1957-10-16

Abstract of GB784854 784,854. Electric analogue calculating systems. AIR TRAINERS LINK, Ltd., [formerly AIR TRAINERS, Ltd.]. Dec. 3, 1954 [Dec. 4, 1953], No. 33840/53. Class 37. An electric analogue computer determining the voltage analgue of the instantaneous product of two or more variables with reduced time delay error, comprises a number of potentiometers which are respectively energized by voltages proportional to the rates of change of the individual variables and adjusted by corresponding electromechanical servo-systems responsive to their respective absolute values, so that an electrical summing device receives voltages representing the respective products of the rate of change of each input variable in turn and the remaining input variables to produce an output voltage representing the rate of change of the product of all the variables, which is electrically integrated to produce the required result. In Fig. 1, voltages representing the rates of change V1 and V2 of variables V1, V2, derived by known means from voltages representing such variables, energize potentiometers 1, 2 adjusted by servo-systems 5, 6 in response to the latter input values to develop voltages proportional to V2 V1 and V1 V2, which are added in amplifier 7 and integrated by circuit 8 (which may be a Miller integrator) to a voltage representing the product y=V1V2. In a modification (Fig. 2, not shown) a similar apparatus is arranged to receive three voltages representing rates of change V 1, V2, V3 of inputs V1, V2, V3; voltages representing the latter operating servo-systems to adjust cascaded potentiometers fed from voltages V1, V2, V3 to produce voltages which are combined and amplified to represent the equations y=V1 V2V3+ V2V3 V1 +V3 V1 V2 which integrated gives a voltage proportional to the product y=V1 V2 V3. In a further modification (Fig. 3) for dividing variable V1 by V2, potentiometers respectively energized by voltages proportional to V1 and ( - V2) are adjusted by servo-systems responsive to voltages proportional to V2 and V1 to develop a combined voltage representing (V2 V1 - VI V2) at the input of an amplifier 12, whose output is applied to a square law potentiometer P adjusted by the V2 potentiometer servo-system to feed back a voltage representing V2<SP>2</SP> to the input whereby the amplifier output voltage is proportional to V1 which after integration is proportional to -. V2 Cumulative errors arising after prolonged operation may be eliminated (Fig. 4, not shown) by developing by known means a further voltage representing the result of the computation without attention to time delay, which is algebraically subtracted from the output of the computing device; the error voltage being applied as a correction to the input of the integrator in opposition to the computation voltage input.

0

1957-10-16

G06G7/16 ; G06G7/00

G06G7/16

GB19530033840 19531204

GB19530033840 19531204

1	Improvements in and relating to analogue computers
	Inventor: BARBER ERNEST EDWARD	Applicant: AIR TRAINERS LINK LTD
	EC:G06G7/16	IPC: G06G7/16;G06G7/00
	Publication info: GB784854 A - 1957-10-16

What we claim is: -

1 An analogue computer giving an output voltage which is the instantaneous product of two or more variable quantities, comprising two or more potentiometer units energised with voltages representing respectively the rates of change of each of the variables adjusted by electromechanical servo systems in accordance with voltages representing the variable quantities to give outputs representing the product of a rate of change of a different one of the variables by all the other variables and means summing the output products of the said units and integrating their sum with respect to time.

2 An analogue computer giving an output which is the instantaneous quotient of two variable quantities comprising two potentiometer units energised with voltages representing respectively the rates of charge of each of the variables adjusted by electromechanical servo systems in accordance with voltages representing the variable quantities to give outputs representing the product of the rate of change of each variable by the other variable, a summing amplifier receiving the output products of the said units and having in its feedback circuit a square law potentiometer the slider of which is continuously adjusted in accordance with the divisor of the variable quotient to maintain the gain of the amplifier inversely proportional to the square of the divisor to produce an amplifier output which is the rate of change of the variable quotient, and means for integrating the amplifier output.

3 An analogue computer according to claim 1 or claim 2 provided with a checking system which evaluates the difference between the integrated output of the device and the theoretically correct value of that output and feeds the evaluated difference as an input into the integrator.

4 An analogue computer substantially as described herein with reference to the accompanying drawings.

For the Applicants, LLOYD WISE, BOULY & HAIG, Chartered Patent Agents, 10, New Court, Lincoln's Inn, London, W C 2.

13 of which is connected, not directly to the amplifier output voltage, but to the slider 14 of a potentiometer 15 supplied with the latter voltage The potentiometer 15 is adjusted by the V, servo and is designed in such a way that as the slider is operated the voltage at the slider follows a square law In these circumstances, the gain of the amplifier 12 is maintained inversely proportional to V,2 so that its output voltage is proportional to Vn V 1-Vlv 2 V,22 y is then integrated as before to give a final resultant voltage proportional to y.

The arrangements described above ensure satisfactory response to change of one or more variables however rapid the change may be; but it is possible for small errors in integration rates to lead, after protracted operation, to an appreciable error in the general or mean level of the computed product voltage For example, the integrator introduces a time factor into the system and any slight inaccuracy of the condenser will result in errors in the output y.

Accordingly, a checking system may be employed, in which a voltage representing the correct general level of the product is separately evaluated by conventional servo-controlled potentiometer means 16 An example of such a checking system as applied to the example in Figure 1 is shown in Figure 4.

The equipment for this system does not necessarily have to be specially provided but can be one provided primarily for another purpose This voltage is algebraically subtracted from the computed product voltage and the resulting difference or error is applied as an additional input to the final integrator, in the appropriate sense.

It will be appreciated that the arrangements described herein are intended to be incorporated in analogue computers in which at least some of the inputs with which the invention is concerned will already be available and will not have to be specially generated This applies, in particular, to the rate voltages.

In the generation of the rate of change of the product (y) the signals used may be reprePROVISIONAL SPECIFICATION Improvements in and relating to Analogue Computers We, AIR TRAINERS LIMITED, a British Company, of Cubitts Buildings, Bicester Road, Aylesbury, Buckinghamshire, do hereby dedare this invention to be described in the following statement: This invention relates to analogue computers for use, for example, in aviation trainers.

It is very convenient in such computers for the variables which are to be mathematically combined to be represented by voltages For the addition of voltages, thermionic amplifiers are ideal but it is not a practical proposition to use thermionic amplifiers in analogue computers to provide as an output a voltage which is the product of two or more input voltages.

784,854 4 784,854 For the evaluation of products, therefore, one uses a potentiometer to the winding of which a voltage representing one variable is applied and the slider of which is positioned in accordance with another variable through the agency of an electromechanical servo A voltage then appears at the slider which is proportional to the product of the two input variables.

The electromechanical servo has the disadvantage that a delay (measurable in milliseconds) necessarily occurs in its response to a change in the input voltage, that is to say, in the case under consideration, between the instant at which the input voltage which controls the potentiometer slider changes and that at which the slider actually responds by motion to the change in voltage Accordingly, if the said input voltage varies continuously, the evaluation of the product will always be somewhat in arrears.

The object of the invention is to enable a resultant voltage representing the transient value of the product of two or more variable voltages to be provided which varies substantially immediately there is a change in the magnitude of any one of the variable voltages.

That object is achieved, in accordance with the invention, by evaluating, by the use of a number of electromechanical positional servos, the product of the rate of change of each variable and all of the other variables, summing the product voltages and integrating the sum.

Expressed somewhat differently, the invention consists in producing the differential with time of the desired product and integrating the result, the differential being obtained by summing a number of products obtained by electromechanical multiplication.

Assume, for example, that the problem is to provide a voltage representing the transient value of y=V 1 V, V, and V being independently variable When differentiated, the equation reads y=V 1 V, + V 2 V 1 For the solution of that equation and the evaluation of y, the apparatus shown diagrammatically in Figure 1 of the accompanying drawings can be used.

Figure 1 shows a potentiometer P, having a voltage Vl applied to its winding, and the slider of which is positioned in a conventional manner in accordance with a voltage V by an electromechanical positional servo (not shown).

A second similar potentiometer P 2 has voltages V 2 and V, applied to it for energising its winding and positioning its slider respectively, the slider being positioned by a second electromechanical positional servo (not shown) Each potentiometer and its associated servo forms an electromechanical multiplying device having an input V 1 or V 2 which is factorised in accordance with the output V or V, of the servo The output of the multiplying device Pl will be a voltage proportional to V V, and that of the multiplying device P 2 a voltage proportional to VV Those two voltages are added in a summing amplifier A the output of which will, therefore, be a voltage proportional to VV 1 +V 1 V, =Y The output y then becomes the input to an integrator I which gives an output voltage proportional to y.

The equation y =V 1 V 2 is thus solved.

Whenever V, or V 2 varies, the voltage across the winding of one or the other of the 80 potentiometers will be varied immediately.

The variation in V, or V, will be transmitted to the slider of the appropriate potentiometer only after the delay inherent in the electromechanical transmission of the servo through 85 which the slider is driven The instantaneous position of the slider will never be quite correct unless the variable which governs it has remained constant for a period longer than the inherent delay The error in the resultant 90 product will, however, always be extremely small and well within the acceptable limit.

The summing amplifier A can be electronic and, therefore, introduce a delay which, being measured in microseconds, is negligible The 95 integrator I can also be electronic and thus introduce a delay which is altogether immaterial.

Thus, the final resultant voltage (y) will vary instantaneously with variation in the value 100 of either of the variables while its value will always be very close indeed to the true value of the product of the variables The error in the magnitude of the product will always be small enough to be negligible and, in any case, 105 immediate response to variation in the value of the inputs is of far greater importance than absolute accuracy of the resultant product.

It has been assumed above that V 1, V,, V, and V, are all available as inputs Should only 110 V, and V,-the rates of change of the variables-be available, V, and V 2 can be obtained from them by integration electromechanically.

Should only V, and V 2 be available, V, and V can be obtained from them by the use of 115 differentiating amplifiers.

Figure 1 is specific to the case of two variables Figure 2 shows diagrammatically an arrangement for use where there are three variables, viz: V,, V 2, V, 120 The differential equation then is Y=VIV 1 V+v,+V 2 V,V 1 +VV,V 2 784,854 law" and is adjusted by the V, servo In 35 these circumstances, the gain of the amplifier is maintained inversely proportional to V 22 so that its output voltage is proportional to V 2 ij 1-vl V 2 =v V 2 y is then integrated as before to give a final 40 resultant voltage proportional to y.

The arrangements described above ensure satisfactory response to change of one or more variables however rapid the change may be; but it is possible for small errors in integration 45 rates to lead, after protracted operation, to an appreciable error in the general or mean level of the computed product voltage.

Accordingly, a checking system may be employed, in which a voltage representing the 50 correct general level of the product is separately evaluated by conventional servocontrolled potentiometer means which does not necessarily have to be specially provided but can be one provided primarily for another 55 purpose This voltage is algebraically subtracted from the computed product voltage and the resulting difference or error is applied as an additional input to the final integrator, in the appropriate sense 60 It will be appreciated that the arrangements described herein are intended to be incorporated in analogue computers in which at least some of the inputs with which the invention is concerned will already be available and 65 will not have to be specially generated This applies, in particular, to the rate voltages.

For the Applicants:

LLOYD WISE, BOULY & HAIG, Chartered Patent Agents, 10, New Court, Lincoln's Inn, London, W C 2.

Three positional servos (not shown) are used, each adjusting two potentiometers, so that the rate of change of each variable can be multiplied by or factorised with both the other variables, as shown.

Clearly, the system can be applied to evaluating the product of any number of variables whilst avoiding delay in response of the final element in the chain, the positional servos corresponding in number to the variables, and the rate voltages being applied to potentiometers driven by the servos.

The term " product " is used herein in its broad sense which includes " quotient " If the product is to provide a voltage representing the transient value of y, V 2 one proceeds by evaluating differential equation y from the V 2 Vl-VI'V 2 Y= V V 22 and then integrating with respect to time.

A number of different arrangements in accordance with the invention can be used for that purpose, one of which is shown in Figure 3 of the accompanying drawing In that arrangement, V 1 and V are factorised to produce a voltage proportional to V VI Similarly, V 2 and V 1 are factorised to obtain VV, These two products are summed in a summing amplifier A, the feedbacks resistor R of which is connected, not directly to the amplifier output voltage, but to the slider of a potentiometer P supplied with the latter voltage The potentiometer P is shaped to give a " square Leamington Spa: Printed for Her Majesty's Stationery Office, by the Courier Press -1957.

Published at The Patent Office, 25, Southampton Buildings, London, W C 2, from which copies may be obtained.

784,854

PATENT SPECIFICATION

Inventor: ERNEST EDWARD BARBER Date of filing Complete Specification: Dec 3, 1954.

Application Date: Dec4, 1953 N Complete Specification Published: Oct 16, 1957.

Index at acceptance:-Class 37, G 2 B( 1: 2: 6), G 3 A(I: 2: 3: 6).

International Classification:-GO 6 g.

ro 33840/53.

COMPLETE SPECIFICATION

Improvements' in and relating to Analogue Computers We, AIR TRAINERS LINK LIMITED, formerly Air Trainers Limited, a British Company, of Cubitts Buildings, Bicester Road, Aylesbury, Buckinghamshire, do hereby declare the invention, for which we pray that a patent may be granted to us, and the method by which it is to be performed, to be particularly described in and by the following statement: -

This invention relates to analogue computers for use, for example, in aviation trainers.

It is very convenient in such computers for the variables which are to be mathematically combined to be represented by voltages For the addition of voltages, thermionic amplifiers are ideal but it is not a practical proposition to use thermionic amplifiers in analogue computers to provide as an output a voltage which is the product of two or more input voltages.

In the conventional method for the evaluation of products, therefore, one uses a potentiometer to the winding of which a voltage representing one variable is applied and the slider of which is positioned in accordance with another variable through the agency of an electromechanical servo A voltage then appears at the slider which is proportional to the product of the two input variables.

The electromechanical servo has the disadvantage that a delay (measurable in milliseconds) necessarily occurs in its response to a change in the input voltage, that is to say, in the case under consideration, between the instant at which the input voltage which controls the potentiometer slider changes and that at which the slider actually responds by motion to the change in voltage Accordingly, if the said input voltage varies continuously, the evaluation of the product will always be somewhat in arrears.

The object of the invention is to enable a resultant voltage representing the transient value of the product of two or more variable voltages to be provided which varies substantially immediately there is a change in the magnitude of any one of the variable voltages.

That object is achieved, in accordance with lPiice 3 s 6 d 1 the invention, by evaluating, by the use of a number of potentiometer units energised with voltages representing respectively the rates of change of each of the variables adjusted by electromechanical servo systems in accordance with voltages representing the variable quantities to give outputs representing the product of a rate of change of a different one of the variables by all the other variables and means summing the output products of the said units and integrating their sum with respect to time.

Expressed somewhat differently, the invention consists in producing the differential with time of the desired product and integrating the result, the differential being obtained by summing a number of products obtained by electromechanical multiplication.

In order that the invention may be thoroughly understood examples in accordance with it will now be described with reference to the accompanying drawings in which:Figure 1 shows diagrammatically an arrangement in accordance with the invention for obtaining the product of two variables; Figure 2 shows diagrammatically an arrangement in accordance with the invention for obtaining the product of three variables; Figure 3 shows diagrammatically an arrangement in accordance with the invention for obtaining the quotient of two variables; and Figure 4 shows diagrammatically a checking circuit as applied to the example of Figure 1.

Assume, for example, that the problem is to provide a voltage representing the transient value of y=V 1 V, V, and V being independently variable When differentiated, the equation reads y V= V 2 + Vs V For the solution of that equation and the evaluation of y, the apparatus shown diagrammatically in Figure 1 of the accompanying drawings can be used 784854 SO Figure 1 shows a potentiometer 1 having a voltage V, applied to its winding, and the slider 3 of which is positioned in a conventional manner in accordance with a voltage V 2 by an electromechanical positional servo 5.

A second similar potentiometer 2 has voltages V 2 and V, applied to it for energising its winding and positioning its slider 4 respectively, the slider being positioned by a second electromechanical positional servo 6 Each potentiometer and its associated servo forms an electromechanical multiplying device having an input V, or V which is multiplied by the servo in accordance with V 2 or V, as the case may be.

The output of one multiplying device-will be a voltage proportional to V 2 V 1 and that of the other multiplying device-a voltage proportional to V 1 V, Those two voltages are added in a summing amplifier 7 the output of which will, therefore, be a voltage proportional to VV 1 +VIV 2 =Y The output y then becomes the input to an integrator 8 which gives an output voltage proportional to y.

The equation y=V 1 V 2 is thus solved.

Whenever V 1 or V 2 varies, the voltage V 1 or V 2 across the winding of one or the other of the potentiometers 1 and 2 will be varied immediately The altered value in V, or V.

will be transmitted to the slider of the appropriate potentiometer only after the delay inherent in the electromechanical transmission of the servo 5 or 6 through which the slider is driven The instantaneous position of the slider will never be quite correct unless the variable V, or V which governs it has remained constant for a period longer than the inherent delay The error in the resultant product will, however, always be much smaller than that which would have been produced had the voltage V, been multiplied by a potentiometer driven by the servo logging V 2 to produce the product y, and well within the acceptable limit.

The summing amplifier 7 must of course be suitable for dealing with the kind of signal which is fed to it, i e whether the signal is A C or D C Also, it must not be such as to produce any appreciable delay Amplifiers fulfilling these requirements are well known in the art to which the invention relates In the preferred form of the invention D C signals are used together with a valve amplifier which introduces a delay measurable in microseconds Similarly the integrator 8 must not introduce appreciable delay Integrators fulfilling these requirements are well known in the art to which this invention relates In the preferred form of the invention the well known Miller integrator is used.

Thus, the final resultant (y) will vary instantaneously with variation in the value of either of the variables while its value will always be very close indeed to the true value of the product of the variables The error in the magnitude of the product will be sufficiently small to have no significant effect upon the overall efficienty of an analogue computer for use with aviation trainers.

It will be observed that the apparatus in Figure 1 yields voltages representing both a quantity (y) and its rate of change (y) Where therefore, there is extensive use of this principle it will be common to have voltages readily available for the rates of change of most quantities as well as the quantities themselves.

Figure 1 is specific to the case of two variables Figure 2 shows diagrammatically an arrangement for use where there are three variables, viz: V,, V,, V,.

The differential equation then is y = VV 2 V,+VV 1 + V,+VV 2 Three positional servos 9, 10, 11 (not shown) are used, each adjusting two potentiometers, so that the rate of change of each variable can be multiplied by or factorised with both the other variables, as shown.

Clearly, the system can be applied to evaluating the product of any number of variables whilst avoiding delay in response of the final element in the chain, the positional servos corresponding in number to the variables, and the rate voltages being respectively applied to potentiometers driven by the servos.

The term " product " is used herein in its broad sense which includes " quotient " If the product is to provide a voltage representing the transient value of VI one proceeds by evaluating differential equation y from the Y= V'22 and then integrating with respect to time.

A number of different arrangements in accordance with the invention can be used for that purpose, one of which is shown in Figure 3 of the accompanying drawing In that arrangement, V, and V, are multiplied to produce a voltage proportional to VVI Similarly, -V 2 and V 1 are factorised to obtain -VV These two products are summed in a summing amplifier 12, the feedback resistor 784,854 sented as A C or D C voltages but in the final integration the signals must be represented by D C voltages.