US2991007A - Polar coordinate aiming device - Google Patents

Description

July 4, 19m E. E. PERRET-GENTIL 2,991,007

POLAR COORDINATE AIMING DEVICE Filed Sept. 28, 1955 5 Sheets-Sheet 1 `uly 4, 1961 E. E. PERRET-GENTIL 2,991,007

POLAR COORDINATE AIMING DEVICE Filed Sept. 28, 1955 5 Sheets-Sheet 2 IN VEN TOR.

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July 4, 1961 E. E. PERRET-GENTIL POLAR COORDINATE AIMING DEVICE 5 Sheets-Sheet 3 Filed Sept. 28, 1955 INVENTO. W 5. fwd* BY M14/.Wa 49T.

July 4, 1961 E. E. PERRET-GENTIL 2,991,007

POLAR COORDINATE AIMING DEVICE Filed Sept. 28, 1955 5 Sheets-Sheet 4 July 4, 1961 E. E. PERRET-GENTIL 2,991,007

POLAR COORDINATE AIMING DEVICE 5 Sheets-Sheet 5 Filed Sept. 28, 1955 INVENTOR. M E. PM- M 2Q/M4 um United States Patent C M' 2,991,007 POLAR COORDINATE AIMING DEVICE Eduard E. Perret-Gentil, Zollikon, Switzerland, assignor to Contraves AG, Zurich, Switzerland, a firm Filed Sept. 28, 1955, Ser. No. 537,138 Claims priority, application Switzerland Oct. 16, 1954 4 Claims. (Cl. 23S-61.5)

The present invention relates to a polar coordinate aiming device-eg. a radar device or a theodolite--for the continuous aiming at a freely movable target from an observation point, i.e. from the emplacement of the aiming device.

In particular the invention relates to an aiming device which comprises at least one adjustment motor, which is steplessly controllable as regards its rotational output speed, for driving each member controlling an associated adjustment coordinate, and means for influencing the adjustment motors in the sense of a reduction of the occurring adjustment errors.

For example for anti-aircraft installations optical aiming devices have become known which consist of the combination of a theodolite with an optical range finder, and comprise adjustment motors for the variation of the optical adjustment coordinates, namely the azimuth angle a, the elevation angle )t and the oblique distance r to the target aimed at with respect to a polar coordinate system defined by the emplacement of the device. Such devices are frequently provided with velocity control appliances in which the adjustment velocities and of the adjustment coordinate Values, i.e. the rotational output speeds of the adjuster motors concerned are left at any time at a constant value until owing to an increase in the adjustment error, as ascertained by an observer for the corresponding adjustment coordinate, it is found necessary, to correct the adjustment velocity by operating a correcting member in such a manner that in the next following phase of observation this adjustment error is reduced.

Fully automatically operating aiming devices particularly radar devices, have become known which are capable of automatically following up the target in that they comprise metering means for ascertaining the adjustment errors, and automatically operating members for influencing the adjuster motors in the sense of reducing the adjustment errors.

When a target moved for example at a constant path velocity on a horizontal circular path about the zenith axis of the observation point, the adjuster motor for the azimuth angle a could continue to run permanently at the same output velocity of rotation, while the adjuster motors for the elevation angle A and for the oblique distance would have each to be at a standstill in a certain rotational position.

This assumption, however, presumes a special case which in practice is hardly realised even approximately. Rather a freely flying target will Hy approximately reetilinearly past the observation point, particularly the modern aircraft and rockets having such high path velocities that even curved flights of such flying bodies correspond much more accurately to a rectilinear ight-path than to a horizontal circular movement about the zenith axis.

Accordingly it is desirable that the aiming device should comprise means which allow to derive control values for the adjuster motors from a short-time following-up of the target, which inuence the rotational output speeds thereof in such a manner that the variations of the ad- 2,99l,07 Patented July 4, 1961 justment coordinate correspond to a rectilinearly continued ight of the target in the direction and at the velocity of the preceding phase of observation. In this case correction magnitudes would have to be introduced then only when the target observed departed from this rectilinearly extrapolated ight path.

This object has been almost reached tentatively in connection with the fire control plants for anti-aircraft guns. Therein the polar coordinates r, a, A of the target aimed at have been currently calculated by means of a system of transformations as varying Cartesian coordinates x, y, z. The rate of variations at, y', a' of these Cartesian coordinates were ascertained, and after smoothing out had been carried out (by ascertaining the mean Value), the amounts Ax, Ay, Az of aiming ahead could be ascertained by multiplication of these values with a time value corresponding to the ying time of the projectile. By the addition of these amounts of aiming ahead to the coordinate values x, y, z of the coordinates of the hitting point xt, yt, zt can be computed in advance. (Such computing devices for fire control plants have been described in detail in a previous British Patent No. 733,086.)

An additional back-transformation device allowed the assessment of the polar coordinates of the hitting point from the Cartesian coordinates, and these pre-calculated coordinates of the target point could be used for precontrolling the gun-laying device.

This kind of feed-back control of a gun-laying device for a straight ight is, however, fraught with noticeable delays, and presumes, that really all the three polar coordinates are ascertained currently. The computing system required necessarily comprises a transformation system for the conversion of polar into Cartesian coordinates, a computer group in Cartesian coordinates, and backtransformation system for regaining polar coordinates.

The present invention allows a substantial simplification in this respect, and allows primarily the adaptation to the particular data of various different problems. Thus it aims primarily at doing Without the aid of an auxiliary coordinate system, and accordingly at needing neither a transformationnor a back-transformation system. Furthermore according to the invention a feed-back control device for rectilinear target movements is to be provided, in which the introduction of correction values of a certain adjustment coordinate does not affect the other adjustment coordinates. Moreover Vby the invention the predisposition is to be set up for controlling individual polar coordinates per se, or in the combination of two only instead of all three adjustment coordinates, in such a manner that their variations correspond to a rectilinear Hight-path of the target.

In a polar coordinate aiming device for the continuous aiming at a freely moveable target from an observation point, according to the invention at least one adjustment motor of steplessly controllable output speed is in driving connection with adjuster means adjusting the said device in respect of each one polar coordinate thereof, and correction means are operatively connected to the said adjustment motor or motors in the sense of reducing the adjustment errors in the polar coordinate controlled by its associated adjustment motor through the associated adjuster means, an arrangement of computer elements being provided which handles a differential equation or a system of differential equations containing at least one of the said polar coordinates, which is variable in time, and its derivatives in time alone, corresponding to a rectilinearly continued Hight of the target aimed at, in the direction and at the velocity of the motion phase immediately preceding in time, the said adjustment motor or motors forming part of, and being controlled by, the said arrangement of computer elements.

It has been found that for the case of a rectilinear iiight at constant velocity a comparatively simple differential equation, or equations, can be formulated either for all three polar coordinates and their derivatives in time, or for two of them only, for example `the azimuth angle and the elevation angle, or for a single polar coordinate only, and their derivatives in time, which equation(s) is (are) capable of being solved by automatically operating arrangements of computer elements, which include the adjuster motor or motors for the polar coordinate or coordinates involved, i.e. are on the one hand influenced by them, and on the other hand influence the said adjustment motor or motors.

In order that the invention may be clearly understood and readily carried into etect, some embodiments thereof will now be described by Way of example with reference to the accompanying drawings, in which:

FIG. l is an isometric spatial representation of the assumptions;

FIG. 2 is an elevation of an optical gun-laying device for anti-aircraft lire control plants with measuringand correcting-members for the azimuth angle, the elevation angle and the oblique distance;

FIG. 3 is a wiringand computing diagram for the straight flight control of the device according to FIG. 2 in all three polar coordinates;

FIGS. 4, 5, 6 are wiringand computing diagrams for the straight ight control of individual polar coordinates;

FIG. 7 shows a wiringand computing diagram for the straight ilight control of the elevation angle with the use of auxiliary values of the azimuth angle control according to FIG. 5. For the sake of simplification it has been assumed that the target to be followed up ies approximately horizontally.

FIG. 8 is a wiring and computing diagram for a rectilinear target movement in the horizontal plane.

According to FIG. 1 a ying body K moves on a rectilinear path k at a uniform velocity. At the xedly chosen observation point an aiming device for constantly aiming at the said target is mounted. The vertical zenith plane z, fori` example oriented in northern direction, through the observation point 0 defines together with the horizontal plane H a polar coordinate system xed in space. For the point K1 of the flight path the local vector 0K1 has the length r1; its projection on the horizontal plane H includes with the intersecting line n of the two planes of reference the azimuth angle al, while the local vector 0K1 includes with its projection 0K1' the elevation angle A1. The length r1 of the vector 0K1' corresponds to the magnitude r1. cos A1. Likewise the point K2 of the Hight path has the polar coordinates a2, z, f2.

In order to make the variations of the coordinate values visible, the triangle 0K1 K1 has been turned into the plane of the triangle 0K2 K2' and has been drawn in this plane as the triangle w1, Obviously the following relations exist:

of2 1-v13=f1(ikv) 21=D=2(l-`ikiv) fz'r1=fn=fa(f,kiv)

wherein the values of the resulting diierences are functions of the time t, the position of the flight path k in space, and the path velocity v.

On the basis of purely mathematical operations which can be carried out by any person skilled in the ant for rectilinear flights at constant path velocity the following systems of differential equations between the running polar coordinates a, A and k measured and their derivatives in time A, and 1", and X and f etc. can be derived:

For a rectilinear movement taking place in the horizontal plane, for example of an armored car, the equations (Ia) and (Ir) are simplified in the following manner):

(III *A) While accordingly in the system of Equations I all the polar coordinate values are interconnected with one another, the system of Equations II is characterized in that merely the individual coordinate values and their derivatives are interconnected in an equation. The Equation IIIA or its simpliiied version HI*A is an example for the interconnection of the values of the azimuth angle and elevation angle and/or the derivatives of these, values in an equation.

All the left hand sides of the above equations have the value zero, provided the magnitudes used have the correct value for a straight flight. When, however, this assumption is not fulfilled, the correction values A, A# and AA have to be introduced with appropriate coeicients, as indicated in each equation by the correction member written yafter on For the time being these correction values may remain disregarded, since they have to be used than only when the target aimed at does not ily on a straight line path and/or is followed up inaccurately.

In FIG. 2 the aiming device is illustrated which consists of the combination of a theodolite with an optical range finder (telemeter). The platform 1 is adapted to be turned relative to the fixed base Z about a vertical shaft, so that the azimuth angle a is variable.

In the columns 3y standing on the platform 1 a horizontal cam'er shaft 4 for the optical instruments, particularly for a telemeter 5, is journalled rotatably. There are three ocular pieces 6, 7, 8 provided, each of which is associated with an observer for a certain polar adjustment coordinate.

Thus, the ocular piece 6 and a correcting hand Wheel 60 are associated with the observer for the azimuth angle a, which he operates then only when he ascertains in his ocular piece that the azimuth angle of the flying body aimed at does not correspond to the azimuth angle adjusted on the device.

In a like manner the observer of the elevation adjustment angle corrects by means of the hand wheel 70 the elevation angle k adjusted on the instrument insofar as he lascertains an adjustment error in this coordinate.

With the distance observer the ocular piece 8 and the hand Wheel 80 are associated. All the adjustments of the members for the control of the adjustment coordinates are effected by adjuster motors which are steplessly controllable as regards their rotational output speed, which motors are built into the other superstructures of the aiming device.

FIG. 3 shows a computerand wiring-diagram for the straight-flight feed back control of an aiming device according to FIG. 2. The individual members are diagrammatically represented in the most simplified manner.

The units denoted M therein are adjuster motors which are designed for turning their respective output shaft at a rotational velocity which in magnitude and direction is proportional to a control voltage which is preferably supplied via an amplifier. It is assumed to be known that such adjuster motors moreover comprise a tachometer generator mounted on the motor shaft (not shown here) which feeds back a voltage proportional to the actual rotational speed to an amplifier (likewise not shown), in order that the whole adjuster motor unit may be stabilized. An exciter voltage of a certain phase position and of constant amplitude and of the same frequency as the control voltage is likewise supplied to the adjuster motor unit in addition to the control voltage.

Moreover in the diagram drawings tachometer generators G are indicated which produce an output voltage which as regards magnitude and sign corresponds to the product of an input alternating voltage (preferably a voltage l of a constant unit amplitude) and the rotational speed of the driving shaft. The construction of such tachometer generators can also be assumed to be known.

Further groups of computer elements are mounted each on a mechanical shaft driven by a respective adjuster motor M, the adjustment angle of which accordingly varies following lany desired function in time. These computer members have the object of multiplying the input voltage supplied to them by a certain function of the angle of rotation of their driving shaft. 'Ihus the members X multiply the amplitudes of their input voltages with-the positive or negative angle of rotation of their driving shaft as measured with respect to an initial position, while the members l/X multiply their input voltages with the reciprocal value of the angle of rotation of the driving shaft. Such computer elements are known in themselves and may e.g. be potentiometer resistors with an appropriate characteristic, or computer condensers.

Other computer elements, which are denoted sin, cos or tan, multiply their Iinput voltage with the sine, the cosine or the tangent, respectively, of the angle of rotation of their driving shaft, and computer members of this kind, too, are known in themselves.

Ihe addition members, denoted -l, add two or more input voltages according to magnitude and sign, so that their output voltages represent the algebraic sum of their input voltages. The same are likewise known in themselves.

With the sign-reversing members are denoted, which are designed for multiplying the input voltages by the value of -1, and practically represent phase reversing members.

Finally correction members P are used which allow to reduce or, if desired, to delay their input voltage to an adjustable extent in order to reduce the effect of their output voltage on the subsequent computer member. They may be voltage dividers; they serve primarily for inuencing the output voltages of the tachometer generators.

As the last kind of computer members there are differential gearings D provided, each having two input shafts and one output shaft, which are designed to add up the angles of their input shafts mechanically.

Provision is made that all the voltages used are alter-f nating voltages of definite and constant frequency, their amplitudes being indicated on the transmission lines, of which one pole only is drawn, either by the constant reference value l or by the value resulting from the action of the computer members. Negative magnitude signs mean that the voltage concerned is turned 180 in its phase position relative to the positive normal values. The input voltages of the computer elements are indicated by arrows pointing towards the elements concerned.

The meaning of the angles of rotation of the rotary shafts indicated by double lines is given by the underlined symbols written on, e.g. i 1 i and here, too, the input magnitudes are characterized by arrows.

In all FIGS. 3 to 7 socalled path-velocity controls are arranged for the individual adjustment-coordinates et, A, r.

For example the adjuster motor M for the azimuth angle a drives its output shaft with a constant rotational speed as long as its control voltage remains unaltered as regards magnitude and sign. This control voltage has accordingly the dimensional value while the angle of rotation of the output shaft then corresponds to the azimuth angle a.

On a hand wheel 60 a correction value Aa of the azimuth angle can be adjusted which in the pertaining differential gearing D is added to the angle of rotation a of the motor output shaft Sa, so that the angle of rotation of this output shaft of said differential gearing corresponds to the value u+Aa. This shaft S,l may be for example the driving shaft of the platform 1 of the aiming device according to PIG. 2, or it can be designed as the control shaft for an :adjuster motor of the azimuth angle coordinate its rotational position being transmitted, if desired, via a so-called electrical intermediate shaft (electro-mechanical remote control means for the transmission of the angle of rotation of one rotor to another rotor) to the adjustment motors concerned. On the shaft of the hand wheel 60 a tachometer generator G is mounted the output voltage of which is proportional to the speed of rotation of the shaft of the hand wheel concerned. Since the observer will naturally endeavour to correct quickly varying adjustment errors of the azimuth angle by turning the hand wheel quickly, while with slowly increasing adjustment errors he will turn the hand wheel but slowly, the output voltage A@ of the tachometer value for the control voltage of the adjuster motor generator represents an appropriately adapted correction M,l concerned. It is reduced in a correction member P,z to an adjustable extent, and is added in an addition member to the control voltage so that also the rotational speed of the adjuster motor is corrected in the correct sense.

Equal path-velocity controls are provided `in all FIGS. 3 to 7 also for the values )t and r, the hand wheels 70 and serving for the introduction of the correction "7 values A). and Ar, respectively, and the output shafts 8 S, of the diierential gearings D concerned adjusting either the shaft 4 for the elevation angle or the shiftablc prism in the telemeter 5, or acting as control shafts for the adjuster motors of these members, if desired.

The wiring diagram according to FIG. 3 corresponds to the system of Equations Ia, Ir, Dt as will be seen without difliculty from the reference values inserted. However, the corresponding differential equations are equal to zero then only, when the target aimed at has been followed up by operating the hand wheels for a suiciently long time, and actually moves at a constant path velocity on an accurately straight trajectory.

As will be seen from FIG. 3, also the values ana, af'

and

which are written into the Equations Ia, Ir and Ik, are transmitted via correction members P to a reduced extent on to the adjuster motors Mj', M M5., for thea-J2, and )..shafts, respectively, so that these values, too, share in being influenced by the corrections. FIG. 3 accordingly represents an arrangement of computer elements which is inuenced by all three adjuster motors for the three adjustment coordinates, which is designed for realizing the system of diierential Equations Ia, Ir, Ik, which contains the three adjustment coordinates and their derivatives in time alone, and for influencing the three adjustment motors accordingly, so that the three output shafts of these adjuster motors rotate accordingly in such a manner that the variations in time of their rotational positions correspond to a rectilinearly continued ight of the target aimed at in the direction and at the velocity of the phase of motion preceding in time. By means of the hand wheels 60, 70, 80, the associated tachometer generators G and correction members P, the necessary correction values forreducing the adjustment errors, resulting from inaccurately following up the target or from the latter not ying uniformly on a straight course, can be introduced into the arrangement.

In FIGS. 4, 5, 6 which represent devices for solving the differential Equations IIa, Hr and Hx, respectively, there are moreover provided adjuster motors Mii, Mff, MX for 5.-, and X-shafts, respectively, to which on the one hand as control voltages the sums of the left hand sides of the equations are supplied, and moreover the correction values -q'AC-t, -g-,ax

respectively, reduced by reduction members P, Pf, P3., respectively are supplied.

Devices according to FIGS. 4, 5, 6 may each serve for the feed back control of one adjustment coordinate per se, which has the advantage, that the correction values for one coordinate do not alect the other coordinates. Moreover feed back control devices according to these figures can be used also for aiming devices, in which not all three polar coordinates, but, as for example in a theodolite, merely the azimuth angle et and the elevation angle A per se, or as with certain radar devices merely the azimuth angle and the oblique distance r are metered.

In the embodiments according to FIGS. 4 to 6, with each adjuster motor for a certain adjustment coordinate an arrangement of computer elements is associated, which is influenced from this adjuster motor and which, on the other hand, generates a control voltage for the same in the sense of realizing that one of the differential equations which contains the adjustment coordinate concerned and/or its derivatives in time alone, which corresponds 8 to a rectilinearly continued ight of the target aimed at in the direction and at the velocity of the motion phase preceding in time (Equations IIa, IIr and IIA, respectively). Here, too, the means for introducing the correction values are indicated in the drawing.

The embodiment according to FIG. 7 concerns a special case in which it is the question of controlling the elevation angle )t adjusted on the aiming device in such a manner that its variations in time correspond to a horizontal light on a straight line of the target aimed at. With the use of the control values a and a, which for example can be derived from a particular azimuth angle control according to FIG. 4, the differential Equation IIIiA can be solved by the wiring arrangement according to FIG. 7. Insofar as the target aimed at does not fly horizontally, correspondingly such manual correction values AA are to be introduced more often. This embodiment is particularly suitable for the rectilinear Hight control of a theodolite, with which the oblique distance r is not metered.

The azimuth angle adjustment is then fed back into its self only in accordance with the Equation Ila and according to FIG. 4 and the total expense for computer members is in this case considerably smaller than that of the combination of the FIGS. 5 and 6 put together, which would fulfill the same requirement for straight line flights of any inclination desired.

The embodiment according -to FIG. 7 corresponds therefore to the case in which an arrangement of computer elements is influenced by the variation of two predetermined polar adjustment coordinates, and is designed for realizing a differential Equation IIIA which contains the two adjustment coordinates and/ or their derivatives in time only, and for influencing one of the adjuster motors, namely the adjuster motor Mk for the elevation angle in such a manner that this coordinate varies in the sense of a rectilinearly continued flight of the target.

FIG. 8 relates to an advantageous control device for an aiming device which follows up the movements of a target in a horizontal plane. The Equations I'r and *a are solved in combination The arrangement of computer elements illustrated in FIG. 8 is inuenced by two adjuster motors Ma, Mr in dependence of the variations of two adjustment coordinates, namely the azimuth angle a and of the oblique distance r, and these adjuster motors are controlled by this arrangement of computer elements in the sense of fullling the equation system I* in such a manner, that the adjustment coordinates inuenced by the adjuster motors vary in accordance with a rectilinearly continued Hight of the target aimed at.

In all embodiments illustrated the correction values Ah, Aa and Ar and the values Aj., A and A1, respectively can be introduced into the arrangement of computer elements in a different way from that illustrated.

It would also be possible to use automatically operating members, e.g. differential photocells, or electric error indicating members for ascertaining the adjustment errors, such as used with automatically following-up radar aiming devices, and to introduce their initial Values into the computer arrangement.

Inherently all the computer elements could be constructed purely mechanically; for example the adjuster motors could be replaced by the combination of motors running at constant rotational speed with steplessly controllable output gearings.

What we claim is:

l. A correction arrangement for a polar coordinate automatic tracking apparatus having tracking devices adjustable to the azimuth angle, elevation angle and distance coordinates, respectively, of a moving target relative to a fixed point by operation of manually operable control means, in combination, a first, second and third closed servo-computer circuit respectively associated with the azimuth angle, elevation angle and distance coordinates of the moving target, each of said circuits comprisaesinet ing at least two sets of analogue computer means, namely a iirst set of analogue computer means including a iirst rotary member, iirst motor means for rotating said iirst rotary member, and transmission means for transmitting rotation of said first rotary member to the tracking device respectively associated with the same coordinate as the particular servo-computer circuit for adjusting the respective tracking device toward the target, said first set of computer means being capable of causing, during a given period of time, a rotary movement of said first rotary member proportional to the integral over such period of the rst derivative in time of the respectively associated coordinate said tirst derivative being represented by a tirst control voltage applied to said iirst motor means, and a second set of analogue computer means including a second rotary member and second motor means for rotating said second rotary member, said second set of computer means being capable of causing, during a given period of time, a rotary movement of said second rotary member through an angle proportional to the integral over such period of the second derivative in time of said respectively associated coordinate, said second derivative being represented by a second control voltage applied to said second motor means, said second set of computer means further including output means operated by said second rotary member and connected with said iirst motor means for furnishing thereto `said rst control voltage depending upon said angle of rotation of said second rotary member; iirst, second and third correction means respectively associated with said azimuth angle, elevation angle and distance coordinates, said correction means being operatively interposed between the respective manually operable control means and the respective transmission means of said iirst sets of analogue computer means, respectively, and each including rotary means for introducing into said transmission means a corrective rotation in superposition on said rotation transmitted to the respective tracking device from the respective iirst rotary member, for reducing any coordinate diierence between momentary values of the respective coordinate of the moving target and the prevailing adjustment of the respective tracking device, and generator means driven by said rotary means for generating a correction voltage proportional to the speed of said corrective rotation; and a plurality of interconnected secondary analogue computer means including groups thereof connected with said generator means, respectively, and operatively connected with said first, second and third servo-computer circuits for adding to said iirst control voltages applied to said rst motor means of said iirst sets of -analogue computer means, respectively, a voltage proportional to said correction voltage generated by the respective one of said generator means, and for applying to the second -motor means of said second sets of analogue computer means, respectively, said second control voltage at values determining the rotation of the respective second rotary members at speeds proportional to il, i, respectively derived from the dilerential equations )t-l-2i- -lsin A cos }\=9TA wherein )1, are said first control voltages representing respectively the iirst derivatives in time of said azimuth angle, elevation angle and distance coordinates appearing as the prevailing adjustment of the respective tracking devices, )1, 1'- are voltages respectively proportional to the second derivatives in time of said coordinates, )t and r are the values of said elevation angle and distance coordinates, respectively, Aa, A A are said generator means of said correction means, respectively, associated with said Vif) azimuth angle, elevation angle and distance coordinates, respectively, a is a coetiicient, and T is a time value, said correction voltages Aa, AA, ai" respectively, being reduced to zero if the target moves steadily along a substantially straight line path and is followed up by adjustment of the tracking devices accurately, in which case the respective second motor means comes to a standstill While the respective first motor means rotates at a constant speed, whereby the manual adjustment of the tracking devices to the varying positions or coordinates of the moving target is accelerated and aided through the operation of the correction arrangement.

2. A correction arrangement for a polar coordinate automatic tracking apparatus, having tracking devices adjustable to at least one of the polar coordinates, namely azimuth angle, elevation and distance, of a moving target relative to a fixed point -by operation of manually operable control means, in combination, a closed servoacomputer circuit associated with said one of said polar coordinates of the moving target, said circuit comprising three sets of analogue computer means, namely a iirst set of analogue computer means including a lirst rotary member, iirst motor means for rotating said first rotary member, and transmission means for transmitting rotation of said rst rotary member to the tracking device respectively associated with the same coordinate as the particular servo-computer circuit for adjusting the respective tracking device toward the target, said rst set of computer means being capable of causing, during a given period of time, a rotary movement of said rst rotary member proportional to the integral over such period of the first derivative in time of said one associated coordinate said first derivative being represented by a Iirst control voltage applied to said tirst motor means, a second set of analogue computer means including a second rotary member and second motor means for rotating said second rotary member, said second set of computer means being capable of causing, during a given period of time, a rotary movement of said second rotary member through an angle proportional to the integral over such period of the second derivative in time of said one associated coordinate, and a third set of analogue computer means including a third rotary member and third motor means for rotating said third rotary member, said third set of computer means being capable of causing, during a given period of time, a rotary movement of said third rotary member through an angle proportional to the integral over such period for determining the momentary values of the time integral of the third derivative in time of one associated coordinate, said second derivative being represented by a second control voltage applied to said second motor means, said second set of computer means further including output means operated by said second rotary member and connected with said iirst motor means for furnishing thereto said first control votage depending upon said angle of rotation of said second rotary member, said third derivative being represented by a third control voltage applied to said third motor means, said third set of computer means further including output means operated by said third rotary member and connected with said second motors means for furnishing thereto said secondv control voltage depending upon said angle of rotation of said third rotary member; correction means respectively associated with one of said azimuth angle, elevation angle and distance coordinates, said correction means being operatively interposed between the respective manually operable control means and the respective transmission means of said lfirst sets of analogue computer means, respectively, and each including rotary means for introducing into said transmission means a corrective rotation in superposition on said rotation transmitted to the respective tracking device from the respective first rotary member, for reducing any coordinate diierence between momentary values of the respective coordinate of the moving target and the prevailing adjustment of the respective tracking device, and

generator means driven by said rotary means for generating a correction voltage proportional to the speed of said corrective rotation; and a plurality of interconnected secondary analogue computer means including groups thereof connected with said generator means, respectively, and operatively connected with said irst, second and third servo-computer circuits for adding to said rst control voltages applied to said irst motor means of said rst sets of analogue computer means, respectively, a voltage proportional to said correction voltage generated by the respective one of said generator means, and for applying to the second motor means of said second sets of analogue computer means, respectively, said second control voltages at values determining the rotation of the respective second rotary members at speeds proportional to 71,1, respectively derived from at least one of the diierential equations sin2 A cos )vl-45@ cos M24-eos2 A) sii sin i 1+2 @OS2 \)=,;,,Ai (for the i coordinate) wherein i, are said iirst control voltages representing respectively the rst derivatives in time of said azimuth angle, elevation angle and distance coordinates appearing as the prevailing adjustment of the respective tracking devices, X, are voltages respectively proportional to the second derivatives in time of said coordinates, )t and r are the values of said elevation angle and distance coordinates, respectively, A, A.,'\, Ar are said correction voltages generated by said generator means of said correction means, respectively, associated with said azimuth angle, elevation angle and distance coordinates, respectively, a is a coefficient, and T is a time value, said correction voltages Aa, AX, Ar, respectively, being reduced to zero if the target moves steadily along -a substantially straight line path and is followed up by adjustment of the tracking devices accurately, in which case the respective second motor means comes to a standstill while the respective rst motor means rotates at a constant speed, whereby the manual adjustment of the tracking devices to the varying positions or coordinates of the moving target is accelerated and aided through the operation of the correction arrangement.

3. A correction arrangement for a polar coordinate automatic tracking apparatus having tracking devices adjustable to at least one of the polar coordinates, namely azimuth angle, elevation and distance, of a moving target relative to a fixed point by operation of manually operable control means, in combination, a closed servocomputer circuit associated with said one of said polar coordinates of the moving target, said circuit comprising two sets of analogue computer means, namely a first set of analogue computer means including a rst rotary member, tirst motor means for rotating said first rotary member, and transmission means for transmitting rotation of said first rotary member to the tracking device respectively associated with the same coordinate as the particular servo-computer circuit for adjusting the respective tracking device toward the target, said rst set of computer means being capable of causing, during a given period of time, a rotary movement of said iirst rotary member proportional to the integral over such period of the rst derivative in time of said one associated coordinate said tirst derivative being represented by a first control voltage applied to said first motor means, and a second set of analogue computer means including a second rotary member and second motor means for rotating said second rotary member, said second set of computer means being capable of causing, during a given period of time, a rotary movement of said second rotary member through an angle proportional to the integral over such period of the second derivative in time of said one associated coordinate, said second derivative being represented by a second control voltage applied to said second motor means, said second set of computer means further including output means operated by said second rotary member and connected with said first motor means for furnishing thereto said rst control voltage depending upon said angle of rotation of said second rotary member; tirst, second and third correction means respectively associated with one of said azimuth angle, elevation angle and distance coordinates, said correction means being operatively interposed between the respective manually operable control means and the respective transmission means of said rst sets of analogue computer means, respectively, and each including rotary means for introducing into said transmission means a corrective rotation in superposition on said rotation transmitted to the respective tracking device from the respective tirst rotary member, for reducing any coordinate diierence between momentary values of the respective coordinate of the moving target and the prevailing adjustment of the respective tracking device, and generator means driven by said rotary means for generating a correction voltage proportional to the speed of said corrective rotation; and a plurality of interconnected secondary analogue computer means including groups thereof connected with said generator means, respectively, and operatively connected with said iirst, second and third servo-computer circuits for adding to said first control voltages applied to said rst motor means of said first sets of analogue computer means, respectively, a voltage proportional to said correction voltage generated by the respective one of said generator means, and for applying to the second motor means of said second sets of analogue computer means, respectively, said second control voltages at values determining the rotation of the respective second rotary members at speeds proportional to X, f, respectively derived from at least one of the differential equations wherein i, are said rst control voltage representing respectively the rst derivatives in time of said azimuth angle, elevation angle and distance coordinates appearing as the prevailing adjustment of the respective tracking devices, X, i", are voltages respectively proportional to the second derivatives in time of said coordinates, a and r are the values of said elevation angle and distance coordinates, respectively, Aa, AX, and A are said correction voltages generated by said generator means of said correction means, respectively, associated with said azimuth angle, elevation angle and distance coordinates, respectively, a is a coeticient, and T is a time value, said correction voltages Aa, Ai, A respectively, being reduced to zero if the target moves steadily along a substantially straight line path and is followed up by adjustment of the tracking devices accurately, in which case the respective second motor means comes to a standstill while the respective first motor means rotates at a constant speed, whereby the manual adjustment of the tracking devices to the varying positions or coordinates of the moving target is accelerated and aided through the operation of the correction arrangement.

4. A correction arrangement for a polar coordinate automatic tracking apparatus having tracking devices adinstable to two of the polar coordinates, namely azimuth angle, and distance, respectively, of a moving target relative to a iixed point by operation of manually operable control means, in combination, a first and a second closed servo-computer circuit respectively associated with said two polar coordinates, each of said circuits comprising two sets of analogue computer means, namely a iirst set of analogue compter means including a rst rotary member, iirst motor means for rotating said first rotary member, and transmission means for transmitting rotation of said iirst rotary member to the tracking device respectively associated with the same coordinate as the particular servo-computer circuit for adjusting the respective tracking device toward the target, said first set of computer means being capable of causing, during a given period of time, a rotary movement of said rst rotary member proportional to the integral over such period of the tirst derivative in time of the respectively associated coordinate said first derivative being repnesented by a first control voltage applied to said first motor means, and a second set of analogue computer means including a second rotary member and second motor means for rotating said second rotary member, said second set of computer means being capable of causing, during a given period of time, a rotary movement of said second rotary member through an angle proportional to the integral over such period of the second derivative in time of said associated coordinate, said second deriva tive being represented by a second control voltage applied to said second motor means, said second set of computer means further including output means operated by said second rotary member and connected with said first motor means for furnishing thereto said first control voltage depending upon said angle of rotation of said second rotary member; iirst, second and third correction means respectively associated with two of said azimuth angles, elevation angles and distance coordinates, said correction means being operatively interposed between the respective manually operable control means and the respective transmission means of said first sets of analogue computer means, respectively, and each including rotary means for introducing into said transmission means a corrective rotation in superposition on said rotation transmitted to the respective tracking device from the respective iirst rotary member, for reducing any coordinate diierence between momentary values of the respective coordinate of the moving target and the prevailing adjustment of the respective tracking device, and generator means driven by said rotary means for generating a correction voltage proportional to the speed of said corrective rotation; and a plurality of interconnected secondary analogue computer means including groups thereof connected with said generator means, respectively, and operatively connected with said first, second and third servo-computer circuits for adding to said iirst control voltages applied to said iirst motor means of said first sets of analogue computer means, respectively, a voltage proportional to said correction voltage generated by the respective one of said generator means, and for applying to the second motor means of said second sets of analogue computer means, respectively, said second control voltages at values determining the rotation of the respective second rotary members at speeds proportional to a, it, r, respectively derived from the differential equations wherein )1, are said first control voltages representing respectively the first derivatives in time of said azimuth angle, elevation angle and distance coordinates appearing as the prevailing adjustment of the respective tracking devices, )1, i are voltages respectively proportional to the second derivatives in time of said coordinates, A and r are the values of said elevation angle and distance coordinates, respectively, Aa, A); A' are said correction voltages generated by said generator means of said correction means, respectively, associated with said azimuth angle, elevation angle and distance coordinates, respectively, a is 4a coefficient, and T is a time value, said correction voltages A, Ait, A1' respectively, being reduced to zero if the target moves steadily along a substantially straight line path and is followed up by adjustment of the tracking devices accurately, in which case the respective second motor means comes to a standstill while the respective first motor means rotates at a constant speed, whereby the manual adjustment of the tracking devices to the varying position or coordinates of the moving target is accelerated and aided through the operation of the correction arrangement.

References Cited in the iile of this patent UNITED STATES PATENTS 2,404,011 White July 16, 1946 FOREIGN PATENTS 706.512 Great Britain Sept. 28, 1951

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