US2848159A - Apparatus for evaluating the rate of change of a magnitude - Google Patents

Description

Aug. 19, 1958 a. H. STEPHENSON EI'AL 2,343,159

APPARATUS FUR EVALUATING THE RATE OF CHANGE OF A MAGNITUDE I Filgd April 17. 1952 STORE ammo O 2 I 5708: F/LLED [2/ AzZ-As 1 w [SH/7th a e/veal I8 I d I 2 I ISM/76H a 0560 l l 3 I 5 I Mvnfora: GEOFFREY HUSON STEPHENSON RICHARD HERBERT BOOTH MAW nrramvs/ United States Patent APPARATUS FOR EVALUATING THE RATE OF CHANGE OF A MAGNITUDE Geoiirey Huson Stephenson, London, and Richard Herbert Booth, Buckinghamshire, England, assignors to Electric & Musical Industries Limited, Hayes, England, a British company Application April 17, 1952, Serial No. 282,854

Claims priority, application Great Britain April 18, 1951 5 Claims. (Cl. 235-61) This invention relates to potentiometers, and especially but not exclusively to apparatus employing potenti ometers for evaluating the rate of change of a variable.

In the specification of United States application Serial No. 207,490 there is described apparatus for evaluating a smoothed rate of change of a variable (say displacement) whose instantaneous value is observed at discrete times. As described in the aforesaid application, and as will hereinafter appear, the smoothing reduces to a minimum the mean square deviation between the observed values of the variable (which values are subject to random errors) and the corresponding set of values represented by the smoothed rate. The smoothing is sometimes referred to as applying a weighting function since the effect of the smoothing is to weigh the evaluation of the rate more in favor of some of the values of the variable" than of others. The apparatus described in the aforesaid specification involves the employment of a tightly coupled inductive potentiometer having sliding contacts which cyclically traverse the potentiomer and the apparatus has the desirable property that observations made outside a predetermined interval referred to as the weighting period play no part in the rate evaluation, so that stale observations do not enter into the evaluation. However, the structure of a potentiometer such as described above has been associated with certain difiiculties and the main object of the present invention is to reduce such difficulties.

According to the present invention there is provided a potentiometer comprising an array of impedance sections, a switch between each section of said array and the next section thereof and between the last section of said array and the first section thereof, each switch 'be ing arranged when. closed to connect adjacent sections, means for feeding electrical signals to fixed points in the respective sections, and means for operating said switches in a cyclic order to connect a cyclically changing plurality of said sections in a series chain, said cyclic order being predetermined to produce the effect of displacing the feed points in succession along the chain. This effect is produced by operating the switches so as to incorporate the impedance sections in succession in the chain at one end and to discard them subsequently from the chain at the other end. As each new section is incorporated in the chain, the previously incorporated sections and with them the corresponding feed points are in efiect displaced towards the end of the chain from which they are eventually discarded, this process being repeated in each cycle.

According to one application of the present invention there is provided apparatus for evaluating the rate of change of a first variable, say displacement, with respect to a second variable, say time, comprising an array of inductances magnetically coupled one to another, a switch between each inductance of said array and the next inductance thereof and between the last inductance of said array and thefirst inductance thereof, each switch when closed being arranged to connect the adjacent inductances,

Patented Aug. 19, 1958 a plurality of impedances one leading to a fixed point on each inductance, means for operating said switches in a cyclic order to connect a cyclically changing plurality of said inductances in a series chain, the cyclic order being predetermined to produce the effect of displacing said fixed points in succession along said chain, and means for applying to said impedances alternating voltages having amplitudes representative of values of the first variable corresponding to values of the second variable represented by said fixed points, the impedance and mutual coupling of said inductances being such that the potential gradient set up along the chain is representative of a smoothed rate of change of the first variable with respect to the second variable. By the potential gradient along the chain is meant the variation in amplitude of the alternating voltage set up between the ends of the chain, the mutual coupling between the inductances being arranged so that the amplitude varies substantially linearly along the chain.

In this application of the invention, means are preferably provided for modifying the cyclic operation of said switches so as to reduce the number of inductances maintained in the series chain. This'provision enables the interval over which the smoothed rate is evaluated to be reduced when the evaluated rate is changing rapidly and is thus more susceptible to error in evaluation, and means may be provided, responsive to variations in the evaluated rateof change or of a magnitude dependent thereon for rendering the means for modifying the cyclic operation of the switches automatically effective when the rate of variation exceeds a predetermined value.

In order that the said invention may be clearly understood and readily carried into effect, the same will now be more fully described with reference to the accompanying drawings.

Figure 1 illustrates diagrammatically one form of apparatus inaccordance with the present invention, and

Figure 2 illustrates mechanism for operating switches in the apparatus of Figure l.

Referring to the drawing, it will be assumed that there is an interval 7 between successive observations of the variable (say x) and that the time rate of change of this magnitude is to be evaluated. The apparatus illustrated is arranged to operate with a maximum weighting period of 9-r,that is, the observations of x taken into account in the rate evaluation cover an interval which does not exceed 91. The total weighting period of one cycle of operations is divided into twenty equal intervals, the starts of which are denoted at times 0, 1, 2 19, the observations of x being made at the times 1, 3, 5 19 on this time scale.

The apparatus comprises an array of ten tightly coupled inductive sections L L sections being shown in the drawing for convenience of illustration. The sections are arranged to have a very high shunt impedance and are not tied to any reference potential. Switches A A A are interposed as shown between each section of the array and the next section and between the last section and the firstsection of the array. Moreover, feed resistances R R R are provided as shown for'feeding signals representative of discrete values of x to one end of the sections L L L from temporary stores which are indicated merely in block form and denoted respectively by the references S S S The construction of the temporary stores S to S forms no part of the present invention and a suitable construction of store is described, for example, in the specification of United States application Serial No. 208,297. For the purposes of the present application, it is suflicient to regard each store as a transformer having a primary winding which is energised by an alternating voltage of fixed amplitude and phase L10 only four of the 3 and having a secondary winding the number of turns of which can be varied by the operation of a series of relays to cause the voltage set up across the secondary winding to be the analogue of an observed value of x, thereby filling the store. During each cycle of operation, the stores S are filled at the times represented by the numbers in the lower row above the stores, the stores having been previously cleared of older information at the times indicated in the upper row of numbers. The voltage analogue fed to a store at a specified time is of course representative of the instantaneous value of x at that time. Moreover, the switches A A are opened and closed in a cyclic manner at the times denoted by the numbers below the switches. An output signal representative of the smoothed rate (x) is obtained from a secondary winding L inductively coupled to the sections L L In describing the operation of the apparatus illustrated in Figure 1 it will be assumed that a time just before the end of a cycle of operations has been reached, that is a time just before time 0. At that time all the switches except the switch A are closed and the stores 8, S are filled with information representative of the values of x at the times corresponding to a time denoted in the lower row of numbers above the stores. The sections L L then constitute a single tightly coupled inductive potentiometer having applied to equi-spaced points thereon signals representative of observations of x at discrete equi-spaced time intervals and a signal representative of the smoothed rate at is obtained from the secondary winding L as explained hereinafter. At time switch A is opened and the store S is cleared while at time 1 the switch A, is closed and the store S is filled with information representative of the latest value of x, i. e. the value at time I. Thereafter until time 2 the sections L L L function as a single potentiometer and in effect the potentiometer has been displaced by one section with reference to the points at which are applied the information representative of the values of x. This process is continued as long as rate measuring is taking place, a cycle of operations being completed in a period of 101. A smoothed value of x is therefore obtained from the secondary winding L and observations made outside the weighting period of 91- have: no effect in theevaluation. Each change in the sections which are connected in series to form the tightly coupled potentiometer has the effect of discarding the oldest value of x in favor of a value of x which has just been observed. The evaluated smoothed rateis therefore always based on the most recently observed values of x.

The theoretical basis of the invention will be illustrated for the case in which the switches are in the states shown in Figure 1. It will, of course, be appreciated that the following discussion is applicable to any state of the switches A A with appropriate changes in the notation. Referring to Figure I, assume that the alternating voltages in the stores S S have amplitudes x x respectively, these amplitudes being representative of successive observations of x at the times 1, 3 19. -Let a, a+v, a+2v a+9v be a set of smoothed voltage amplitudes having an arbitrary constant rate of change. The deviation between any value of x say x,, and the corresponding smoothed value a+rv is x,a-rv. The criterion for minimum mean square deviation between the values x x x and the values a, a-l-v a+9v is that should be a minimum. Differentiating partially with respect to a and v gives Therefore the criterion for minimum mean square deviation is where each of the resistors R R R has the value R. The currents in the sections of the potentiometer formed by sections L L are as indicated, there being of course no current in the section L Since this potentiometer is not tied to any reference potential, it is apparent that 1g r=l Hence f if if? The first condition for minimum mean square deviation is therefore satisfied. Moreover, if the output current of the arrangement is zero or, in other words, if the ampere turns of a potentiometer formed by the sections L L are zero, then This follows from the fact that i flows through nine sections, i flows through eight sections, and so on. This is the second condition for minimum mean square deviation and, although in practice it is not possible to arrange that the ampere turns of the potentiometer are exactly zero, the condition is sufficiently approached for practical purposes by arranging that the sections L L have, as aforesaid, a very high shunt impedance. The potential gradient set up along the potentiometer formed by the interconnected sections is, therefore, within the limits of practical error, representative of the desired smoothed rate of change of x.

In the operating mechanism for the switches A A which is illustrated in Figure 2, numbered terminals are shown and it is to be understood that the numbers denote the times in a cycle of operation at which these terminals are earthed. Normally, that is when not earthed, each of the terminals is biased to a D. C. level of +18 volts and earthing is eifected at the appropriate times by means of a suitable rotary selector switch which maintains each terminal in its turn at earth potential for a period, for example, of milliseconds. In Figure 2 the operating mechanisms of only two switches namely A and A are illustrated, and corresponding parts of the two mechanisms are denoted by the same reference letters but differentiated by the sufiixes l and 2. The operating mechanisms for all the switches are in fact identical apart from the times when the terminals are earthed, which times in the case of the mechanisms not shown can be derived by cyclic permutation on the basis of the timings indicated in Figure 1. Only the operating mechanism for the switch A will be described, it comprises a main relay winding B connected in series with a rectifier C between terminals earthed respectively at times 1 and 7. The

i l l l .5 winding B when energised closes a holding switch D which when closed connects the junction of B and C to an earth line B. The winding B when energised also closes a control switch F for an auxiliary relay winding G thereby closing a current path through G from a terminal earthed at time 18 to a second earth line H. When G is energised it closes the switch A and also another switch J When the latter switch is closed a resistance K is connected as shown from the upper end of G to one side of a two-way switch N and thence, depending on the state of the switch N either to the earth line H or to a bias source of +18 volts. Ganged master switches M and M are connected in the earth lines E and H respectively, the apparatus being conditioned for operation by closing the master switches. The switch N may be operated automatically by a relay P which is responsive to the output of an amplifier Q included in the feedback loop of a servo system, or alternatively the switch N may be manually operated. The input to the servo system is the present value of the magnitude x, and the output of the amplifier Q in addition to operating the relay P drives a servo motor U which operates a follow-up potentiometer V. This latter device has a negative feedback connection W from V to the input of the amplifier Q. It is arranged that in operation of the apparatus the switch N is normally maintained in the position indicated in full-lines, but if the output of the amplifier Q exceeds a certain small value the relay P is energised to change the state of switch N and connect the resistance K to the 18 volts bias source.

Until it is desired to commence rate measurement, switches M and M are left open. When, with the switches M and M thus open, terminal 1 is earthed at time 1 relay winding 13; is energised through the rectitier C and the switches D and F are momentarily closed. As soon as the earthing pulses on the terminal 1 has ceased current ceases to flow in winding B and switches D and F re-open. As switch M is open no current flows through winding G and switch A is unaffected.

As soon as it is desired to commence rate measurement, switches M and M are closed. Suppose this is just before time 1. Thus when at time 1, terminal 1 is earthed winding B is energised as before but now contacts D can pass a holding current through the earth line E and switch M thus keeping the winding B in an energised condition in spite of the terminal 1 being returned to a positive potential of 18 volts. Closure of the switch F energises the winding G since current can now flow from the terminal 18 to the earth bar H, and the switches A and J become closed. Assuming the switch N is in its normal state as indicated in full lines, closure of the switch J connects the upper end of G to earth via the resistance K but the resistance K is by-passed so long as switch F is closed so that the closure of switch J has no immediate effect. This state is maintained until time 7 at which time terminal 7 is earthed momentarily, winding B is de-energised, and switches D and F are opened. The reason for arranging that the switches D and F are opened at time 7 will appear subsequently. Relay winding B thereafter remains de-energised until time 1 in the next cycle of operation. The opening of switch F does not however, de-energise the winding G since current can now flow from the terminal 18 through the alternative path provided by switch J resistance K and the switch N to the earth bar H. The resistance K is arranged to have substantially the same magnitude as the resistance of winding G and therefore the opening of the switch F although it does not de-energise winding G has the effect of halving the current through the winding G The situation thus attained is maintained until time 18 when the terminal 18 is earthed, de-energising the winding G and thereby opening the switches A and I Nominally at the same time, the store S of the preceding inductive section L is cleared. It is arranged that this clearance is eifected by de-energization of a series ofrelays having a winding of the same resistances as the winding G but not, however, associated with a series resistance such as K sothat it carries double the current of the winding G just prior to time 18. This has the eifect of causing the switch A to open just before the store S is cleared so that there is no riskof the section L being coupled into the potentiometer after its store has been cleared. When the store S is filled at time 1 the fact that two relays have to operate before switch A is closed, whereas only single relays have to 0perate to fill the store S ensures that the store-is filled just before the switch A is closed.

During this ro ressivelinkin of the sections L L to L the system has a weighting period less than 91-, the weighting period beingin fact equal to the number of switches A A etc. which has been closed. There is thus no need to introduce any external control to ensure that the system settles inthe shortest possible times.

If the acceleration of the magnitude x is large'the output of the amplifier Q will increase due to the inevitable time lag in the servo loo and when the amplifier output exceedsthe aforesaid low value relay P operates to change the state of switch N and connect K to the 18 volt bias source. When the switch N is in this condition the opening of the switch F at time 7 (as above described) has also the effect of opening the switches A and J since no potential dilference exists at therelevant time across G and K in series. This means that the switch A remains closed only from time 1 to time 7, that is for a period of 37', and similarly each of the succeeding switches A etc., remains closed for the same reduced period. In this way the Weighting period of the apparatus is automatically reduced from 91- to 31- in dependence upon the output of the amplifier Q which in turn is dependent upon accelerations of the quantity x. The form of the weighting function is, moreover, accurately maintained even when the weighting period is reduced.

The servo-system Q, U, V, W, is illustrated merely to show one method whereby the switch N can be operated in dependence upon acceleration of x. Other means are available, for example the switch N may be arranged for operation in dependence upon information as to the currents in the feed resistances R R Alternately if x represents for instance the magnitude of one Cartesian component of the position of an object such as a ship or an aeroplane, and apparatus precisely similar to that described herein is provided for measuring the rate of change of another Cartesian com ponent y, then the course angle C of the objects motion, which is equal to the inverse tangent of y divided by x may be obtained, for instance by means described in United States application Serial No. 207,728, now Patent No. 2,781,967. The rate of change c of C may be measured by means similar to those described herein and a large value of 0 may be used to operate switch N.

What we claim is:

1. A potentiometer comprising an array of impedances, a switch between each impedance of said array and the next impedance thereof and between the last impedance of said array and the first impedance thereof, each switch being arranged when closed to connect adjacent impedances, means for feeding electrical signals to fixed points in the respective impedances, and means for operating said switches in a cyclic order to connect a cyclically changing plurality of said impedances in a series chain, said cyclic order being predetermined to produce the effect of displacing the feed points in succession along the chain.

2. Apparatus for evaluating the rate of change of a first variable with respect to a second variable comprising an array of inductances magnetically coupled one to another, a switch between each inductance of said array and the next inductance thereof and between the last a inductance of said array and the first inductance thereof, each switch when closed, being arranged to connect the adjacent inductances, a plurality of impedances one leading to a fixed point on each inductance, means for operating said switches in a cyclic order to connect a cyclically changing plurality of said inductances in a series chain, the cyclic order being predetermined to produce the eflEect of displacing said fixed points in succession along said chain, and means for applying to said impedances alternating voltages representative of values of the first variable corresponding to values of the second variable represented by said points, the impedance and mutual coupling of said inductances being such that the potential gradient set up along the chain is representative of a smoothed rate of change of the first variable with respect to the second variable.

3. Apparatus according to claim 2 including means for modifying the cyclic operation of said switches so as to reduce the number of inductances connected in the series chain, thereby to reduce the interval over which.

the smoothed rate of change of the first variable is evaluated.

4. Apparatus according to claim 3 wherein the means for operating each switch includes a main relay, means for maintaining said main relay energised during part of each cycle of operation of said switches, an auxiliary relay arranged to be energised when the main relay is energised and associated with hold means for maintaining said auxiliary relay energised for a longer part of each cycle, said auxiliary relay being arranged to operate the respective switch and said means for modifying the cyclic operation of the switches comprises means for rendering the hold means for each auxiliary relay inoperative.

5. Apparatus according to claim 3 comprising means responsive to a variation in the rate of change of the first variable for rendering said means for modifying the cyclic operation of the switches automatically efiective when the rate of said variation exceeds a predetermined value.

References Cited in the file of this patent UNITED STATES PATENTS 2,474,074 Sunstein June 21, 1949 2,567,532 Stephenson Sept. 11, 1951

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