1957-10-16

Abstract of GB784853 784,853. Electric analogue calculating systems. AIR TRAINERS LINK, Ltd., [formerly AIR TRAINERS, Ltd.]. Dec. 3, 1954 [Dec. 4, 1953], No. 33839/53. Class 37. For analogue computation of the values of a complex non-linear function of a variable without inherent time delay, a voltage representing a simple linear or non-linear function of the variable is produced from the input voltage by static electric means to approximate to the required function, without time delay, and is additively or multiplicatively combined with a voltage produced by a servo-potentiometer device responsive to the input voltage as a correcting function of the variable, to produce an output voltage accurately representing the required complex function. In Figs. 1, 3, the complex function f3(Vl) represented by curve (a) is equivalent to the product of a simple function f1(V1) and a correcting function f2(V1), and static device D (which may be a fixed voltage divider, a transformer, a thermionic amplifier, or the like) supplied with a voltage proportional to V1 derives a voltage proportional to f1(V1) (which may, e.g., be parabolic) represented by curve b to energize a potentiometer p, adjusted by an electromechanical servo-system EM responsive to the input voltage and wound in accordance with function f2(V1) represented by curve c. The slider voltage V2 is then proportional to f1(V1)f2(V1)=f3(V1) as required, with reduced error due to operational time delay. Similarly, the complex function f3(V1) equivalent to the sum of a simple function f4(V1) and a correcting function f5(V1) is derived (Figs. 2, 4, not shown) by energizing a static electric device with a voltage proportional to V1 to produce a voltage proportional to f4(V1), and similarly energizing a servosystem to adjust a constant voltage energized potentiometer designed to produce a slider voltage proportional to f5(V1); the voltages being additively or subtractively combined at the input of an amplifier whose output is proportional to f3(V1)=f4(V1)+f5(V1) as required.

0

1957-10-16

G06G7/26 ; G06G7/00

G06G7/26

GB19530033839 19531204

GB19530033839 19531204

US3128376 (A1)

1	Improvements in and relating to analogue computers
	Inventor: BARBER ERNEST EDWARD; SIMPKIN KENNETH HENRY	Applicant: AIR TRAINERS LINK LTD
	EC:G06G7/26	IPC: G06G7/26;G06G7/00
	Publication info: GB784853 A - 1957-10-16
2	Non-linear function generator
	Inventor: EDWARD BARBER ERNEST; HENRY SIMPKIN KENNETH	Applicant: GEN PREC SYSTEMS LTD
	EC:G06G7/26	IPC: G06G7/26;G06G7/00
	Publication info: US3128376 A - 1964-04-07

What we claim is: i 5

1 An analogue computer deriving an output voltage which is a specified nonlinear function of a variable input voltage, and employing a servo-potentiometer device automatically positioned by the input volt 2 o( age, in which a voltage representing a simple approximation to the specified function is obtained directly from the input voltage by static means as defined herein and the servo-potentiometer device contri 125 characteristic to give at its slider the required non-linear addendum to the approximation voltage.

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

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

butes only those corrections to the simple function voltage required to modify it to the specified output function voltage.

2 An analogue computer according to S Claim 1, in which the approximation voltage is applied across the potentiometer and the latter has the appropriate nonlinear characteristic to give at its slider the specified output function voltaee.

3 An analogue computor according to Claim 1, in which a constant voltage supply is applied to the potentiometer and the latter has the appropriate non-linear PROVISIONAL SPECIFICATION.

Improvements in and relating to Analogue Computers.

We, AIR TRAINERS LIMITED, a British Company, of Cubitts Buildings, Bicester Road, Aylesbury, Buckinghamshire, do hereby declare this invention to be described in the following statement:This invention relates to analogue computers.

For providing, in such computers, a voltage proportional to a non-linear function of a variable voltage, it is usual to use voltage dividing means comprising a shaped potentiometer the slider of which is automatically positioned in accordance with the variable voltage by an electromechanical positional servo The disadvantage of such means is that the servo is not immediately responsive to changes in the variable and the resultant voltage therefore does not accurately represent the transient value of the 4 o quantity being computed There is always a lag between the instant of change in the value of the variable and the production of the desired voltage The lag is measured in milliseconds but can appreciably impair the performance of a computer.

In the case of linear functions and certain simple non-linear functions the required voltage can be produced without the interposition of mechanical motion and so with a lag which is measured in microseconds and which is acceptable Complex functions, however, cannot be so derived, or at least only by the introduction of unacceptable complications.

The invention is an application of the principle that a complex function can be expressed as a modification of a more simple function Thus, the non-linear function represented by the curve a in Figure 1 of the accompanying drawings can be expressed as the product of the linear function represented by the line b and the non-linear func.

tion represented by the line c The same non-linear function a could equally well be expressed (Figure 2) as the algebraic sum of a linear function d and a non-linear function e It is possible (especially by the use of thermionic equipment) to obtain parabolic and other simple non-linear functions of a variable voltage, and in appropriate 70 cases such functions may be so produced to give a closer first approximation than the linear functions such as a and d.

According to the invention, the value of a desired non-linear function of a variable is 75 continuously computed by the production, by static means of a basic voltage representing the value of a relatively simple function of the variable approximating to the desired function, and the correction of 80 that voltage by the appropriate further function of the variable which is produced electromechanically.

By "static" means is meant means in which there is no mechanical mass which 85 has to be accelerated when the variable changes, and no other lag-producing characteristic such as a thermal capacity which has to be satisfied before there can be any effective response A thermnionic 90 amplifier is an example of such static means; a potential divider comprising a potentiometer having a fixed tap is another example; a transformer is yet another example An electromechanical servo having a slider 95 which is moved under the influence of change of a variable, however, is not static because of the inertia of the slider and other moving parts Nor is the electrically heated thermo couple static in the sense in which 100 the term is used here because there must necessarily be a delay in its response to operation of the input as a result of its thermal capacity.

The basic voltage, being produced without 105 involving the acceleration of mechanism, will vary simultaneously with variation of the variable The correction, being made electromechanically, will be subject to the time delay inherent in the mechanism and will, 1 O 784,853 accordingly, not be wholly accurate during changes The error will, however, be smaller than that which would result from the wholly electromechanical evaluation of the complex function because the effect of the delay is felt only by the adjusting factor.

By the choice of conditions giving rise to a basic voltage which fairly closely represents the complex function, the error can be reduced to very small proportion indeed.

Two example of an arrangement in accordance with the invention are shown in Figures 3 and 4 of the accompanying drawings.

Figure 3 shows diagrammatically an arrangement for solving the equation:V 2 = f(V) = fl(V) f_,(V 1) in which V 1 is a variable; fi is a complex function (for example function a of Figures 1 and 2) of the variable; f, is a simple function of the variable capable of being evaluated by static means in a simple manner; and f, is an adjusting function capable of being evaluated electromechanically.

D is a static device (for example a fixed voltage divider, transformer, or thermionic amplifier) responding to the variable V, to produce the basic voltage fl(VJ)-for example the linear function b of Figure 1which is applied to a potentiometer P.

EM is an electromechanical positional servo which also receives the input V 1 and serves to position the slider S of the potentiometer in accordance with V 1.

The potentiometer winding is graded in depth in accordance with the function f 2 (for example function c in Figure 1) so that the voltage V 2 which is tapped off through the slider is proportional to the product of f/(VJ) and f 2 (V).

The voltage across the potentiometer P will vary simultaneously with variations in V, The position of the slider S will also vary with variations in V, but only after the delay inherent in the mechanism of the servo EM The resultant voltage V will, therefore, not be accurate in transient conditions but it will at least change simultaneously with change in the variable V 1 and to approximately the right degree In other words, immediate response of the resultant voltage is ensured and the error arising out of the delay in response of the servo is minimised.

Figure 4 shows an arrangement for solving the equation:V 2 = f 3 (V 1) f (V 1) f 1 (V 1) ft; being, for example, again the curve a of Figures 1 and 2, and fl and f being respectively the curves d and e of Figure 2.

D and EM correspond to the devices D and EM in Figure 3 The output f (V) of the static device D, however, is fed to an electronic summing amplifier A.

The servo EM again serves to position the slider S of the potentiometer P but the latter receives in this case a constant voltage Vk and is so wound that the voltage tapped off from the slider is of such a positive or negative magnitude as is required, according, to the value of V 1, to be added to or subtracted from the output of the device D to produce the desired resultant voltage In other words, the potentiometer is wound in accordance with f,.

The output of the potentiometer, i e.

f.,(V,), is fed to the summing amplifier A the output of which is therefore f(V)+ 1,(V) = V 2.

As in the case of Figure 3, Vo will vary simultaneously with variation of V, and the delay inherent in the servo EM will be felt only in the evaluation of the adjusting factor f,(V,).

As previously stated, the device D could be such as to produce a non-linear function if required in the interests of close approximation, but such function will, of course, always be less complex or more regular than the function which is finally to be computed.

For the Applicants:LLOYD WISE, BOULY & HAIG.

Chartered Patent Agents, New Court, Lincoln's Inn, London, W C 2.

Abingdon: Printed for Her Majesty's Stationery Office, by Burgess & Son (Abingdon), Ltd -1957 Published at The Patent Office, 25, Southampton Buildings, London, W C 2, from which copies may be obtained.

l 784,853

PATENT SPECIFICATION

Inventors:-ERNEST EDWARD BARBER and KENNETH HENRY SIMPKIN.

Date of filing Com plete Specification: Dec 3 1954.

Application Date: Dec 4, 1953 No 33839153.

Complete Specification Published: Oct 16, 1957.

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

International Classihieation:-GO 6 g.

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 providing, in such computers, a voltage proportional to a nonlinear function of a variable voltage, it is usual to use voltage dividing means comprising a shaped potentiometer the slider of which is automatically positioned in accordance with the variable voltage by an electromechanical positional servo The disadvantage of such means is that the servo is not immediately responsive to changes in the variable and the resultant voltage therefore does not accurately represent the transient value of the quantity being computed There is always a lag between the instant of change in the value of the variable and the production of the desired voltage The lag is measured in milliseconds but can appreciably impair the performance of a computer.

In the case of linear functions and certain simple non-linear functions the required voltage can be produced without the interposition of mechanical motion and so with a lag is measured in microseconds and which is acceptable Complex functions, however, cannot be so derived, or at least only by the introduction of unacceptable complications.

The invention is an application of the principle that a complex function can be expressed as a modification of a more simple function.

lPrice 3 s 6 d l According to the invention, the value of a desired non-linear function of a variable input voltage is continuously computed in a computor employing a servo-potentiometer device automatically positioned by the input voltage, by deriving by static means a voltage representing a simple approximation of the desired non-linear function, and modifying the simple approximation to give the desired output function by means of a voltage produced by the servo-potentiometer device.

By "static" means is meant means in which there is no mechanical mass which has to be accelerated when the variable changes, and on other lag-producing characteristic such as a thermal capacity which has to be satisfied before there can be any eflective response A thermionic amplifier is an example of such static means; a potential divider comprising a potentiometer having a fixed tap is another example; a transformer is yet another example An electromechanical servo having a slider which is moved under the influence of change of a variable, however, is not static because of the inertia of the slider and other moving parts Nor is an electrically heated thermo couple "static" in the sense in which the term is used here because there must necessarily be a delay in its response to variation of the input as a result of its thermal capacity.

The basic voltage, being produced without involving the acceleration of mechanism, will vary simultaneously with variation of the variable The correction, being made electromechanically, will be subject to the time delay inherent in the mechanism and will, accordingly, not be wholly accurate during changes The error will, however, be smaller than that which would result from 784,853 784,853 the wholly electromechanical evaluation of the complex function because the effect of the delay is felt only by the adjusting factor.

By the choice of conditions giving rise to a basic voltage which fairly closely represents the complex function, the error can be reduced to very small proportions indeed.

In order that the invention may be thoroughly understood it will be further explained with reference to the drawings accompanying the Provisional Specification in which:Figs 1 and 2 show examples of curves of complex functions which can be expressed as a modification of a more simple function.

Figs 3 and 4 show diagrammatic arrangements in accordance with the invention for evaluating the functions shown in Figs 1 and 2.

The non-linear function represented by the curve a in Figure 1 can be expressed as the product of the linear function represented by the line b and the non-linear function represented by the line c The same nonlinear function a could equally well be expressed (Figure 2) as the algebraic sum of a linear function d and a non-linear function e It is possible (especially by the use of thermionic equipment) to obtain parabolic and other simple non-linear functions of a variable voltage, and in appropriate cases such functions may be so produced to give a closer first approximation than the linear functions such as a and d.

Figure 3 shows diagrammatically an arrangement for solving the equation:V, = f 3 (V,) = f,(V,) f 2 (V,) in which V 1 is a variable; f, is a complex function (for example function a of Figures 1 and 2) of the variable; fh is a simple function of the variable capable of being evaluated by static means in a simple manner; and f 2 is an adjusting function capable of being evaluated electromechanically.

In Figure 3 D is a static device (for example a fixed voltage divider, transformer, or thermionic amplifier) responding to the variable V 1 to produce the basic voltage f,(VJ-for example the linear function b of Figure 1-which is applied to a potentiometer P.

EM is an electromechanical positional servo which also receives the input V, and serves to position the slider S of the potentiometer in accordance with V 1.

The potentiometer winding is graded in depth in accordance with the function f 2 (for example function c in Figure 1) so that the voltage V, which is tapped off through the slider is proportional to the product of f,(V) and f 2 (V 1).

The voltage across the potentiometer P will vary simultaneously with variations in V 1 The position of the slider S will also vary with variations in V 1 but only after the delay inherent in the mechanism of the servo EM The resultant voltage Vo will, therefore, not be quite accurate in transient conditions but it will at least change simultaneously with change in the variable V 1 and to approximately the right degree In other words, immediate response of the resultant voltage is ensured and the error arising out of the delay in response of the servo is minimised.

Figure 4 shows an arrangement for solving the equation:V 2 = f 3 (V,) = f 4 (V 1)+f 5 (V,) so f 2 being, for example, again the curve a of Figures 1 and 2, and f, and f being respectively the curves d and e of Figure 2.

D and EM correspond to the devices D and EM in Figure 3 The output f L(V) of 85 the static device D, however, is fed to an electronic summing amplifier A.

The servo EM again serves to position the slider S of the potentiometer P but the latter receives in this case a constant voltage Vk 90 and is so wound that the voltage tapped off from the slider is of such a positive or negative magnitude as is required, according to the value of V 1, to be added to or subtracted from the output of the device D to 95 produce the desired resultant voltage In other words, the potentiometer is wound in accordance with f,.

The output of the potentiometer, i e.

f A(V), is fed to the summing amplifier A 100 the output of which is therefore f/(V)+ f 1 (Vi) = Vo.

As in the case of Figure 3, V 2 will vary simultaneously with variation of V, and the delay inherent in the servo EM will be felt 105 only in the evaluation of the adjusting factor f 5 (V 1).

As previously stated, the device D could be such as to produce a non-linear function if required in the interests of close approxi 110 mation, but such function will, of course, always be less complex or more regular than the function which is finally to be computed.