Патент USA US3044715код для вставки
July 17, 1962 c. c.w||_|_H1TE 3,044,705 LIMI'I'ER SYSTEMS Filed Dec. 8, 1958 6 Sheets-Sheet 2 F/G. 2 Rfb LL » YYY /26 RL' 24 F/G. 2A IOVGEUTLPUTA E /NPU T VOL TA GE F/G. 4 /Nl/ENTOR y 6.6. W/L/_H/TE ATTORNEY July 17, 1962 C. C. WILLHITE LIMITER SYSTEMS Filed Dec. 8, 1958 Säì Ú 6 Sheets-Sheet 5 X im V@RODk@ .w.2k /NVE/vrof? C. C. W/LLH/TE BV Wm 7%. #2g A 7' TORNEY July 17, 1962 c. c. wlLLHlTE 3,044,705 LIMITER SYSTEMS ' Filed Deo. 8, 1958 6 Sheets-Sheet 4 F/G. 6 LIN/TER LIN/TER /44 ROTA TOR _ AMPLIFIER L/M/TER \ CIRCUIT T Lul/TER LIN/TER L .7 l F/a. 6,4 50 Ffa. 6B V, _,a' L l ,a /N VEN TOR @y c. c. W/LLH/rf www. “fÁ-LQ A TTORNEV July 17, 1962 C. C. WILLHITE 3,044,705 LIMITER SYSTEMS Filed Dec. 8, 1958 6 Sheets-Sheet 5 fm@ „ÉlQN .Élmm /A/l/EA/rof?V C. C. W/ L L H/ TE Arron/vir July 17, 1962 C. C. WILLHITE 3,044,705 LIMITER SYSTEMS Filed Deo. 8, 1958 6 Sheets-Sheet 6 QQ ><I là mm QOKVRQ /NVEA/ro/P C. C. W/LLH/ 7'E ATÍ'ORNEY -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.