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United States Patent im 



[75] Inventor: Stanley Paul Clurman, Cherry Hill, 

[73] Assignee: RCA Corporation, New York, N.Y. 

[22] Filed: Apr. 20, 1972 

[21] Appl. No.: 245,909 

Related U.S. Application Data 

[63] Continuation-in-part of Ser. No. 133,572, April 13, 
1971, abandoned. 

[52] U.S. CI 318/184 

[51 ] Int. CI. 2 H02P 5/28 

[58] Field of Search 318/174, 175, 176, 178, 


[in 3,988,653 
[45] Oct. 26, 1976 

[56] References Cited 


2,415,405 2/1947 Barney "318/184 

3,238,432 3/1966 Amberger 318/184 X 

3,500,157 3/1970 Goto 318/184 X 

3,593,078 7/1971 Domshy et al 318/180 

Primary Examiner — Donovan F. Duggan 
Attorney, Agent, or Firm— Raymond E. Smiley;. 
Edward J. Norton 



Passive or active networks responsive to changes in 
motor drive current alter the motor drive voltage or 
phase to damp hunting of the motor. 

2 Claims, 25 Drawing Figures 

U.S. Patent Oct. 26, 1976 Sheet 1 of 8 3,988,653 

70 ^! ST ™ Fig. 3. 






/t^-o J WINDING 


L| j 5^ 


7 1 



Fig. 2a. 


Stanley P. Clurman 


U.S. Patent Oct 26, 1976 sheet 2 of 8 3,988,653 


• nrirLrLrLri 
d LTLnrLTLru 






Vo Vo 





* o-^mmmm 

h 'VtrHf. 


Stan ley P. Clu rm an 

oy A 


U.S. Patent Oct. 26, 1976 sheet 3 of 8 3,988,653 


Fig. 4b \ 



Ai=Ai max siTi27rfTit 






* at 

% dt 


V M Fig.4f. 

Fig. 4e, 







Stanley P. Clurmar, 


U.S. Patent oct.26, 1975 sheet 4 of 8 3,988,653 







0. ' ketone) . 

- ^ . — — ^ 






ideal negative 






V 1 

Fig. 5. 















Fig. 6. 



Stanley P. Clurman 


U.S. Patent Oct. 26, 1976 sheet 5 of 8 3,988,653 


106 — ^ 




Fig. 7. 



Stanley P. Clurman 


U.S. Patent Oct. 26, 1976 sheet 6 of 8 3,988,653 








* [ 


Stanley P. Clurman 



U.S. Patent Oct. 26, 1976 sheet 7 of 8 3,988,653 

V DC ■- V 

dl-_|dJ +| W 
dt" K Qdt K vdt 

Fig. 10 

Fig. 12 

U.S. Patent oct.26, 1975 sheet 8 of 8 3,988,653 


= ko+Ak 

V = Vo 
k T =k 

= Vo-V, 
T = k (f Ak 


Fig. 11 





The invention desribed herein was made in the per- 
formance of work under a NASA contract and is sub- 
ject to the provisions of Section 305 of the National 
Aeronautics and Space Act of 1958, Public Law 
85-568 (72 Stat. 435; 42 U.S.C. 2457). 10 

This is a continuation-in-part of my copending appli- 
cation Ser. No. 133,572, filed Apr. 13, 1971, now 



"Hunting," or small random excursions of the rotor 
in a synchronous motor, is a long known phenomenon. 
While driving a constant torque load, the rotor motion 
may have superimposed on its steady synchronous 
speed a meandering of its rotor phase angle about that 20 
of the constant rotating field vector. This excursion is 
usually oscillatory with a characteristic period, but may 
have ah amplitude and phase which vary randomly. 
Small synchronous motors which are used in timing and 
recording devices often display this behavior. The con- 25 
sequent time displacement error may be objectionable 
or even intolerable in certain precision applications, 
notably in tape drive motors for video tape recorders. 

In the prior art, changes in motor speed have been 
detected by a tachometer attached to the motor shaft. 30 
The output of the tachometer is then fed back through 
suitable electronic devices to alter the motor driving 
signals in a sense to reduce the hunting. Another ap- 
proach is to feed a voltage proportional to the motor 
oscillations to an eddy current torque brake which acts 35 
to apply a varying amount of torque to the motor to 
reduce the hunting. Each of these prior art systems 
suffers from a response lag since a mechanical action 
must take place either to determine the presence of the 
hunting or to reduce it. This slows down the rate of 40 
recovery which may, in critical operations, be unac- 
ceptable. Further, in this approach the additional 
equipment required to sense very small velocity 
changes and to develope the damping torque is in itself 
complex and expensive. 45 


FIG- 1 is a block and schematic showing of a tape 
drive system employing a synchronous motor; 

FIG. 2a is a schematic drawing of a motor drive cir- 50 
cuit suitable for the motor of FIG. 1; 

FIGS. 2b through 2/ show waveforms present at vari- 
ous points in the circuit of FIG. 2a; 

FIG- 3 is a vector diagram showing the relationship 
between the stator field and rotor magnetic axis in the 55 
motor of FIG. 1; 

FIG. 4 is a drawing of the waveforms present in the 
circuit of FIG. 1; 

FIG: 5« is a schematic drawing of one type of imped- 
ance network suitable for use in damping the hunting of 60 
the rotor of FIG. 1; 

FIGS. Sb and 5c are curves of impedance versus 
frequency which are useful in explaining the operation 
of trie circuit of FIG. 5a; 

FJGS. 6a and 6b are schematic drawings of other 65 
impedance circuits useful in the circuit of FIG. 1; 

FIGS. 6c and d are curves of impedance versus fre- 
quency of the circuits of FIGS. 6a and 6b; 

FIG. 7 is a schematic showing of a motor control 
circuit which employs another impedance circuit; 

FIG. 8 is a block diagram of an alternate version of 
the circuit of FIG. 1; 

FIG. 9 is a block and schematic drawing of a modi- 
fied portion of the circuit of FIG. 8; 

FIG. 10 is a block and schematic drawing of a further 
embodiment of a motor control circuit; 

FIG. 11 is a graph showing the relation of motor 
torque as a function of rotor phase angle and applied 
voltage; and 

FIG. 12 is a block and schematic drawing of a further 
alternate version of the arrangements of FIGS. 8 and 9. 


A synchronous motor comprising a stator portion 
and a rotor portion is characterized in that the rotor 
may oscillate about an average angular position relative 
to the field of the stator as the rotor rotates. Passive or 
active networks responsive to changes in a parameter 
of motor drive current alter the motor drive voltage or 
phase to damp hunting of the rotor. 


In FIG. 1 there is shown, somewhat schematically, a 
synchronous motor 10 which may be of the hysteresis 
type. The motor is shown as having two stator windings 
12 and 14, but the number of windings is not critical. 
Rotor 16 is connected to a shaft 18 which in turn is 
connected to a capstan 20. The shaft is supported for 
rotation by a ball bearing assembly 22. 

Such a motor may be adapted to drive a load such as 
a magnetic tape 30 from a pay-out reel 32 over capstan 
20 to a driven take-up reel 34. A suitable read/write 
transducer 36 may be suitably positioned to read from 
or write audio and/or visual signals onto the tape. 

The stator windings receive power from a motor 
drive circuit 40 to be described shortly. The motor 
drive circuit 40 is connected to a source of potential, 
V , and through an impedance 42 to a source of refer- 
ence potential such as ground. V , in a preferred em- 
bodiment, is a direct voltage which supplies a current 
i DC to the motor drive circuit 40 and impedance 42. The 
interaction of igc and impedance 42 is very significant 
as will be discussed later in the description. A capacitor 
Cfl connected across the impedance may be used to 
bypass ripple to the direct current as will be explained 

FIG. 2a shows the details of the motor drive circuit 
40. It includes a first section 40A for driving phase A 
and a second similar circuit 40B for driving phase B. As 
the two circuits are similar, only the details of 40A are 
shown. Circuit 40A comprises first and second PNP 
power transistors 50 and 51, the emitters of which are 
connected to potential source V . The collectors are 
connected respectively to the phase A winding and to 
the collectors of third and fourth NPN power transis- 
tors 52 and 53. The emitters of transistors 52 and 53 
are connected to impedance 42. The bases of first and 
fourth transistors 50, 53 are connected together and to 
one stationary contact 62 of a relay 60 which, while 
shown to have mechanical contacts, is preferably a 
solid state switch. The bases of second and third tran- 
sistors 51 and 52 are connected together and to an- 
other stationary contact 64 of relay 60. The relay 60 
may have its movable contact 66 alternately connected 
between the stationary contacts 62 and 64. The transis- 
tors connected to the stationary contact engaged by the 





movable contact are placed in their conducting state 
and the other two transistors are off. The relay may be 
driven at the rate of 400Hz by an oscillator circuit 
which is common to both sections 40A and 40B. The 
oscillator circuit may comprise an oscillator 54 which 
may, for example, be a crystal oscillator with a fre- 
quency of 1600Hz as shown in FIG. 2b. This is coupled 
to a first toggle flop 55 which toggles (changes state) in 
response to positive-going signals from the oscillator. 
Thus the output of toggle flop 55 is an 800Hz signal as 
illustrated in waveform c of FIG. 2. Toggle flop 55 is 
coupled directly to a second toggle flop 56 and via 
inverter 57 to a third toggle flop 58. These toggle flops 
also change their state in response to positive-going 
signals. The waveforms at the outputs of inverter 57 
and of toggle flops 56 and 58 are shown respectively in 
waveforms d, e and / of FIG. 2. The output of toggle 
flops 56 and 58 are 400Hz signals, the output of ele- 
ment 58 lagging the output of 56 by 90°. Toggle flop 56 
is coupled to relay 60 in drive circuit 40A. Toggle flop 
58 is coupled to a similar relay in drive circuit 40B 
which is identical to section 40A. The emitters of tran- 
sistors 52 and 53 in circuit 40B (Phase B) are con- 
nected to impedance 42 in the same way as circuit 40A. 

In the discussion of the operation of the circuit 40 2 $ 
which follows, the waveforms g through j of FIG. 2 
should be referred to. Assuming that relay terminals 62 
and 66 are connected, transistors 50 and 53 will be 
rendered conductive. Therefore, current will pass from 
source V through transistor 50, through stator winding 30 
A in one direction, through transistor 53 and then 
through impedance 42 to ground. After one-half a 
cycle, the output of the toggle flop 56 causes contact to 
be made between terminals 64 and 66 rendering tran^ 
sistors 51 and 52 conductive and transistors 53 and 50 
nonconductive. Then current passes from source V 
through transistor 51 through the stator winding A in 
the opposite direction through transistor 52 through 
impedance 42 to ground. Circuit 40B applies current in 
similar fashion to stator winding B except that the 40 
phase of the current supplied to the phase B winding 
lags the current supplied to the A winding by 90°. 

Waveform g of FIG. 2 shows the voltage as it appears 
at winding A. Waveform h of FIG. 2 shows the voltage 
delayed by one-fourth cycle as it appears at winding B. 45 
The voltage is shown to have a frequency, /„, equiva- 
lent, for example, to 400Hz and a voltage (plus or 
minus) equal to V . Actually the voltage is slightly less 
than V due to the transistor drops, but this may be 
neglected for practical purposes. The current i DC , as 
illustrated in waveform j of FIG. 2, operates about a 
steady value i„ and has a ripple frequency f T equal to 
four times the driving voltage frequency, /„. The ripple 
current may be bypassed by C fl (FIG. 1). 

A motor of the type described, while producing a 
constant torque, operates at a constant average speed. 
FIG. 3 shows the relationship between the stator field, 
illustrated as line 70, the rotor magnetic axis, illustrated 
as unbroken line 72, and a reference zero phase vector 
line 73, where line 70 is at angle 6 to line 73 and line 72 60 
is at angle <f> to line 73. In theory, the rotor magnetic 
axis lags the stator field by a constant angle for a con- 
stant torque which may be labeled <j> . The stator field, 
in most general terms, will have a phase angle 6, with 
respect to some reference. When the stator field is at 65 
constant phase and frequency, 6 may be considered 
zero (i.e., lines 70 and 73 coincide). Actually, the oc- 
currence of hunting causes momentary changes in 

torque such that the instantaneous angle <t> is equal to 
<£„ ± A</> as shown by dotted lines on either side of a line 
72. In fact, <j> is substantially proportional to torque 



Further, as is also known to those skilled in the art, the 
direct current, i DC , in a motor operated efficiently, is 
also substantially proportional to torque 



It therefore follows from formulas 1 and 2 that 

'dc <* </> 

A motor used to drive magnetic tape such as illus- 
trated in FIG. 1 is subject to torque pertubations (i.e., 
small temporary changes in torque). These torque per- 
tubations might by caused by a number of things such 
as, for example, dirt in bearing 22 (FIG. 1 ) or a binding 
of the tape at the pay-out reel 32 or tape-up reel 34. 
Such pertubations are known to cause "hunting," a 
sinusoidal oscillation of the rotating magnetic axis 
about its average angle, <f> . Since the rotor phase angle 
has a value (j), proportional to torque, T, it may be 
considered to be compliantly coupled to the stator field 
by a torsional spring with a stiffness k T . The dynamic 
interaction of the rotor compliance and the rotor iner- 
tia, I, results in an oscillatory system with a natural 
resonant frequency, /„, and is determined by the equa- 




Waveform a of FIG. 4 shows the relationship above. 
The negative sign of <£„ is established when it is remem- 
bered that the rotor magnetic axis lags the stator field 
which is assumed to be a reference. At each instant in 
time the rotor is at an angle A<£ relative to <f> and is 
determined by the equation: 

A<£ = AtfnnjSin 2irf„l 




The frequency f„ is small when compared to the driving 
frequency of the motor, / . Frequency /„ may be on the 
order of 10Hz; A^> mox may vary between a fraction of a 
degree to about 10° and <f> may vary from zero to about 
60°, increasing with increasing loads. Waveform b 
shows the direct current ioc supplied to the motor drive 
circuit of FIG. 1. ioc is the instantaneous sum of i , the 
average current, and Ai, the variation about i„ where 

M = Awsin 2Ttf,t 


From Formula 1 it is known that the lag angle de- 
creases as torque decreases. Therefore, the required 
driving current decreases so that ki max and A(^ max 
occur at the same point in time. Waveform c shows the 
oscillatory velocity or rate of change of <£, d^/dt. The 
sign of d<j>ldt is established when it is remembered that 
$ is a lagging angle or negative displacement. The im- 
portance of this waveform becomes apparent when it is 
recalled that, as is well known in linear vibration the- 
ory, the damping torque required to reduce the oscilla- 
tions of a mass (i.e., the rotor) is proportional to the 
velocity of that mass (not the displacement) and the 
two are 1 80° out of phase. This waveshape is shown at 
waveform d. Therefore, if the damping torque of wave- 
form d can be developed, the rotor will maintain the 
desired angle </><>. 

5 6 

Normally, hysteresis motors are considered to be -; iirf r 2 c (9) 

constant speed devices which, in the snychronous ' + < 27r /) 2fi2c " 2 
mode, operate independently of voltage. However, in 

fact a change in driving voltage will influence the rotor illustrated in FIG. 5c. An ideal negative impedance line 

phase angle. The inventor has discovered that, for the 5 is shown dotted for comparison. This negative portion 

class of motors described, instantaneous rotor phase ha s a maximum negative value which may be deter- 

angle is a relatively linear function of voltage for a min ed by differentiating formula (9) with respect to/, 

constant torque load, over small voltage variations. The This peak occurs where 
required damping torque, then, may be developed if 

the AC voltage supplied to the stator windings varies in 10 *■•_ l (10) 

direct proportion to the damping torque curve of FIG. 2vRC 
Ad. The AC voltage, in an absolute sense, in turn is 

equal to the DC voltage delivered to the motor drive Once the natural frequency is known and a suitable 
circuit. The direct voltage V M at the motor drive circuit resistor R value is selected, the value of C can easily be 
is equal to V„ — \ z where V z is the voltage drop across determined. The circuit of FIG. 5a has the advantage of 
impedance 42 (FIG. 1). simplicity, imexpensiveness and the fact that the capac- 
The voltage drop across an ideal impedance which itor 78 can also act to bypass the ripple current. Unfor- 
will produce the required damping torque is shown in tunately, the inphase component of the impedance 
waveform e. FIG. 4/ is a vector diagram which, in a dissipates power. This may be undesirable, particularly 
sense, summarizes the data presented in waveforms a in a low power device such as a portable video re- 
through e of FIG. 4. It shows the phase relationship corder. 

between the changes in rotor angle A$, changes in A second circuit configuration which accomplishes 

current Ai, the derivatives of the two, V 2 , the voltage the damping more efficiently, is shown in FIGS! 6a and 

drop across z, and V^, the voltage drop across the 25 6b. This is a parallel LCR circuit comprising a resistor 

motor circuit 40. Since the current is 1 80° out of phase 76, a capacitor 78 and an inductor 80. This circuit has 

with rotor angle, the derivative of the current is also its own resonant frequency below the resonant fre- 

1 80° out of phase with the rotor velocity. The ideal V z quency /„ of the motor. FIGS. 6c and 6d show respec- 

is proportional to di/dt and lags i DC by 90° for an effi- tively the inphase and imaginary components of the 

cient motor. As will be seen below, by utilizing a proper 30 impedance of FIGS. 6a and 6b. It is desired to have the 

impedance element 42 (FIG. 1) the proper voltage maximum negative reactance occur at the rotor reso- 

drop across the stator windings may be developed to nant frequency, /„. For typical circuits this will occur 

reduce the hunting action. when 

From waveforms b and e of FIG. 4 it can be seen that 

in the required impedance 42, the current leads the 35 1 

voltage by 90° . A capacitor has this relationship, how- 2ir ^ Lc 
ever, the impedance of the capacitor decreases with 

increasing frequency. Therefore, the maximum positive is approximately 5 percent less than /„, the exact 

and negative excursions of V z would decrease in an amount being dependent on the relative value of R. A 

absolute sense with increasing frequency. Since V M = 40 detailed mathematical treatment is deemed not neces- 

V — V* and since V is fixed, the maximum positive sary as this information is available in basic circuit texts 

and negative excursions of voltage would decrease with and is similar to that described in connection with FIG. 

increasing frequency. This is undesirable since at 5. This circuit has the advantage over that shown in 

higher frequencies, a higher damping torque is required FIG. 5a in that the real portion of the impedance is at 

which means higher voltage swings are required. 45 a relatively low value at or near the resonant frequency 

A negative inductor would be characterized by the and also at zero frequency thus keeping power dissipa- 

voltage lagging the current and by increasing imped- tion in V ? to a minimum. 

ance with increasing frequency. This device is of course FIG. 7 shows yet another motor damping circuit. A 

unattainable. It may, however, be approximated when transformer 84 has a primary winding 86 in the DC 

one again considers the motor to be like a torsional 50 current path of the motor drive circuit. The secondary 

spring. It is known that a given motor with a given 88 of the transformer is series coupled to a limiting 

inertia has a given and determinable natural resonant resistor 90 and control windings 96 of two saturable 

frequency of oscillation, /„, as expressed in equation inductors 92 and 94. A bias winding 98 in each of the 

(4). Therefore, a circuit can be developed that has a saturable inductors is series connected to a source of 

negative impedance over a small range about that natu- 55 bias potential 104 and a limiting resistor 106. A third 

ral frequency. FIG. Sa illustrates a suitable impedance set of windings 100 in inductor 92 is connected in series 

comprising a parallel combination of a resistor 76 and with the phase A motor winding. A similar set of wind- 

a capacitor 78. Such a circuit has an impedance. ings 100 in inductor 94 is connected in series with 

phase B motor winding. 

z= r - i ivfR'c 60 The purpose of transformer 84 is not to alter the 

1 + (2tt/) z /j^ voltage in the motor drive circuit, but rather to merely 

sense the current passing through the circuit, or more 

That is, it has a real portion accurately the derivative, di/dt, of that current. Since 

the primary winding 86 of the transformer does not 

1 + (2ir/wc* (8) 65 have to develop the iZ voltage drop required for the 

damping torque, it can consequently be a physically 

illustrated at FIG. 5b and an imaginary or quadrature smaller inductance. Damping is produced, not by vary- 

impedance portion ing the voltge supplied to the motor drive circuit as 


before, but by varying the impedance in series with the 
motor windings. This effectively alters the voltage at 
the stator windings. For small variations of series im- 
pedance, this will have a comparable effect to that of 
small voltage variations. 5 

Since either a plus or minus current in the control 
windings, only, would only lower the impedance of 
windings 100, an effect is required to make this imped- 
ance change linear with the plus or minus control cur- 
rent. This effect is provided by the bias windings 98, '0 
which have a constant DC current. Now a plus or minus 
control current will increase or decrease the average 
impedance established by the bias current. 

A capacitance C R across secondary winding 88 of 
transformer 84 acts to bypass the ripple frequency in 15 
the DC current as illustrated in waveform j of FIG. 2. It 
may be of small electrical value and of small physical 
size. The inductor is not tuned as was the inductor of 
FIG. 6 so that its L-C resonance is higher than that of 
the rotor resonant frequency. The inductor is a normal 20 
"positive" inductance with its impedance voltage-drop 
always proportional to di/dt and leading the DC current 
by 90°. The required damping action is obtained by 
choosing the polarity of the control windings so that the 
impedance of the saturable inductors decreases as the 25 
DC current develops a positive di/dt. The damping 
action will now be equivalent to that of the ideal nega- 
tive inductance shown as a dotted line in FIGS. 5c and 
6d. The advantage of the circuit of FIG. 7 is that the 
reactor voltage and therefore impedance is affected at 30 
the motor frequency of, for example, 400Hz rather 
than the lower motor resonant frequency of, perhaps, 
10Hz. This requires much smaller magnetic cores and 
therefore the saturable reactors may be physically 
small and of light weight. Further, the optimum lagging 35 
impedance component is obtained over the full fre- 
quency range by selecting the polarity of reactor wind- 
ing connections rather than by approximately it over a 
narrow band through L-C tuning. Further, a physically 
large capacitor (such as capacitor 78 in FIGS. 5 or 6) 40 
is not required. 

The impedance circuits dealt with so far as illustrated 
in FIGS. 5, 6 and 7 have all been passive circuits and 
have all operated by varying an impedance in series 
with the motor or its drive circuit. The hunting action 45 
also may be damped by introducing a momentary phase 
shift 6 of the stator field about the zero reference 73 of 
FIG. 3, as in FIG. 8. FIG. 8 shows a motor drive circuit 
40 as illustrated and described in connection with 
FIGS. 1 and 2a feeding the two stator phases A and B 50 
of a synchronous motor. The 1 600Hz source 54 shown 


line is shown as a transformer, the secondary of which 
produces a voltage e. The secondary is connected as 
one input to a differential amplifier 122 having a gain 
G. The output of the differential amplifier labeled as a 
voltage E is coupled to the delay circuit 120 to deter- 
mine the amount of delay in that circuit. The output of 
the amplifier is also coupled to a differentiator 124, 
which may be a conventional R-C differentiator. The 
output of the differentiator is coupled as a negative 
second input to differential amplifier 122. In the quies- 
cent state (that is, the motor not hunting) the delay 
circuit will cause a 400Hz signal to be delivered to the 
motor drive circuit at zero reference angle. However, 
for the more general case, the current in the DC lines to 
the motor driver is proportional to the difference be- 
tween the stator field phase angle <j> and the rotor phase 
angle <j> as illustrated by the vectors of FIG. 3. That is 

ioc = *„(»- 4) 


where k a is the motor angle-current transfer function. 
The DC current in the motor drive circuit passes 
through transformer 42 which develops a voltage in its 
secondary e proportional to the derivative of current. 
That is 

e = M di/dt 


where M is the mutual inductance of the transformer. 

e = M k a 

I de 

d, ) 


Amplifier 122, in the absence of a signal from the 
differentiator 124, amplifies the signal e to produce the 
signal E which is fed to the delay circuit. E effects a 
phase shift = k p E, where k p is the transfer function of 
the delay circuit. E is also proportional to (d0/dt — 
d<£/dt) if the amplifier input is only e. However, E act- 
ing on delay circuit 120 is required to be responsive 
solely to d<£/dt. Therefore the dfl/dt term must be can- 
celled. That is the purpose of differentiator 14. The 
derivative of E, dE/dt, is proportional to d0/dt. There- 
fore, E equals the sum of the two inputs to the amplifier 
times the amplifier gain G, or 


, /„ k de \ 

e) -\ G 17- nr) 


where K is an arbitrary constant. Substituting for e, 

(d§__ d±_\ 
Mk ° \d, dt )' 

E - (cMk„ ■ -jp J - {cMk„ 

M-\ _ / GK d6 \ 

dt ) \ k p ' dt ) 


in FIG. 2a as being contained within the motor drive 
circuit is here separated therefrom and instead of driv- 
ing toggle flop 55, drives a voltage controlled delay 
circuit 120 which in turn drives toggle flop 55 in the 
motor drive circuit. Delay circuit 120 delays the lead- 
ing edge of the pulses from the oscillator a nominal 
amount such as l/16th of a period. Then positive and 
negative voltages applied to terminal 121 advance or 
retard proportionally the pulses from delay 120. Im- 
pedance 42 in the motor drive circuit direct voltage 

60 By adjusting the output of the differentiator so that G . 
K/kp = (GM&„), or K = (Mk a k p ), the derivative is 
eliminated, leaving E = — (GMk„)d<|>/dt. For practical 
closed loop stability, however, K cannot be less than 
{Mk a kp) but it may be slightly (about 10 percent to 50 

65 percent) greater. In summary, then, as soon as a change 
in DC current occurs indicative of the departure of the 
rotor magnetic axis from its nominal <f> , E acts on delay 
circuit 120 to appropriately advance or retard the sta- 




Ri + LS 

■v t = 


R, + LS 





tor field from its zero angle, thereby producing the 
proper damping torque to inhibit the hunting. 

FIG. 9 shows an alternate approach to the amplifier 
and differentiator of the circuit of FIG. 8. Here e is fed, 
not directly to amplifier 122, but rather through resis- 5 
tor 128 to the amplifier 122 and to a capacitor 130. 
The opposite end of capacitor 130 is connected to a 
source of reference potential, such as ground. When 
the R-G circuit has the value (RC) = (GMk fc p ), the 
amplifier output E will be identical to that of FIG. 8. 10 
For practical closed loop stability, however, (RC) 
should not be less than (QMk a k p ) and may be some- 
what (about 10 percent to 50 percent) greater. The net 
result is an incremental torque proportional to d<£/dt 
and the motor hunting will be damped out. . 

FIG. 10 is a further embodiment of a motor control 
circuit. As shown in FIG. 10, a voltage V + V, is ap- 
plied to motor drive circuitry 140. The motor drive 
circuitry 140 may be of the type shown and described 
in connection with FIGS. 1 and 2. The motor drive 
current /, on lead 142 is coupled to one terminal 144 of 
a resistance (R,) 146. The other end of resistance 146 
is coupled to a point of reference potential, shown as 
ground 148. The voltage e 2 at terminal 144 is the input 
signal to an amplifying device 150, which has a transfer 
function of 0- The amplifying device 150 may include 
voltage amplifier and power amplifier portions, which 
provide an output voltage V 2 on lead 152. the voltage 
V 2 is coupled through a resistance (R 2 ) 154 to the 
primary winding 156 of a transformer 158. The voltage 
Vi, which forms a portion of the voltage applied to the 
drive circuitry 140, is provided from V 2 by a secondary 
winding 160, through the transformer action of the 
transformer 158. 35 

The circuit of FIG. 10 is effective to reduce motor 
hunting, by dynamically altering the magnitude of the 
voltage V„ :%' Vi supplied to the motor 162. 

To reduce hunting, a corrective torque is introduced 
to the motor 162, which is opposed to the hunting 40 
velocity <£, i.e. the rate of change of the rotor angle </>. 
The corrective torque is developed by changing the DC 
supply voltage by V,. Therefore, it is necessary to make 
Vj proportional to <jb, the hunting velocity. 

An error signal e 2 is obtained by sensing the motor 45 
DC current /,. However, e 2 is affected by both <$> and V,. 
If V, were directlly proportional to e 2 , a voltage would 
be applied to the motor which would be partly propor- 
tional to 4>, but, which also would feed back Vj. By 
selecting given values for the time constant, provided 50 
by R 2 and L of the transformer, the V, feedback com- 
ponent of e 2 is substantially eliminated and a desired 
value of V, proportional to <£ is provided. 

The equations further defining the operation of the 
arrangement of FIG. 10 are as follows: 55 

using Laplace Transform notation: 


V, (R 2 + LS) = MSV 2 = GMSe 2 

But, e 2 = I1R1, and 

V, (R 2 + LS) = GMRjSi, 

Sii = -A: a S<£ + /t B SVj where; 

k a = constant relating a change in current i\ with a 65 

change of rotor angle <f> for constant voltage. 
k v = constant relating a change in current j, with a 

change in voltage for constant rotor angle ^>. 


V, (R 2 + LS) = GMRi (-k a S<j> +k v SV,) 

R 2 V, + LSV, = -(GMk a R,) S</> + (GMk„R,) SV, 

R 2 V, = -(GMk a R,) S<j> + (G A Lk„R -L) SV, 

V, = - (GMk a ■ -&- ) S<t> + -^-(GnA„«, - 1 )SV, 

when (G h k v R,) = 1 
.thenK. — (ca#*.^-) f- 

The damping phenomenon of the motor is seen when 
it is considered that the synchronous motor behaves 
like a torsion spring with a torsional stiffness, k T . The 
plot of FIG. 1 1 relates the motor torque to rotor phase 
angle <f> and applied voltage, with the dashed line por- 
tion 166 indicating the locus of operation on the motor 
curves. The torsional stiffness k T varies with voltage so 

= k -V— = k K+y, =k (i+ Ji-W + 



AA = A„ 


and k = k T for a constant supply voltage. 

When the motor drives a steady load, T , with a 
steady phase angle <t> , the differential equation of mo- 
tion about <t> is 

H + Ki<f> = -T 

J^ + (k„ + M)(^ + A^)=T () 

J = Moment of Inertia of the rotating system 

T„ = steady torque load = k <f>„ 

since u = T„ 

j$ + T.-^-+kM(}+ •**-)= ° 

This is a non-linear differential equation. When &k/k 
varies periodically with A$, and is small, for example 
less than 0. 1 , the last equation can be closely approxi- 
mated by the following: 


j<t> + r„ ■—{- kM = o 




J$ + -p?-v, + kA4> = o 

From the equations for the transformer coupled cir- 
cuit of FIG. 10, 

Since </> has been referenced in the negative direction, 
the minus sign is dropped from V,, and 

j$ + 


GMk a 


+ *„A<j) = 




This is the equation of a damped oscillation where 
the bracketed term is the damping coefficient. 

The circuit of FIG. 12 is effective to reduce motor 
hunting by altering the phase angle of the stator field 6 
of the motor 168, so as to induce a damping torque. 

The arrangement of FIG. 12 operates to reduce hunt- 
ing in the manner shown and described with respect to 
FIGS. 8 and 9. 

In FIG. 12, the current through motor 168 is coupled 
to the amplifier 170 through an RC network, shown in 
dashed line box 172. The RC network comprises resis- 
tance (R,) 174 and (R 2 ) 1?6. One end of the resis- 
tances 174 and 176 are coupled to a point of reference 
potential, shown as ground 178. The other end of resis- 
tance 174 is coupled to input terminal 180 and a first 
terminal 182 of a capacitance 184. The other end of 
resistance 176 is coupled to an output terminal 186 and 
a second terminal 188 of the capacitance 184. 

In FIG. 12, the RC network of dashed line box 172, 
performs the equivalent function provided by the com- 
bination of the transformer circuit 42 of FIG. 8 with 
either, the input network of resistance 128 and capaci- 
tance 130 of FIG. 9, or the differentiator of dashed line 
box 126 of FIG. 8. 

That is, it can be shown that the transfer function of 
the RC network of FIG. 12, will produce a signal e 2 
which is substantially solely proportional to the hunting 
velocity <j>, in a comparable manner described with 
respect to the circuitry of FIGS. 8 and 9. 

This will be understood from a consideration of the 
following equations, in which e 2 is the input signal to 
amplifier 170. The relationship between e 2 and i, the 
motor current, using Laplace Transform notation is; 

(ft,ft,Q s, 

(R, + R 2 ) Ci + / 








This can be rearranged and written so that, 

This is an optimum damping signal, since e 2 is propor- 
tional to d<j>/dt. 

This invention has been described in terms of a direct 
rather than alternating driving voltage. 

Where. the motor is driven directly from AC lines, 
there will, of course, not be DC current available as an 
indicator of rotor phase angle <j>. An equivalent signal 
may be obtained from a true wattage sensor placed in 
the AC lines. This wattage signal may be amplified to 
drive current through the primary of a transformer, the 
current being proportional to the wattage that was 
sensed. The voltage at the secondary of the transformer 
will be proportional to the derivative of the wattage and 
therefore proportional to the rotor hunting velocity. 
This signal is amplified and used to control saturable 
reactors similar to those in FIG. 7 or to vary the AC 
voltage to the motor and thus effect the damping 

What is claimed is: 

1. In combination: a synchronous motor comprising a 
stator and a rotor characterized in that said rotor may 
oscillate about an average angular position relative to 
the field of said stator as said rotor rotates; 

electronic drive means responsive to a source of 
direct potential for producing an alternating signal 
coupled to said stator for causing said rotor to 

means responsive to changes in a parameter of said 
potential received by said drive means for produc- 
ing a signal proportional to said parameter; and 

means coupled to said drive means and responsive to 
said signal proportional to said parameter for 
changing one of the amplitude and phase of said 
alternating signal in a sense to reduce hunting of 
said rotor. 

2. In combination: 

a synchronous motor comprising a stator and a rotor 
characterized in that said rotor may oscillate about 

■ =(Ri« a C) [-f-]-(R, + R 2 )C ^jj- 



■ [*-] " l> % 

f"] = [>*■*. 


k « dl J 


k a = a change in motor current for a change in rotor 
angle <f>, for a constant stator angle $. k p = the 
transfer function of the delay circuit and describes 
the proportionality of the stator phase shift 6 to the 
voltage E. Substituting equation (3) into equation 
(2) and rearranging shows; 


an average angular position relative to the field of 
said stator as said rotor rotates; 

means adapted to receive a direct current for produc- 
ing alternating signals to drive said motor; 

current sensing means producing signals responsive 
to said current supplied to said means for produc- 
ing said alternating signals; and 

E 1 = -(R,RA) &-+ (R,R 2 C) [(A„* P C) - ^rXc 7 ) "]^t~ (4) 

when ( (W) ) - <*-*» c >- 

the right hand term of equation (4) equals zero. Thus, 

<> 2 = -(KiR 2 a„) 




means responsive to changes in said current sensing 
means signals coupled to said means for producing 
alternating signals for altering one of the amplitude 
and phase of said alternating signals thereby reduc- 
ing the oscillation of said rotor. 

$ $ $ $ $