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Патент USA US3044715

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July 17, 1962
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3,044,705
LIMI'I'ER SYSTEMS
Filed Dec. 8, 1958
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July 17, 1962
C. C. WILLHITE
LIMITER SYSTEMS
Filed Dec. 8, 1958
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-United States Patent()
1
CC
3,044,705
Patented July 17, 1962
I
2
3,044,705
It is a still further objectrof this invention to limit a
total vector magnitude in a manner which satisfies the
actual requirements on both order magnitude and direc
LIMTTER SYSTEMS
Charles C. Willhite, Convent Station, NJ., assignor to
tion, in a system where the total order is composed of
Bell Telephone Laboratories, Incorporated, New York,
two or more components.
N.Y., a corporation of New York
In the numerous control systems now in use, the out
Filed Dec. 8, 1958, Ser. No. 779,020
10 Claims. (Cl. 23S-l89)
put orders or signals may represent the analogs of >any
This invention relates to systems for selectively limit
may be the analog of translational or lateral acceleration,
one of a number of types of data. Thus an output order
ing a total vector quantity comprised of two or more com
ponent vector quantities.
In control systems, e.g., missile guidance and auto
matic machinery, the physical motion of the machine
components is controlled by signals. Taking the case of
the missile, it may be guided by steering orders or signals
issued by the ground guidance and control equipment.
10
velocity, distance, force, pressure, charge, frequency,
time, et cetera. In such systems where two or more
orders are sent to the same piece of equipment, it is fre
quently desirable that the total order magnitude be con
fined or limited in some selected fashion. Thus, if the
total order is represented as a vector quantity comprised
of two or more components, orthogonal or otherwise, it
These orders are calculated by a computer and transmit
ted to the missile via the beam of a missile tracking radar.
may be desirable to limit the vector magnitude to a
greater extent in some directions than in others,lor to
Upon receipt of an order the electronic control system in
even limit it in some irregular fashion in the various di
the missile deilects the missile control surfaces until a 20 rections it may assume. Such a limiting, however, cannot
lateral acceleration of the magnitude of the received
readily be accomplished by simply imposing maximum
order is experienced.
limits on the several componentsthereof.
The total lateral acceleration of the missile is controlled
It is accordingly a furthe-r object of this invention to
by two pairs of ailerons. These-are mounted such that
impose limits, on a total vector quantity, which may be
the acceleration caused by one pair is ninety degrees, >or 25 of a variety of magnitudes in the different directions that
in space quadrature, from that caused by the other pair.
the total vector may assume.
Separate orders are issued to each pair.
The invention in its broadest aspects comprises the con
The magnitude of the steering orders issued by the
computer must be limited to values determined by aero
dynamic considerations and the structural strength of the
cept of limiting the component vector quantities between
selected limits, transforming the limiting component vec
tor quantities into vector quantities which are angularly
dis-posed with respect to said limited vector quantities,
maximum limits on the orders issued to each set of con
and then applying a second set of limits to the trans
trol surfaces. However, inasmuch as the two sets of con
formed vector quantities. The second set of limits may
trol surfaces are operated independently of one another,
be the same as or different from the limits initially ap
a “full” deflection of both sets will result in 1.4 times the
plied. Also, after the second stage of limiting the com
lateral acceleration caused by a full deflection of one set.
ponents may again lbe transformed and again limited.
This, of course, can result in missile failure unless the
In one speciñc embodiment of the invention the afore
maximum orders issued to each set of control surfaces
mentioned circular or near-circular order limiting may be
are fixed at values such that the total lateral acceleration
achieved. To this end, orthogonal component vectors
40 are limited, to the same extent, in a pair of amplifier type
never exceeds that which is permissible.
lf a given maximum acceleration order is ñxed for each
limiters. This, then, initially limits the total vector quan
aileron pair, then the total lateral acceleration that can
tity to a square. The limited components are then ro
be achieved will fall within an acceleration “squaref’
tated (i.e., transformed) through an angle of forty-five
However, the acceleration limits of the missile itself, being
degrees and square limiting of the original magnitude is
missile itself, and thus it has been the practice to place
determined primarily by the structural design thereof,
are nearly constant as a function of lateral acceleration
direction. That is, the acceleration limits of the missile
proper fall with a “circle” A “circular” or “near-circu
applied to the rotated components in a second pair of
ampliñer type limiters. The total vector sum of the new
limited components is thus limited to an Octagon, the
Octagon being defined by the common area of two equal
lar” order limiting would be superior to a square because
squares with common centers and rotated forty-tive de
the prevention of missile failure requires that the corners 50 ‘fgrees with respect to each other. For many purposes this
of the square fall on the edge of the circle and, there
approach to a circle would be suihcient. However, it will
fore, in some acceleration directions a circular order lim
be appreciated that an even closer approach to a circle
iting would permit forty percent more acceleration than a
may be achieved by providing several additional stages
square order limiting. Thus, it is desirable not to simply
of hunting and rotation.
~
,\
place fixed limits on the orders controlling the aileron 55
By selection of the limits imposed and the degree and
pairs, but rather arrange the limits so that the vector sum
stages of rotation, the pattern within which the total vec
thereof will never exceed aA given magnitude.
'
tor must fall can be made `to take almost any desired
Similar problems arise in the control of automatic
shape or con?gunation. Thus, in two dimensions the
machinery. It may, for example, be desirable that the
total vector may be lirnted to a square, rectangle, Octagon,
operating portion of the machine move certain distances 60 any given polygon, an approximation to a circle or to an
in predetermined orthogonal directions, but that the total
ellipse, et cetera. Further, the restriction on the length
movement never exceed a critical value.
Assuming se
lected order signals cause movement in selected orthog
onal directions, these order signals can, of course, each
and direction of the total vector may be made to have a
minimum as well as a maximum; or going one step further,
it may be made to have regions within the main area or
be limited so that the vector sum thereof never exceeds 65 pattern where the total vector is not permitted.
the determined critical value. However, this is done only
The principle involved applies as well to three corn
by unnecessarily restricting the degree of movement in
ponent vectors as to two, or to three dimensional com
each of the said orthogonal directions.
ponents.
'
It is an object, therefore, of this invention to limit a
These and other objects and features `of the invention
total vector order magnitude independently of the order 70 may be better understood by a consideration of the fol
direction, in a system where the total order is composed
lowing detailed description when read in connection with
of two or more components.
the drawings in which:
3,044,705
3
4
vector is then expressed in terms of vectors lying along
FIG. 1 is a schematic diagram in block form of a limit
the x, y axes.
er system in accordance with the present invention;
To perform the desired rotation, devices producing
FIGS. 1A and 1B are vector diagrams useful in ex
sines and cosines must be used. These may each produce
FIG. 2 is a typical, amplifier type limited circuit that Cl either a single sine or cosine function (nonlinear potenti
ometers) or both sine and cosine together (resolvers,
may be used in the system of FIG. l;
plaining the operation of the system of FIG. l;
square-card sine potentiometers, phase-shifting capaci
FIG. 2A illustrates the transfer characteristics of the
tors).
circuit of FIG. 2;
FIG. 3 illustrates the variation that can be obtained
in the vector pattern of the system of FIG. l through the
Such devices are discussed in detail in the afore
mentioned Radiation Laboratory textbook (pp. 104-120).
In the system of FIG. l, single sine and cosine elements 16,
17, 18 and 1% are used.
inclusion therein of the circuit of FIG. 2;
The limited vector quantity u
is fed directly to the (cos 0) elements 16 and to the (sin
0) element 18 via the (_1) ampliñer 21. The latter is
simply a unity gain amplifier that inverts the sign or po
larity of the input signal. The limited vector quantity v
is fed directly to the (sin 0) element 19 and to the (cos 0)
FIG. 4 illustrates a still further variation in the vector
pattern of the system of FIG. l;
FIG. 5 is a schematic diagram of another embodiment
of the present invention;
FIGS. 5A and 5B are vector diagrams useful in ex
element 17. The degree of rotation of the vectors is de
plaining the operation of the system of FIG. 5;
FIG. 6 is a schematic diagram in block form of still
another embodiment of the invention;
FIGS. 6A and 6B are vector diagrams useful in explain
termined by the angular displacement of an input shaft
coupled to each of the elements 16-19. The products
ing the operation of the FIG. 6 embodiment of the inven
FIG. 7 is a schematic diagram of a still further embodi
added in the adder or `summing amplifier 22 to give x;
similarly, (v cos 6)and (--11 sin 0) are formed in elements
17 and 1S and added in summing amplifier 23 to give y.
ment of the present invention;
FIGS. 7A to 7E are vector diagrams useful in explain
ing the operation of the embodiment shown in FIG. 7;
The quantities x, y are then fed to the limiters 14 and
15 wherein they are limited to any given extent. In the
explanatory diagram, FIG. 1B, the vectors are shown as
u cos 0 and v sin 0) are formed in elements 16 and 19 and
tion;
being rotated through an angle of forty-five degrees, with
limiting of the original magnitude applied to the rotated
FIG. 8 is an embodiment of the invention wherein the
total vector is limited to a predetermined three dimension
components. Thus the total vector is limited to an octa
al pattern; and
FIGS. 8A to 8D are vector diagrams useful in the ex
30 gon, the Octagon being defined by the common area (as
planation of the three dimensional system of FIG. 8.
shown in solid lines) of two equal squares with common
Referring now to FIG. l, there is shown therein a ñrst
pair of amplifier type limiters 11 and 12, a rotator 13 en
centers and rotated forty-five degrees with respect to each
other.
If circular limiting is desired, as in the case of a missile,
the Octagon “limit” will for most cases prove to be a suf
closed by the dotted box, and a second pair of amplifier
type limiters 14 and 15. The invention is not dependent
ficiently close approximation. However, it will be real
upon or restricted in any fashion to any particular limiter
circuit and, as will be apparent to those skilled in the art,
the only limitation on the limiter circuits that may be
ized from the foregoing that an even closer approach may
be had by providing additional stages of limiting and
rotation. For example, three rotational stages may be
utilized is that dictated by the function to be performed.
Limiters (also known as function generators) of various 40 used, each providing a twenty-two and one-half degree
vector rotation, with limiting of the same amount applied
configurations are shown and described in “Analog Meth
to the original and successively rotated vectors.
ods in Computation and Simulation,” by Soroka, McGraw
In FIG. 2 there is shown a typical amplifier type limiter
Hill Book Company (pp. 203-207); and “Electronic Ana
that may be used in the system of FIG. l, the transfer
log Computers,” by Korn and Korn, McGraw-Hill Book
characteristics thereof being shown in FIG. 2A. The
Company (pp. 271-279).
limiter comprises a standard operational amplifier 24 hav
With a first signal or component quantity, designated
u, applied to limiter 11 and another signal or component
ing multiple feedback paths. Within the limits imposed,
quantity, designated v, applied to limiter 12, the vector
the output voltage varies as an inverse function of the
input voltage, the exact relationship between the two
FIG. lA. ' It has been assumed, in FIG. lA, that the limits 50 being determined by the respective values of the feedback
resistance (Rfb) and the input resistance (R1), as shown
applied to each signal are equal and of the same magni
in FIG. 2A. The feedback path 25, comprising a diode
tude in both the positive and negative directions. Ifeither
and voltage source E, limits the output voltage to a posi
of these conditions does not prevail the vector sum will
sum thereof will be limited to a square, as illustrated in
tive value equal to E. If the output voltage were to at
then be limited to a rectangle. Further, for purposes of
explanation of the invention, the component quantities, u, «
v shall be -assumed to be orthogonal; howover, it will be
clear to those skilled in the art that the principles of the
tempt to exceed E, a low impedance conducting path
would exist through feedback path 25, and any additional
input current to the amplifier would be balanced by cur
invention are equally applicable to component quantities
rent through this branch with no increase in output volt
which bear some other angular relationship to each other.
age. Similarly, the feedback path 26, comprising a diode
The limited, vector quantities u, v are fed to rotator 60 and voltage source E/2, limits the output voltage to a
negative value equal to E/ 2.
FIG. 3 illustrates the variation that may be obtained in
13 wherein they are rotated through any predetermined
angle. Such rotation devices are well known in the art
and the one utilized in the system of FIG. l is essentially
the same as that disclosed in “Electronic Instruments,” by
Greenwood. Holdam and MacRae, volume 2l, Radia
the vector pattern of the system of FIG. l should the
limiter circuit of FIG. 2 be substituted for limiter 12. In
this instance, the v vector is limited in the negative
tion Laboratory Series (pp. 158-160).
direction to one-half the original value (i.e., E/2), the
The rotation or transformation of the vector compo
nents u, v lying along the u, v coordinate axes, to the coor
dinate axes x, y can be expressed by the equations
that the modification has the effect of eliminating the
shaded portion of the total vector pattern.
x=u cos‘ H-l-v sin 0
y=-u sin @-l-v cos 0
other limits remaining as they were. Thus it will be seen
70
To obtain a total vector pattern such as that shown in
FIG. 4, the x and y vector components are limited in the
negative direction to one-third the original value, all other
limits remaining the same. Thus, from the few foregoing
examples, it will be clear that the total vector may be
Accordingly, if the trigonometric functions of the vectors
u and v are combined in the indicated manner, the total 75 limited to almost any desired polygonal pattern simply
where 0 is the angle through which the axes are rotated.
3,044,705
by controlling the limits imposed and the degree of vector
rotation. Further, just as successive square limiting can
provide an approximation to a circle, so in similar fashion
an approximation to an ellipse can be achieved through
several stages of rectangular limiting.
vector is limited is assumed to exceed that'to which the v'.
vector is limited. It will be understood, of course, that
any desired limits can be set for the u and v vectors'sim-ï .
ply by using voltage sources 38 of appropriate values.
if the limited vec-tor quantities Li and v, from the lim-V
In the description so far it has been assumed that pre
iters 31 and 32, are both of a value less than the mini
selected fixed limits and degrees of rotation are applied.
inuin value `selected therefor, nei-ther of the relay coils
It will be clear, however, t0 those skilled in the art, that
A and B lwill lbe energized and hence neither of the vec
the limits applied in each amplifier limiter circuit need not
tor quantities u, v will be delivered to rotator `13. If,
be fixed but rather canbe varied continuously or periodi 10 however, one, or both, of the vector quantities exceeds,
cally in almost any desired manner. Likewise, the degree
in either the positive or nega-tive direction, lthe preselected
of angular rotation may be varied automatically in re~
minimum limits, the associated relay coil, orcoils, will be
sponse to some signal. Such a variation in the total
energized. The energizaition of either relay coil closes
vector pattern may be desirable in certain instances. For
the associated switch contacts with the result that the u
example, in the case of missiles, it may at times be neces 15 and v vectors are both delivered to the rotator i3. Acsary t0` alter the total vector pattern as the missie altitude
eordingly, the u and v vectors are always passed on tothe
or missile velocity increases.
rotator i.“ when either, or both, exceed the minimum
In the embodiment shown in FiG. 5, the u and v vector
value set therefor. "the result of this operation is illus~
components are restricted to a minimum value as Well
trated in FIG. 5A ywherein the rectangular’ pattern 23
as a maximum. With the input component quantities 20 is shown provided »with a minimum restricted region or
applied to the limiters 31 and 32, the vector sum thereof
hole 3G.
will be limited, in maximum value, to a rectangle, as illus~
The rotator 13 is lsimilar to that shown in FIG. l
trated at Z3 in FIG. 5A. The u vector is limited to the
and, in like manner, it rotates vectors u and v through
same extent in the positive and negative directions, while
a predetermined angle, which in FIG. 5B is shown as
the v vector is limited to a much greater extent in the 25
thirty
degrees. These rotated vectors are then delivered
negative direction.
to limiters iii, i5 wherein they are limited to any selected
The outputs of limiters 31 and 32. are delivered to the
extent. In the case illustrated in FIGS. 5A and 5B, the
rotator 13, via separate pairs of parallel connected switch~
maximum limits imposed on the u, x, y and -l-v vectors
ing contacts, and to the limiters 33 and 34, respectively.
are equal, only the limiting of the v vector in the nega
These latter limiters provide the energization current for
relay coils A and B, respectively, and the coils in turn
serve to actuate or “close” the normally “open” switch
contacts A and B. Limiters 33 and 34 coact with the
relay units A and B to limit or restrict the u and v vector
quantities to predetermined minimum Values.
The limiters 33 and 34 are of the type shown in FIG.
6.1001) of the Sorolra book and each comprises a stand
ard operational ampliñer 39 having a high impedance
feedback and a pair of input series circuits. Considering
the circuit for limiting the u vector, the output of limiter L
31 is fed to the pair of paral el connected series paths 35
and 36, each of which includes a diode 37 and a voltage
source 38. The polarity of the voltage sources 38 and
tive direction being different. Again, it will be realized
that the total vector can be limited to -a wide variety of
patterns and, in similar fashion, the hole or minimum re
stricted region can `be of a variety of shapes.
FiG. 6 illustrates another manner of providing a given
vector pattern with a `hole or restricted region located
therein.
The limiters 41 through 44 are similar in na
ture to the limiters of FIG. 5 numbered 3l through 34,
respectively. Accordingly, ywith the `orthogonal compo
nent quantities u, v delivered thereto, a total vector pat
tern such as shown in FiG. 6A can be achieved. In
FiG. 6A, the vector quantities u, v are both substantially
limited, lin maximum amplitude, ln lthe nega-tive direction
the direction of easy current iiow of the diodes 37 are re~
and thus the hole is made `to appear in the lower left
versed for the two paths.>
In the series path 35, voltage source 33 back-biases the
diode 37 so that no current Will ñow therein unless the
readily seen, however, that by selection of Ithe maximum
input voltage is of a positive value which exceeds voltage
source 38.
In like manner, no current will flow in series
path 36 unless» the input voltage is of a negative value 0
in excess of source 38.
The paths 35, 36 are connected to the input of opera
tional ampliiier 39', while the output of the latter is _fed
directly to relay coil A. The parameters of the amplifier
are chosen so that no output signal is produced in the
absence of an input signal and thus the relay remains nor
mally `deenergized. If, however, the it vector is of a mag
nitude which exceeds the value chosen for voltage sources
3S, it will be coupled to the input of high gain amplifier
39, by one of the series paths, and an output will thus be
produced *by said amplifier to energize the relay coil A.
The output of limiter 32 is, in like fashion, fed to
limiter 34 for the purpose of energizing the relay coil B
should the v vector exceed a preselected amplitude in the
hand corner vof .the »total vector pattern.
It will be
limits imposed upon the u and v vectors the hole can be
made to appear in any other desired position in said pat
tern.
The vector quantities u, v are limited and then fed,
respectively, to a pair of adders or summing ampliiiers ,
49, 50 along with ia pair of negative, direct current,
biasing potentials u', v’. The negative biasing potential
il’ has the effect of shifting the origin of the u vector to
the right, as shown in FIG. 6A. In like manner, the
negative biasing potential v’ fwhen added to the vector
quantity v effectively shifts the origin thereof in the up«
ward or positive direction.
Tha-t is, the v vector is re
duced in amplitude in the positive direction `by an amount
equal to the negative biasing potential v’. Such a shift
ing, of course produces no ¿c_iiect on the overall shape of
the vector pattern.
The output signals from »adders >49 and 50 'are deliv
ered to the rotator 13 and then after rotation to the lim~ `
iters 14 and 15.
the selected minimum values for the v vector need not be 65 If the initial limiting >applied to the u and v vectors
is identical, the -total vector pattern, at this stage, =will
the same as that selected -for »the u vector and, further,
be a square with the point of `origin of the component
these minimum values can be diiïerent for the positive
vectors located at some position from the center thereof.
and negative directions.
This is the situation assumed in FIG. 6A. Now if said
Let it now be assumed desirable to provide the rec
tangular vector pattern `29 of FIG. 5A with a rectangular 70 origin is shifted to the center of this square, by means
of additive biasing potentials as shown, and a forty-five
hole or region therein (30) in which the total vector is
degree rotation is applied, followed by an equivalent
not permitted to fall. The minimum limits chosen for both
square limiting, the total vector pattern will »appear as
positive or negative direction.
It should be noted that
the u and v vectors are the same for the positive and nega
an Octagon with a hole or restricted region therein, as
tive directions, but the minimum value to which the u 75 shown in FIG. 6B.
3,044,705
Since, as previously explained, the degree of rotation
or limiting may be of any extent, it will be clear that
almost any two dimensional vector pattern can be
achieved and a hole or restricted region can be provided
therein at any position. Also, the hole may be of any
size or shape. For example, the hole could assume a
square or rectangular configuration by simply controlling
ythose potentials which determine the minimum values for
8
poses prove sufficient, However, still further limiting of
the total vector pattern is possible. For example, with
the system shown in FIG. 8, the total vector may be
limited further in the y--z plane. To this end, the output
signais from limiters 14 and 15 are fed to a reverse rotator
S2. This rotator is similar in nature to the rotator’13 and
merely serves to reverse the rotational etïect produced by
the latter. Thus, if rotator 13 provides a forty-five de
grec rotation of the x, y vectors, the reverse rotator 82
the u and v vectors. And, as the shape of the total vec
returns the latter to their original axial positions. It will
for pattern can be made to assume an octagonal, or l0
be clear to those skilled in the art that such a reverse rota
other, conñguration simply by successive limiting and
rotation, so in like fashion the hole could be made oc
tagonal or otherwise.
FIG. 7 is a further modification of the present inven
tion wherein the total vector pattern is provided with a
plurality of holes or restricted regions. The limiters 5i
through 54 are similar to the limiters of FIG. 6 numbered
41 through 44, respectively, and hence the total vector
will initially be limited as shown in FIG. 7A.
The lim
ited vector quantities u and v are then delivered to the
pair of adders 59 and 6€, respectively, along with nega
tive biasing potentials u', v’. As in the case of FIG. 6,
these biasing potentials serve to displace the origin a
predetermined amount dependent upon their magnitude.
This displacement is shown in FIG. 7B.
The output signals from the adders 59, 69 are fed
tion may or may not be needed depending upon the addi
tional limiting to be performed. In the present case, it
has been assumed desirable to limit the three dimensional
pattern in a predetermined manner with respect to the
original , x, y and z axes.
The vectors lying along the y and z axes are delivered to
the rotator S3 from the reverse rotator S2 and limiter 81,
respectively, and after a predetermined degree of rotation,
the rotated vector quantities are fed to limiters 84 and
85. From FIG. 8B, it will be seen that the total vector
is initially limited to a square in the y-z plane. `In FIG.
SC, this square 86 is shown symmetrically disposed about
the intersection of the y, z axes and superimposed thereon
25 is a rectangular limit pattern 87 established by the rotator
33«limiter 84, 35 combination. As previously explained,
the total vector will thus be limited in the y-z plane to
to a second set of limiters 61, 62. These limiters >are in
the common area of the superimposed patterns, as illus
essence the same as limiters 51, 52 with the exception
trated by solid lines in FIG. 8C. This limiting in the
that the maximum limits imposed are chosen so that the
y-«z plane, taken in combination with the octagonal limit
total vector pattern defined thereby falls outside the vec 30 ing in the x-y plane, results in a three-dimensional limit
tor pattern established by limiters 51, 52. As illustrated
pattern such as shown in FIG. 8D.
in FIG. 7C, the total vector pattern 56 established by
The vector quantities from limiters 84 and 85 are de
limiters 61, 62 encompasses in all directions the vector
livered to reverse rotator 88, which serves to reverse the
pattern 57 established by limiters 51, 52. The pattern
56 includes, in addition, a hole or restricted region 6e“
formed by the combined action of limiters 63 and 64
and relay units C and D. Thus, at this point the total
vector is limited to the area of overlap between the suc
cessively established vector patterns, which area of over»
rotational effect produced by rotator 83. Thus, the output vectors quantities, x, y and z are returned to their
original axial positions, but the vector sum thereof is
limited to the three dimensional pattern of FIG. 8D.
Essentially, the present invention relates to the concept
of selectively limiting a total vector quantity which is com
lap or superposition is deñned by the vector pattern 57. 40 posed of two or more component vector quantities. The
However, two holes or restricted regions have now been
component vector quantities may represent the analogs of
provided in pattern 57 `within which the total vector is
not permitted to fall.
The output signals from limiters 61 and 62 are deliv
ered, via the switch contacts C, D, to the adder circuits
67, 68 where they are respectively added to positive bias
ing potentials u", v". These positive biasing potentials
produce a -result »the opposite of negative biasing poten
tials u', v’ and hence the origin is shifted to the left and
downward as illustrated in FIG. 7D. These positive bias
ing potentials are of a lesser magnitude than the negative
biasing potentials u', v’.
the same or different types of data. For example, when
a force or pressure acts throughout a period of time, it
may be desirable to limit the force-time relationship in a
manner whereby a given maximum force is permitted to
act only for a short period and as the applied force de
creases the said period increases in some selected way.
Function generators based on the utilization of diode
characteristics may be used at signal frequencies well into
the megacycle region. If the vector signals to be limited
are alternating current, a special rotatable transformer
called a resolver is utilized to provide the necessary rota
The adders 67, 68 are coupled to the input of rotator
tion or transformation.
13, while the output of the latter is coupled to the input
While the present invention has been described by refer
of limiters 69, 70. Assuming a forty-tive degree rotation, 55 ence to particular embodiments thereof, it will be under
the vector pattern established by limiters 69, 70 appears as
stood that numerous modifications may be made by those
illustrated at 71 in FIG. 7E, the total vector pattern thus
skilled in the art without actually departing from the
being indicated by the solid lines.
spirit and scope of the invention.
Accordingly, a total vector pattern can be achieved hav
What is claimed is:
60
ing one or more holes or restricted regions therein at pre
selected positions. Such a pattern could find use, for
example, in automatic machine processes in those situa
tions where it is necessary to mill, plane or cut certain
regions of a surface while omitting others.
FIG. 8 shows a system in accordance with the present
invention wherein the .total vector is limited in three di
mensions. The limiters 11, 12, 14 and 15 and the rotator
13 function in the same manner as the identically num
bered elements of the FIG. 1 system, and hence the total
vector will be limited to an octagon in the x-y plane, as
illustrated in FIG. 8A. If maximum limits are now im
l. In a system for selectively limiting a total vector
quantity which is comprised of component vector quanti
ties, means for limiting each of said component vector
quantities between selected limits, means for transform
_ ing the limited component vector quantities into second
vector quantities which are angularly disposed with re
spect to said limited vector quantities, and means coupled
to the output of the transforming means for limiting each
of said second vector quantities between selected limits.
2. In a system for selectively limiting a total vector
quantity which is comprised of two or more component
vector quantities, means for imposing selected limits on
each of said component vector quantities so that the vec
posed upon the z vector in limiter 81, the total vector
will be limited to a three dimensional pattern such as
tor sum thereof is restricted to a ñrst predetermined vector
shown in FIG. 8B.
Such a three dimensional limiting will for many pur 75 pattern, means for transforming the limited component
3,044,705
vector quantities into second vector quantities which are
angularly disposed with respect to said limited component
pattern which is defined by said first and second vector
patterns, and means coupled to at least one of said lim
vector quantities, and means coupled to the output of the
iter means for providing at least one region within said
transforming means vfor imposing limits on each of said
total vector pattern in which the total vector'quantity
second vector quantities so that 'the vector sum of said 5 is not permitted to fall.
second vector quantities is restricted to a second prede
8. In a system for selectively limiting a total vector
termined Vector pattern, whereby the total vector quantity
is restricted to a total Vector pattern which is defined by
said ñrst and second Vector~ patterns.
quantity which is comprised of two component vector
quantities, limiter means for imposing selected limits on
each of said component vector quantities so that the
3. In a system for selectively limiting the magnitude
vector sum thereof is limited to a first vector pattern,
of a total vector quanti-ty which is comprised of orthogonal
means for transforming said limited component vector
component vector quantities, means for limi-ting the ampli
quantities into second vector quantities which are angu
tude of each of said orthogonal vector quantities between
larly disposed with respect to said limited component
selected limits, means for rotating the limi-ted orthogonal
vector quantities, limiter means coupled to the output of
vector quantities through a given angle, and means cou 15 the transforming means for imposing limits on each of
pled to the output of the rotating means for limiting the
said second vector quantities so that the vector sum of
amplitude of each of the rotated vector quantities between
said second vector quantities is restricted to a second
selected limits.
'
vector pattern whereby the total vector quantity is re
4. In a system for limiting the magnitude of a total
stricted to a total Vector pattern which is defined by said
vector quantity which is comprised of a pair~ of orthogonal
first and second vector patterns, and means coupled to at
component vector quantities, means for limiting the ampli
least one of said limiter means for providing a plurality
trude of said pair of orthogonal component vector quan
of'regions Within said total vector pattern in which the
tities to the same extent in both the positive and negative
total vector quantity is not permitted to fall.
directions, means for rotating the limited orthogonal com9. In a system for limiting, to a predetermined three
ponent vector quantities through a preselected angle, `and 25 dimensional pattern, a total vector quantity which is com
means coupled to the output of the rotating means for
prised of three orthogonal component vector quantities,
limiting the amplitude of the rotated orthogonal com
means for imposing selected limits on two of said orthog
ponent vector quantities to the same extent as the limits
imposed by the first-mentioned means, whereby the total
onal component vector quantities so that the vector sum
thereof is limited to a ñrst vector pattern, means for trans
vector quantity is limited to an Octagon.
30 forming said limited component vector quantities into
5. In a system for limiting the magnitude of `a total
second vector quantities which are angularly disposed
vector quantity which is comprised of two component
vector quantities, means for limiting the amplitude of
each of said component vector quantities between selected
maximum and minimum values, means for rotating the
limited component vector quantities through a predeter
mined angle, and means coupled to the output of the ro
tating means for limiting the amplitude of the rotated
component vector quantities between selected limits.
with respect to said limited component vector quantities,
means coupled to the output of the transforming means
for imposing limits on each of said second vector quan
tities so that the vector sum of said second Vector quan
tities is restricted to a second vector pattern, and means
for limiting the other of said orthogonal component vec'
tor quantities between selected limits, whereby the total
vector quantity is restricted to a total vector pattern which
6. In a system for selectively limiting a total vector 40 is defined by said first and second vector patterns and
quantity which is comprised of a pair of orthogonal com
ponent vector quantities, means for imposing selected
the limits imposed by the last-recited means.
l0. In a system for limiting, to a predetermined three
dimensional pattern, a total vector quantity which is
comprised of three orthogonal component vector quan
pattern, means coupled to the first-mentioned means for 45 tities, means for imposing selected limits on two of said
providing at least one region Within said vector pattern
orthogonal component Vector quantities so that the vector
in which the total vector quantity is not permitted to fall,
sum thereof is limited to a first vector pattern, means
means for transforming the limited component vector
for rotating the limited orthogonal component vector
quantities into second vector quantities which are angu
quantities through a given angle, means coupled to the
larly disposed with respect to said limited component Vec 50 voutput of the rotating means for imposing limits on each
tor quantities, and means coupled to the output of the
of the rotated orthogonal component Vectors so that the
limits on each of said component vector quantities so
that the vector sum thereof is limited to a ñrst vector
transforming means for imposing selected limits on each ‘
of said second vector quantities.
7. In a system for selectively limiting a total vector
quantity which is comprised of t-wo component Vector
quantities, limiter means for imposing selected limits on
each of said component vector quantities so that the vec
vector sum thereof is limited to a second vector pattern,
means for limiting the other of said orthogonal component
vector quantities between selected limits, means for ro
tating the said other orthogonal component vector quan
tity and one of the former two limited orthogonal com
ponent vector quantities through a given angle, means
tor sum thereof is limited to a first vector pattern, means
coupled to the output of the last-mentioned rotating means
for transforming said limited component vector quantities
for imposing selected limits on each of the orthogonal
into vector second quantities which are angularly disposed 60 vector quantities rotated thereby so that the vector sum
with respect to said limited component vector quantities,
thereof is limited to a third vector quantity pattern,
whereby the total vector is restricted to a total vector
limiter means coupled to the output of the transforming
pattern which is defined by said first, second and third
means for imposing limits on each of said second vector
quantities so that the vector sum of said second vector
vector patterns and the limits initially imposed on said
quantities is restricted to `a second vector pattern whereby 65 other orthogonal component vector quantity,
the total vector quantity is restricted to a total Vector
No references cited.
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