by proper design.
such as use of very thin core steel laminations.

Generated voltage can be accurately expressed as

lg (ice) - Elm Um).

This relation is independent of thevalues of El and 32°

The last expression for In gives for very low and very high freq-

 

uencies,
E
' m 31 3 31 L—
as cc-yeo . Im-r or C -90°

 

3 co
so Eg-s 0 -90°.
At the two limits given, the Value of lg names the suns values as
above when determined using the relations from the references 1. 2 and 3

previously cited. The same values will not necessarily be obtained by the

two methods for intermediate values of frequency.

- 9 —

Representation of the field circuit as in Figure 4 unfortunately
complicates system calculations, since the effective R and L values are
no longer constant. In addition, it appears that satisfactory results
can be obtained by using the conventional series B and L field repre-
sentation, therefore this method will be used in further calculations.
However, it is the writers’ belief that the relation ngw) - KIfUfl)
should not be assmned without qualification as done in the references
cited.

The value of field inductance L was determined by applying sinu-
soidal voltages at 20 cps to the field circuit, with a series B and c
path connected in parallel with the field. The R and 0 values were ad-
Justed to resonance at this frequency with equal currents in both
branches. Then if R, and L. are equivalent series values for the field,
32 and L could be determined from the following relations derived on

the basis of Figure 4:-

n. - 31.3%.!
32 +a32L

L - 1322
O 322 * @2112

at resonance, cm, - El?"-

°r ‘0 ”W
The values determined on this basis were 32 - 9620 ohms,
L - 37.25 Henries.
If desired, tests may be made at two frequencies, e.g. lo and 20

cps, and then 32 and L may be calculated fran the 3. expression above,

- 10 -
or the 1.. expression alone.
Using the conventional method, the transfer function relating

output voltage and field voltage for the generator may be written as

Kean (Jan)

A
Ls.
S
U
I

If 3
(Jon) 0 . Kcl
3? ’ 1? "‘°’ W

Kc Kc

1*:“11! 1"“0
3:

1.39 - 1.39
1 + ”37025 1 + J!” .1025.
364 '

Here the value of Ko is the value obtained from steady state test

 

Kch (3“,

 

since lim Kch UM) - KO.
(040

The above expression for K060 (5.) neglects the generator amture
time constant. By actual measurement, the value of this tine constant
was found to be .000805 at full load, at which lead the time constant
would be a m. This value was assuned to be negligible and ans
therefore neglected.

W

in uplidyne generator was used to furnish field current to the gen-
erator. Its own control field current was in turn supplied by an elec-
tronic amplifier. The particular anplidyne used was serial number Ill-

2076, rated 250 volts, 1 anpere, mufactured by the General Electric

Oanpam.

.. 11 ..

The amplidyne generator 5'5 may be described as a two stage power
amplifier of the rotating type. The effect of two stages of amplifica-
tion through the use of one rotating armature is obtained by making use
of the phenomenon of armature reaction, a phenomenon detrimmtal to the
operation of the usual IX: mchine.

In a simple no generator, such as the one used in this system, desr‘
cribed above, the armature revolves in a flux field set up by field an-
pere turns. it no load, no current flows in the armature. However,
when a load is connected to the generator brushes, a current flows in
the armature circuit, resulting in a new magnemotive force preportional
to the number of tune, and to the current in the armature. This now
me acts in a direction in quadrature with the Lil-IF due to field ampere
turns. In the simple Dc generator, this results in a distortion of the
flux field, referred to as armature reaction. In this case it is a
harmful effect, which must be at least partially neutralized to obtain
satisfactory generator operation.

In the amplidyne, the brushes set in the position corresponding to
the brushes in the simple generator, are short circuited, .so the cross
m, or armature reaction EMF becomes a large value, much larger in fact
than the m due to field ampere turns. Another set of brushes is placed
on the commutator, in quadrature with the short circuited brushes. Volt-

ages are induced in the armature due to rotation within the flux set up

5 Alexanderson, Edwards and Bowman. "The Amplidyne Generator, a Dynamo-
electric Amplifier for Power Control", GE Review, Vol. 43, p104,
March 1940.
6 Fisher, Also. "The Desim Characteristics of Amplidyne Generators".
AIEE Transactions, Vol. 59, p939, 1940.

.. 12...
by the cross EMF mentioned. Current is supplied to a load connected to
these brushes.

A new new is of course set up by the load current flowing in the
armature. This new 1MP has a direction tending to oppose the original
field m, and therefore must be neutralized. This is done by allowing
the load current to flow through compensating windings, wound on the
same poles as the original field (also called the control field), with
polarities such that the control field In? and compensating field we
are additive.

Figure 5 shows the internal connections of the amplidyne.

CQ‘ Cl F4~ F‘- F!
Comp ARMAN“ ' CoNTROL.
FL o. g 2) I l i has. i

Internal Connections of uplidyne Generator
Fig. 5

Under open circuit, or no load conditions, the uplidyne circuit

may be drawn in equivalent form as a pair of simple D0 generators, in
cascade, as in Figure 5.

I.» I |__—_¢
‘9 %

Equivalent Circuit for Amplidyne Generator

   

Fig. 6

.. 13 ..

The same diagram will apply for load conditions, when a load is
connected at the output terminals, if perfect commnsation exists. If
less than perfect counpensation exists, a rigorous analysis must include
the effect of a negative feedback from load current to input current.
Overcompensation would be equivalent to positive feedback. At no load,
no armature reaction effect can exist in the final stage, therefore no
feedback need be considered whether compensation is perfect or not.

Considering a current I, in the control field at no load, the mg-
netisation curve of the first stage describes the relation between 31
and 11. The design of the magnetic circuit is such that negligible core
saturation takes place through a range of operation corresponding to
rated values. Actual test on the amplidyne verified this statuent.
The steady state relation between 3.1 and 11 is therefore linear and may
be expressed as

E

11 steady state '

The sane statements as to saturation are true for the relation

between E2 and I therefore

q,
E
—..2. 3 K2.
1.; steady state

These constant relations will be assmned to hold for the sinusoidal
case as well, for the same reasons as previously stated (Page 7 ). That
is 3 E

11 IQ
However, as a matter of record, a phase shift was found to exist

between Eq (M) and 11 (Joe). The existence of this shift had also been

- 14 ..
shown by Fisher (reference 6). No shift was found to exist between
132 (Jon) and 1,; (Joe), from tests made by the writer.
The quadrature or short circuit path current Iq, is related to the

quadrature voltage 3,; by the quadrature axis impedance, or

 

Kqu (.103) ' 33- (Jw) - 1 - 1/Bq _
Bq Rq + .1an mg + q

where Tq is the time constant of the short circuit path.

It is desired to write the transfer function between fig (30:) and
11 (50:3) for conditions in which the amplidyne output current flows through
the generator field. It should be noted that this condition exists whethr‘
er the output generator is loaded or not, although generator fie 1d current
must vary to some degree between these conditions. The question as to
whether the amplidyne is canpletely compensated or not must then be con-
sidered. Tests made at steady state showed that the amplidyne was somewhat
undercompensated; in other words, the drop in output voltage as the ampli-
dyne was loaded was greater by an amount corresponding to the degree of
undercompensation, than that predicted on the basis of armature resistance
alone. r

This undercompensation would have the effect of slightly decreasing
the total phase shift through the amplidyne, therefore system analysis neg-
lecting this effect should give conservative results as to phase shift.
For this reason, the internal feedback effect on phase shift was neglected.
However, the effect on magnitude was determined exactly in the steady state

test made to determine the constant Kb.

.. 15 -
The amplidyne transfer function for load conditions can then be

written as

r. n 1 s
Kbeb J 11 (Jan) 1, (Jan) x 32W») 1 Ti' (aw)

lezx‘l _ Eb

 

 

 

The value of the constant Kb may be determined from steady state

test under load since

Ibo. (an) in Kiszq

Kb
steady state .60 1 * 5mg

Test indicated that Kb - 3.3 x 104 volts/imp.

 

The above constant corresponds to a voltage gain of 19 for the em-
plibne, and a power amplification of 1745, considering an amplidyne
field resistance - 1740 aims.

The value of Tq - as“ determined by taking an oscillogram of
32 (Joe) and 11 (Joe) under no load conditions at a frequency of 9.68 cps.
The measured phase shift was -39.8 degrees, resulting in a time constant
sq - .0157 from o - ten-1 (-arq).

The amplidyne control field constants were determined in the ease
manner as outlined on page C! for the no generator field. The values in
this case are, referring to Figure 4,

L - 108 Henries, Rz - 13700 oils.

.. 15 .-

The amplidyne output armature inductance was neglected in writing
the amplidyne transfer function, since this inductance is small compared
with that of the generator field which is connected to the amplidyne
output in the complete system circuit.

e 1 E1 ct i f e

in additional amplifying element ahead of the amplidyne generator
was desired to increase the amplification of the error signal and thereby
obtain a high system accuracy. An electron tube type of amplifier can
perform this function very well, since power and current input to the
amplidyne control field are very low, less than 0.1 watt at 5 milli-
amps. at full excitation. The anplifier must be of the direct coupled
type to respond to no signal voltage, and should have good linearity
at normal signal levels to permit system analysis by linear methods.

In addition, it should have relative freedcsn from drift and erratic
changes in gain. Such a device was not available, therefore the design
of a suitable amplifier was undertaken. Figure 7 shows the circuit of
the amplifier finally developed, which met the above requirements.

Since the ainplidyne control field has a mid-tap, a three terminal
connection was used between amplifier output stage and the field. A
pair of 6L6 tubes was used for this output stage, connected in differen-

tial amplifier? connection. Using this arrangement, the no-signal tube
currents cancel since they flew in opposite directions toward the field
mid-tap. A coumon cathode resistor results in a fixed bias since current

7 Valley and Wallman. Vacuum Tube Amplifiers. Vol. 18, Radiation Lab-
oratory Series, KIT, p New York: McGraw-Hill.

 

 

amndfimii UQ
Sui séeEQ £53U
N. 6.wa

 

 

 

 

 

 

 

 

 

 

 

 

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A“
77'
‘
M

 

 

 

 

 

 

 

 

 

r‘
:5;
l
;. :
I. is
:ld
I
F—'
c:
c:
3:
‘f
_J
i
indwz
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h
[c

 

 

 

 

 

 

 

 

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.. 18 .-
increments due to signal are (+) in one tube and (-) in the other and of
equal magnitude.

1 double triode tube, a 631.7, was used as a voltage amplifier stage
ahead of the pair of 6L6's. A differential amplifier connection was also
used in this case.

It was decided to incorporate negative feedback in the amplifier to
improve linearity and freedom from sero drift. Feedback arrangements in '
direct coupled amplifiers are complicated by the necessity for direct
coupling, and the consequent lack of isolating elements, such as trans-
formers.

To achieve isolation of feedback signal frau amplifier input signal,
an additional stage was added at the input end, consisting of a 637
double triode connected as a cathode followers. The feedback signal was
then fras output outer terminals to the ass? cathode resistors.

The circuit permitted single ended input at the gain potentiometer
33, so the cathode terminal could be grounded to minimise hum and stray
pick-up effects.

Values of tube constants were determined for the particular operat-
ing points in each case by reference to manufacturers characteristic

curves. Values of circuit components were

33 - 20000 ohms. BU . 1500 chns.
Bl - 5000 ohms. 31,3 - 850 ohns.
hpl - 71900 chins. Ra " 200000 ohms.
Bu - 1500 ohus. 3P2 - 570000 cine.
RR - 7500 Chas. 3b - 100000 ohss.

(Hg and m, are the potentiometers for gain and zero balance adjustment,

respectively. )

3 mo.

.. 19 ..

The above values, and a 300 volt plate supply, gave grid bias values
of 4.2 volts, 6.25 volts, and 98 volts respectively for stages 1, 2 and
s. '

In the following analysis to determine the anplifier transfer func-
tion, currents and voltages are incremental values resulting from input
signal. The current 13 is not current change through the entire upli-
dyne field. The voltage e2 is voltage change between 61.6 grids, and 01

the corresponding voltage change at the 6SL7 grids. The voltage a.

is input signal with B3 at maximum gain setting. The current 11 is
current change in 63? plates.
The gain of the 63L? stage is a simple constant
e
i . fi_ . m - 46.2

.1 1+EL2 1+ 50000
3P2 6m

K2-

 

Considering the output stage as a current source, where Z}. is im-

pedance of entire lnplidyne field,
£1. a 1131 so 01 3 21131

92 - K201 - 321131

13 " 2:
2 ZLt-Zl'Ps

_ ganngiIFI’N
Z'l + al’p3

13z1.‘ . WKZHEIMZI
Zr. * arm

of
I

” - i s ,
rpl " 31 2(31: e 200000)

. all? - 1131) - anngllfllrpLSZ£
rpl * 31 (31 + 200000) (Z; t ers)

 

11 1 + L131 + 93333315235 - ”1°-
”pl + 31 201500 x (21, + 2 rpg) 2(rp1 + 31)

 

 

'5 z
[2.82+5700x10 x46.2x1500:200000 1,]_ .'

 

1 i

1 201500 I: (z; + 40000) 1650
2 , z; + 40000
e. (42.02 21. + 11.30001 1650

32 . gambling . 15.8 x 105
11 zL . at,“ 757m

Therefore, the amplifier transfer function relating amplidyne field

current to signal volts is

:11 . 11 x 13 227.3
0. I; E 2L 1- as:

is a function of (:00), this is

227.3
(31 + 2685) + 301.1

 

i
3.0,, (38:) - -—3 ”my
°s

The steady state value as w-to in the above expression results in

a voltage gain of 89.5 which checks DC experimental values.

31 and L1 are constants of the amplidyne field, previously determined

a. 31 - 1740 ohms and L1 - 108 Emiries giving .

227 s .0514
G m) ' ' I
K“ a (J 4425 + Janos 1'": 3a: .0'5'41

 

- 21 -

C sit on L Transfe ction and Stead Sta 8 S
Analysig

Having determined the transfer functions for individual control com-
ponents, we may now write the composite transfer function for the block
labelled ”control elements" in Figure 1. This is sometimes referred to
as an Open loop transfer function, since it is a total clmracteristic 0f
the control elements when the system loop is Open; however, when the
feedback loop is closed, it represents the ratio of output to error.

The composite transfer function KG (3w) is the product of the transfer
function of the separate cascaded canpcnents. Then,

K8 (and) - KaGa (.160) x Kbi (3m) 1 KcGo (in)

_ .0514 x 3.3 x 104' x 1.39
l + 10) .0844 l + Jr .0157 l + 360 .1025

.. 2360
(1 + Jo: .0244) (1 + Joe .0157) (1 + .105 .1025)

Dimensionally this is a numeric, since it is the ratio of output
volts to error volts.

Assuming that the feedback loop can be closed, and that the systan
will then function satisfactorily, the steady state error may be calcu-
lated. At steady state the value of KG (303) is

1im
two->0 KG (1») - K - 2350.

The relation between input, output and error is
Error - Input minus output, due to unity negative feedback,

or E-I-O

but%.K so can.

-22..
thenEcI-KE
E(1+K)-I

and E- I -_.*.._-.000431.
1+K 2360

 

This indicates that error volts under load should equal 0.043% of
input or reference volts which is well within the desired 0.1% error.
However, the assimption that the system will function satisfactorily is
not necessarily valid. Additional analysis based on frequency response
is necessary to show whether or not the system will be stable, due to

the presence of time legs in the control canponeuts.

 

The algebraic manipulations carried out in the last section for
steady state conditions can also be performed with the sinusoidal quan-
tities.9 Thus, if the symbol for output volts is R5 (:00), that for

error volts E (Joe) and that fcr reference cr imput volts 3:; (Joe),

£351 (Jan) - KG (50))
or a. (Jan) - n (.183) m (in)
n (is) - E2 was) - E5 (am)

E2 (is) - B (so) KG (aw)

than n (188) [1 + m (35)] - E2 (.153)

E... m) .___1.__.__.
82 ‘5 l + m (30))
which is the relation between error and input volts.
Similar manipulations lead to E3. (Jab) - co
E2 1 7’ KG (0

which is the relation between output and input volts.

9 Brown and Cainpbell. Op. Cit. p140.

.. 23 -
At any particular frequency, e.g. on, m (.103) itself reduces to a
magnitude and an angle much may be then plotted as a vectorlo, 0?, as

illustrated in Figure 8. The expression for

 

 

 

 

Illustration of Output Vector Locus Plot

 

Fig. 8
&- (3m) becomes
I‘2
‘2 . 1 + '01" '2

run this relation, |or| [sissy be considered to represent :5. the
output vectc, and 1 + Ice] [2 to represent 32. the input vector. But
the vector BF drawn from the (-1 + 10) point to? is exactly 1 e IOPHE
so this is the input vector 32. Also frms the relation
' 32 (Jan) - 3 (Job) + I; (Jen).
it is evident that the vector 30, inch has the constant magnitude of
unity and the constant phase mgle of sore degrees, represents the error

voltage 3.

1° Brown and cupteii. 0p. cit. p152.

-. 24 -

The locus of the tips of the output vectors for the range of freq-
uencies from zero to infinity results in an output vector locus plot,
such as the curve through 035, “is 525. This is sanetimes referred to as
stnyunist diagrss.

The lyquist stability criterion“ states that any feedback system
will be unstable if the output vector locus plot passes through or encir-
cles the (-1 + .10) point on the co-ordinates. This is apparent also frm
the fact that as the locus passes tin-ough this point, input has becase
equal to zero and the output to input ratio has become infinity. Whether
the systan will be stable if the locus passes below the (-1 + 30) point
depends on the character of the roots of the open loop transfer function.
That is, the function KG“) must have no poles in the right hand half of
the (s) plane. The function KG(s) is the transfer function in LaPlace
notation, and may be formed by substituting (s) for (Jan) in the expression
for KG (Jan).

The concept of phase mrgin is of importance in discussing stabil-
ity. Referring to Figure 8. the phase margin is defined as the angle
equal to 180 degrees minus 0, at the frequency where the vector 0? has
unity magnitude. Therefore in accordance with the quuist criterion, the
phase margin must‘be positive for the systms to be stable.

To bring out explicitly the relations between frequency and both am-
plitude and phase, it is desirable to plot attenuation and phase diagrans
for the system under discussion. The attenuation diagram is a plot of

amplitude in decibels versus radian frequency; the phase diagram a plot

11 Brown and Campbell. Op. cit. p170.

- 25 -
of phase angle versus radian frequency, using a semi-logarithmic freq-
uency scale. The amplitude in decibels is calculated from the relation
Amplitude in decibels - 20 x loglo of (anplitude
expressed as a numeric) ,
To plot these curves for the composite transfer function KG (Jed),

we first separate terms and set

 

K II 2360
1 + 50: .0244 1 L, J EL
41
Ga (.160) " 1 1

 

 

 

l+Jco.0157 ' 1+J'w

1 1

(JG) - I

63 1 ‘F :05 .1025 1 + J m
. 9.75

 

 

 

Amplitude expressed in decibels may be added arithmetically to
11nd total amplitude.
The value of K in decibels is

K (Rb) - 20 loglo 2:360 - 57.5 up.

. l
Themagnitude orclis lull -

W

For frequencies such that 21-. << l, '6” 41 and for frequencies
4

 

41
Such that 3:17)) 1. ' qu 93-, so these limits may be considered asymp-

totes to the uplitude curve. These asymptotes cross at l - $1;

or .01 . 41 radians/sec.

.. g5 ..
At frequencies less than 01 - 41, the asymptote is unity or zero
I). At frequencies greater than 031, the asymptote is a straight line
with a negative slope of 20 Db per decade.
Similarly far Gg, the "break" frequency is
£02 - 63.7
and for GB. 045 - 9.75.

The attenuation rate is also 20 Db per decade for 62 and (:3.
The PM“ 811810 for 31 is, by rationalising the expression for 61 (.103)
O1 - -tan"1 (51-).

As n+0, 019 zero degrees,

as ans-no, 014(40) degrees, and

at the break frequency, (ET) - 1, so 91 - -tan‘f1 l - (-45) degrees.

zero and (-90") are asymptotes to the phase angle curve, but other
points in addition to 45° must be calculated to establish the shape of
this curve. For all curves of this type however, tan 0 - 2 at two times
the break frequency, so 9 I ~63.45°; also tan 9 - 1/2 at one-half the
break frequency, so 9 - ~26.55°. In addition, these angles are com-
Elementary.

Attenuation and phase curves are drawn for G1, Ga and 63 in Figure 9.
By adding amplitudes at specific frequencies, and adding the value for
the K term, and adding angles at specific frequencies, the composite
curves of Figure 10 are obtained. These curves represent the amplitude
‘1. mid phase or for KG (in).

To apply the Nyquist criterion, we read the phase angle frm Figure

10 at the frequency where A! - zero Db. This angle is -251 degrees.

 

 

v. e-*uvi

...+1.1
7
.Ir...

#7. v0 tidy!

...v¢t41. . s

ee-stvtv.a e e

T.-.
. s. 3.. .e ...
.140evo1s. 2.9..

i...

,4.

1.. -.e...a.

V..........e...
— i
l .

a ,.. ....

 

 

 

.. 29 ..
me phase margin is then 180 .-’ 251 - 471°, the negative phase margin
indicating that this systan will be unstable, that is sustained oscilla-
tions will exist. This statemait was verified by test.
W A

The simplest method for obtaining stable operation of this system
is to reduce the value of K by about 50 Db by reducing amplifier gain.
Reference to Figure 9 shows that this would have the effect of lowering
the A, curve such that the phase angle would be about 160° when the A.”
curve crosses the zero Di line. However, this method would have the
effect of greatly reducing system accuracy, therefore other means are
called for.

Another method would be to add a phase lead networklz in the error
path ahead of the amplifier. This would tend to decrease the phase
angle, however, it would also tend to accentuate the unwanted high freq-
uencynoise inherent in this system due to the D0 generator cmutator
ripple.

The best method for stabilization in this case involves the use of
frequency sensitive elements to feedback a signal from amplidyne output
to amplifier input”, to modify the attenuation and phase characteris-
tics of this part of the system leap. The feedback element used was a

double R-O network as shown in Figure 11.

12 chestnut and Mayer. 0p. cit. p265.

13 Chestnut and Mayer. op. cit. p273 and 230.

-30-

 

 

¢___lz J!
K j?
NETNORK C2, CI
INF/‘1’ Rs. 2 NETNQRK
' OuT‘PuT’
c5 <9

Diagram of Double n-c feedback letwcrk.
Fig. ll

The actual connection to amplifier input was between the second
63? grid and ground, at the point marked 1. in Figure 7, with polarities
to give negative feedback.

The optimum Band 0 values were determined by a ombination of anal-
ytical and experimental methods to yield the end result of a control trans-
fer funotion allowing stable system operatim, and at the same time giv— I
ing the simplest possible form for the transfer function to simplify
system analysis.

It was found desirable, in addition, to add a phase lag network
ahead of the amplifier to attenuate and minimize the masking effect of the
cannutator ripple fed back fran the generator output. This network had

the form shown in Figure 12.

 

0——~www + 4-
R: _ l
N: TwoRK c3 Narwomc
fairer our pu'r'
i? 4.

 

Diagram of Phase Lag network.
313. 12

The block diagam for the stabilised systu then took the form shown

 

 

 

 

 

 

 

 

 

 

 

 

in Figure 13a
Amfkioyfla
. j Corfu?
DC. 5. E,
AMFL‘nFiez P—->
-
V
A E5 DeuGLE 1
R-C.
NETNoRK J

 

 

 

Block Diagram for Stabilized System.
Fig. 13
The minor loop including amplifier, amplidyne md double 1-0 network
must be reduced to an equivalent series transfer function for-purposes of
oyster: analysis. The constants for Figure 11 were
31 - 6000-0— (“13 at 433-34 *
cl - 15.8 nfd.

32 I 500—“—
02 I 15nd.

- 32 -
Letting T1 . 3101, T2 - 3262, T21 - R201, the transfer func-
tion of this network is, in LaPlace notation,
2

EB 42 Tszs
E1 (I ) W I 2
rlrgs + (T1 + T2 * T21)s + l

.07 s2
e2 . 155.41. + 1420

 

The transfer function of amplifier and amplidyne canbined, with
minor leap open, is K116“ (s) - K‘KBGMINBH)

1695
(l + .0244s) (1 + .0157s).

Relations with minor 100p closed are,

EB“) " F331”,
31(3) " [30(3) TENN] KnGlflfl)

. [30m - a, slug Knclfla)

31(8) [1 + F3K11°ll(')] " John) 311511“,
therefore the relation between 31(s) and 30h) with minor leap closed is

 

1‘1 KllGlfl”
‘5‘" 1 + rhKnGm-i
443 x 104
. We?)

 

 

e07 I 4:43 1 104 32

1+
(.2 + 155.4s + 1420)(s + 41)(s + 53.7)

443 x 104(e2 + 155.4s + 1420)
s4 + 250.1s3 + 33.05 x 10413 + 55.53 x 104s + 3.72 x lo6

- 33 -

It is necessary to factor numerator and denominator to facilitate
an attentuatien and phase response study. The method credited to
Porter“ was found the most useful for factoring the quartic equation
in the denominator.

The factored form is

31.”) . 44.3 x 104(s + 9.75Hs + 145.?)
n .
° (:2 + 1.67s + 11.5)(s2 + 258.4s + 33 x 104),

The transfer function for the phase lag network of Figure 12 is,

for high load impedance,
1
:P.(s) 1- ._J!§L__. . 1
< 1 l + sages
+
RS EJ-

 

1 , 410
1 + .00245! I "' 416

withB3 - 1220 ohms, c3 - 2mfd.

The new composite transfer function for the control elements is,

. E' B ' e,
m(s) iii-1(a) xi:- (s) 3H (s).

The last ratio is the transfer function of the generator in lie-Place

notation, er

 

, 1.39 _ 13.53
K3°3(" l + .1025s 77-9275“ ”1"“

mm . 246.5 x lo8 (a + 9.75)(s + 145.7)
(s + 410)(s2 + 1.57s + 11.3)(s' + 253.4. + 33 x 104“. * 9.75)

14 chestnut and Mayer. Op. cit. p131.

..34 -
Fran this we obtain the new control transfer function KG (.151) (noting

that the (s + 9.75) toms will cancel) as follows,

1 a:
KG(.1a>)- 2360:” +£1.57)

5:2 cc
(“’36”1’fi'.'+3m "1" 3:5le JTm)

Writing the factors separately,

 

KIZ‘SGO

G1-1+

 

m2 +3“

1 - —— -—
11.3 6.78

1

l-Lt-JL
332104 1275

G4-

 

The factors 63 and G4 result free the corresponding toms in the ex-
pression for mus), each term having two conjugate couple: roots.]'5

Factor 63 will have straight line attenuation asymptotes, one along
the zero Db line, the other at a slope of (-40) Db per decade, with the
break frequency 555 - JET; - 3.35. The enact shape of the attenuation
curve near the break frequency, and the shape of the corresponding phase
curve can be found most readily by reference to published curves such as

in reference 15. However, the dwping factor must be lmown. For factor

63 this will be,

15 Chestnut and layer. Op. cit. p310.

-35-

3.36
2 x 6.78

(13 I .248.

For factor G4, break frequency Mg, and damping factor d4, are deter-

mined in the same manner. They are dig - 575 radians/sec.
d4 - .226

The attenuation rate for factor G]_ is (+20) Db per decade, and
break frequency is 552 - 145.7 radians/sec.

The attenuation rate for factor Gg is (-20) D) per decade, and
break frequency is use - 410 radians/sec.

The phase angle curve for factor 62 is constructed as described in
section 711. The phase angle curve for factor 61 is similar, except the
angles are positive.

is before, the K term represents on the decibel scale

K(Db) :- +67.5 Db.

Figure 15 shows the attenuation curves corresponding to each tens
of G (1m). Dotted lines are the asymptotes, and solid lines the exact
curves. The phase angle curves for each term are shown in Figure 16.
Symbols A1 and 61 represent attenuation and phase curves fn' factor G1,
and so on. Finally, the composite attenuation er mnplitude N}, and
phase Or are shown in Figure 17, for KG (Jce).

The canposite attenuation curve indicates that when amplitude is
zero Db, frequency is 250 radians/ sec. Reference to the phase curve
shows that at this frequency, the phase angle is (-164) degrees so

Phase margin - 180 - 164 - +16 degees.
The positive phase margin indicates that the system is stable. Test

of the system also showed stable Operation, extending throng:- all values

-35..

I“

 

 

 

 

 

 

 

 

        

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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...... . {not iota .. to... s. ,m
seesaw. neckinwmrkmm ....__

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as s
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-39-

of load fran zero to approximately 20% overload, and for all values of
input voltage fron zero to 250 volts. Sudden changes in lead or input
voltage caused only manentary oscillations which were quickly damped out.

It is of interest to note that, according to a theorem of bode,16
restricted to minimum phase systems, the attenuation and phase shift
curves are definitely related to each other. Without attempting to state
or canpletely explain the theorem, we practical result is that the slope
of the attenuation curve at zero Db is usually a good indication of the
phase shift at this point. A slope of 40 Db per decade is usually found
to be an upper limit for this slope if phase margin is to be positive.
In this case, the original system having emessive phase shift, had a
slope, or attenuation rate of (-64) Db per decade, whereas the stabilised
system had a slope of approximately (-23) Db per decade.

Steady state tests for error volts in the final, stabilized systas
showed an error voltage of 0.09 volts at no load, and 0.19 volts at full

load (12 nperes) when input volts was set at 250 volts. Therefore,

10.9.

No lead error - - .00036 or .036%.

.10

Full load regulation - - .0004 or .04%.

Full load error - ig' - .00075 or .075%.

These values are well within the limit of 0.1% error established at

”1. beginning of this paper.

.-.......OOOOOOOOOOOOOOO000..........

15 '
81198133111: and liayer. 0p. cit. p297.

 

The usual function of a voltage regulator is to maintain the output
voltage of a system at a fixed value, or at an accurate correspondence
with a fixed reference or input voltage. Disturbances in such a systun
result generally free the sudden addition of load on the output device.
Therefore the transient response of the system following a disturbance
at the output is of major interest. For purposes of analysis, we may
redraw the system block diagram as shown in Figure 18, in which devia-

tions from steady state values are emphasised."

 

A E E
. qu ) A13 a,

 

 

 

 

 

 

Simplified Block Diagram for Syst'us Subject to Output Disturbance
Fig. 18
ED is a step function voltage disturbance introduced at the output
terminals. It will be considered negative in value, due to a voltage
drop, and therefore has the value ")ED) 0(t) or in Mlace notation

-I?.L, where )Eplis magiitude of disturbance.

A E, A 1'3, andA 3.! are incremental values of control input (error
volts), control output and terminal voltage respectively, resulting from

the step disturbance. it is seemed that ED has a mall enough value

17 Gardner and Barnes. Transients in Linear Systons. Vol. 1, 1942,
p192, New York: Jolm Wiley and Sons.

.. 41 -
so that the control canponents will not saturate, therefore we may assmne
linearity and the control transfer function previously deve10ped should
‘PPly.

No input or reference voltage is shown in Figure 18, since the in-
crunental values referred to are independent of the value of the refer-
ence voltage. This results from the fact that the principle of super-
position applies in a linear system.

The relations existing are

A Ms) - - Anhdue to unity negative feedback.

A 25m - Ash) mm

- -AEg(s) KG(s)
but A If“) -A33(s) +Bp(s)
- mm.) mm +an

Alarm [1 + mm] - snm

therefore

A 39(3) ’ ...—£123.!)— . -IEDI
l + KG“) s [1 + m(s)l .

The control transfer function for the unloaded system may be written

 

mm .. 9131 . 292.5 2 10° (s + 145.7)
3(a) (s + non-5i 1.67s + 11.3)(52 + 258.4s + 33 x 104)
then A 353(3) - -LEDI 'IEDI

 

8[1;KG(8)] . s[1+ Be]

- lEnl BM
s [3(a) + KMflT

- 42 -

therefore. AE‘Ms) '-

-IED|(s + 4lo)(s2 + 1.67s + 11.3)(s2 + 258.4s + 33 x 104)
s(s6 1- 670.11!4 + 43.71 x 104s3 + 135.9 x 105sz + 294.8 x 103s + 42611010)

 

The inverse LaPlace of this expression will yield the time expres-
sion for change in terminal voltage. As a preliminary to finding the
inverse LaPlace, the denominator must be factored. In this case, the
most straightforward method to accanplish this is to find first one
real root, which we know exists in a polynomial of odd degree, and then
find the remaining roots by the method of Porter previously mentioned.

Had two of the terms in the expression for KG(s) not cancelled,
the denominator in AEvfls) would have been a sixth degree polynomial,
and much more difficult to factor. The (s + 9.75) term in the transfer
function of the double n-c network was the result of choosing a and O
values to yield such a term, in order to cancel the (s + 9.75)term in
the generator transfer function and at the same time properly stabil-
ize the system.

The factored expression is

‘1‘!)
31(3)

 

A. 3m)" " 4313)

.. “H' + 410)(s2 + 1.67s 4- 11.3)(s2 + 258.“ + 33 x 104)
s(s + 259) [(s + 68)2 + 267.62] [(e + lama + 4443'

The denaninator may be also written,

 

31(8) '-
s(s + 259)(s + 68 + 3267.5)“ + 68 -1267.5)(s + 137 +1444)“ + 137-1444).

-43..

The inverse LaPlace of A Et(s) will be of the form

1 '1 ABMs) '- ’IEDI [01 + 028‘" + cos-fitainplt + 842‘“2tsinsgt]
Where 3' s 259
0‘1 - 68, 81 - 267.5
“2' 137. 32"”- 444-
The constants and phase angles must now be evaluated by partial
fraction methods.

‘1‘!)
31(8) I '3 0

O
H
I

410 x 11.3 x 33 x 104
259 x 7.51 x 184 x 21.5 x 184

02 - [(s + 259) A1“)

- 3.59 x 10"4

 

31(8) s = -259

, 151 x 5.55 x 33 a: 10°
1.08 x 2.119 x 259 x 1810

-056

03 - 23 (s + 68 - 3267.5fl]
51(8) 8 - -68 + 3257.5

(-2.28 -;7.84) x 1012 _ +3(7.54 -.12.28) x 102

 

 

 

(7528.5 + :31) x 1810 (328.3 - .131)
.160250
. 315 . 2,475 [79.150
350 Iii".

Afls)
31") s - -l$7+1444

 

c4 . 2.1 [(s + 157 4444)

(-14. - j1:12:15) x 1810 _ -5(1315 - .114) x 1810
(11.25 + 15.14) x 1012 (11.25 + 55.14) x 1012

 

-44-

. 1317 -90°
1280 23-5°

 

.. 1.08 L—lls.5°.

 

The time function of terminal voltage change then is

A not) ideas)
- - IEDI £5.59 x 10-4 - .552’259‘
+ 2.475e-68t sin (257.5t + 79.150)
+ 1.03843," sin (44% - 118.6°)] .

The value of this expression at time equal zero is nearly (-lxp) ),
which is correct from physical reasoning since the control system can-
not respond instantaneously to any disturbance. After time 0.01 sec.,
the third term, having the constant 2.475, accounts for nearly all of
the runaining transient.

Figure 19 is a plot of the transient time function Ana”),
plotted in per unit values with magnitude )ED) as a base. The curve
shows an initial overshoot of approximately unity, and an oscillation
of about 2-1/2 cycles which disappears in approximately 0.07 sec. If

[an] is unused equal to one volt, the ordinates may be read directly
in volts.

As a check on the actual transient perfolmance of the system, an
oscillogram was taken of terminal voltage resulting from the sudden
application of load. In order to obtain a trace frm which magnitudes
could be read, it was necessary to apply a large disturbance. This
was done by suddenly connecting a load resistance of 21.8 ohms to the
initially unloaded system. After the transient had died out, the meas-
‘ ured load current was 11.5 amperes, or nearly full load on the output 1

generator. On the basis that the generator armature impedance is

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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5 45 ..

entirely resistive, the magnitude of disturbance ED may be calculated
as IEDI - 11.5 x 1.356 - 15,6 volts,
where amature resistance - 1,356 olms, ~

The oscillcgram, shown on page+7, gives the following results:-

1, The terminal voltage drape to a very low value (theoretically
zero) at the instant of cementing the load resistance, due to the
presence of inductance in the armature circuit. At this instant, the
current and voltage relations may be expressed by the equation

E8 - in‘I-iRL1Ldi/dt

there B.‘ is armature resistance, R; the load resistance, and I. the
armature inductance. The current initially increases very rapidly, as
shown by the shape of the current trace, making the tom 1. di/dt
account for nearly all of the generated voltage at this instant.
Therefore, the term 15R;l - terminal voltage, is negligible. The cur-
rent trace shows an exponential current rise, rather than the step
function assmned in the calculations, where armature inductance was
neglected,

This effect due to armature inductance has no important effect
on the response of a practical control system, and therefore may be
properly considered a separate phenomena, In the case of the control
system under discussion, the magnetic circuits of the anplidyne and
output generator become saturated when error reaches a value of approx-
imately 0.5 volts. Error values larger than this can therefore produce
no additional controller output, therefore the initial terminal voltage
drOp can be neglected for output disturbances of 0.4 volts or larger.

It may be noted that the transient due to armature inductance

-47-

 

 

.. 4,8 —
disappears in less than 0.01 second, in.the present case.

2. The initial rate of recovery, after the inductance effect is-
past, is less than the calculated rate. This is again due to saturar
tion in the control elements. The result is that the factor K in.the
control transfer function KG (Jafl is no longer fired in.value but ac-
tually varies from a very low value up to the calculated value of 2369,
as error voltage varies from a very high.va1ue, to values less than
0.4? volt.

3. The duration of the transient is approximately 0.15 seconds.
This represents very satisfactory performance, although the value is
larger than the duration of 0.07 sec. determined from the calculated
transient response.

4. The oscillogram.brings into view the ripple content of output
generator terminal voltage, which is a characteristic of the generator
itself. This ripple is made up principally of a 120 cycle wave result-
ing fran the four pole construction of the machine, and the rotational
speed of 1800 m, plus a higher frequency cansutator ripple.

The control system can do nothing to minimize this ripple content
since the control elements in cascade act as a low pass filter. Refer-
ring to Figure 17, it may'be seen that radian frequencies in.excess of
230 radians per sec. are attenuated. This corresponds to a frequency
of 36.6 cycles per sec., which is considerably lower than the 120 cycles
per sec. mentioned. It will be recalled that the phase lag network of
Figure 12, pag93! , was included in the system for the purpose of
blocking this ripple fresh the amplifier input. Even if this had not

been done, the other control elements would have acted as an effective

.. 49 ..
low pass filter.

It might appear that the generator output voltage is not very
effectively regulated as long as this ripple is present. However,
for most applications, the ripple has no practical importance as
long as the no component of output voltage is held constant. The DC
component isbhere referred to in the sense that the actual output
voltage can be analyzed by methods of Fourier series into the sum of
a no, or constant, term plus a series of sine and cosine terms. The
controller responds principally to the no component due to the low
cut-off property mentioned previously.

In these special cases where the ripple would be objectionable,
a specially designed, low ripple generator might be used, or else
filtering of the output current might be resorted to. If an output
filter is used, the feedback signal should preferably be taken from
the output of the filter, that is directly across the load as before.
In such a case, the transfer function of the filter must be deter-
mined and included in the overall control transfer function mu).
W

The steps in the developnent of a feedback control system have
been described and an analysis of the oyster has been presented. The
test results show that the system performs satisfactorily under both
steady state and transient conditions.

Certain assmnptions are necessary in the analysis of a system of
this type, in order to apply linear analytical methods. For ample,
straight line magnetization curves are assmned for the rotating

elements, although the actual curves are known to be non-linear.

 

View of Direct Coupled Electronic Amplifier and Power Supply

 

View of Amplidyne Generator with Driving Motor

‘11I,I|l [I‘ll IIIIII‘II‘ 1.
‘

- 51 -
Simplifications and approximations are necessary but must be carefully
‘ applied to minimize resultant errors.

many of the present difficulties in working with feedback control
systans have to do with measurements of magnitudes, phase angles and
frequencies in the low frequency range between 1 and 80 cycles per sec.,
particularly where low energy levels are involved. These quantities
can be measured by use of the mystic cscillograph but this method
is time consuming due to the need for setting up and adjusting the os-
cillograph, and developing the cscillograph negatives. The cathode
ray cscillograph may be used for magnitude measurements, to limited
accuracy, but does not permit direct frequency and phase measurements.
This device is, however, quite useful as a null indicator in connection
with bridge circuits and phase shifting networks. The development of
suitable indicating instruments for direct measurement of magnitude,
frequency and phase at low frequencies would greatly facilitate work
on feedback control systems.

The generation of voltages at low, and at the same time adjust-
able, frequencies is a necessary preliminary to measurements at these
frequencies. The work of the writer was greatly simplified in this
respect due to the availability of an B-G oscillator capable of sup-
plying low frequency voltages.” The development of this oscillator
was carried out as a research project at nichigan State College.

The principles of the control system described in this paper may

be readily extended to the voltage control of A0 generators, and to

O O O O O I O '0 O O O O O O O C O O O O O O O O O O O O O O O O O O O O O

1" anonett, Roy John. Wm. Unpublished ms. thesis.
Michigan State College, 1950, 42 numb. leaves, 17 figures.

[I I‘l I

 

- 52 ..
the control of current at the output rather than voltage, for either

10 or ID systems. In addition, the same principles may be applied to
servanechanisms, with modifications having to do with the necessity
for controlling the position or speed of a mechanical load, rather

than a voltage or current.

-53-

BIBLIOGRAPHY
Listed in order of reference.

James, Nichols and Phillips. Theory of Servomechanisms. First Ed. 1947.
New York: MoGraw-Eill.

Chestnut and Mayer. Servomechanisms and Regulating System Design. Vol. 1,
1951. New York: John Wiley and Sons.

Brown and Campbell. Principles of Servomechanisms. 1948. New York:
John Wiley and Sons.

Bryant and Johnson. Alternating Current Machinery. First Ed. 1935.
New York: ncGraw-Hill.

Alexanderson, Edwards and Bowman. The Amplidyne Generator, a Dynamo-
electric Amplifier for Power Control. G. E. Review, Vol. 43, p104,
March 1940.

Fisher, Alec. The Design Characteristics of Amplidyne Generators.
AIEE Transactions, Vol. 59, p939, 1940.

Valley and Wallman. Vacuum Tube Amplifiers. Vol. 18, Radiation laboratory
Series, MIT, New York: John Wiley and Sons.

Smollett, Roy John. An R-C Oscillator. Unpublished M.S. Thesis, Michigan
State College, 1950. 42 numbered leaves, 17 figures.

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