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Feb- 13, 1952 c. E. G. BAILEY 3,021,071 SERVO SYSTEMS Filed Oct. 25, 1956 2 Sheets-Sheet 1 F@g .1. PR/OA’ ART 11 F, 7 M] k --->-- P] ————>D] V S’ \V r S V [IF A A M/l/E/V‘M W .a. a“? By 65.174 121%)‘ ATTDRIVE)’ Feb. 13, 1962 C. E‘ G. BAILEY 3,021,071 SERVO SYSTEMS Filed Oct. 25, 1956 ‘ 2 Sheets-Sheet 2 AMPLIFIER //VVEA/7OQ WW5 s, 422.44% a)’ $94‘ a M United v-Stat€S Patent ; "3C6 ’ “ ' , :1 t 3,021,071 . Christopher E. G. Bailey, London, England, assignor to J ’ . (Cl. 2359-180) 3.021.071 . 2 . a , tentiometer P1 and the voltage F1 is, therefore, dependent ' I upon the product of the positions of the shafts D1 and ‘D2. A feedback voltage F2 applied to the input of the ampli?er A; may -be derived from any suitable .point The present invention relates to servo systems adapted to solve simultaneous equations. ., A feedback loop is shown applying an electrical varia tion. F1 from the potentiometer P2 tothe input of the ampli?er A1. The voltage across the terminals of the potentiometer P2 is derived from the wiper of the po Filed Oct. 25, 1956, Ser. No. 618,291 Claims priority, application Great Britain Nov. 9, 195 4 Claims. , shaft D2‘ constituting the outputqofythe second servo. The Solartron Electronic Group Limited, Thames Dit . , Patented Feb. '13, 1962 A, and an electro-mechanical transducer in the form of amotor M2 driving a potentiometer P2 and an output SERVO SYSTEMS ton, Surrey, England , . > ~ according to circumstances, as shown, for instance from The invention makes use of what are known as closed loop servo systems, that is to say systems in which an The loop gain of the system A1M,P1P2 depends upon input variation applied to the input of a servo gives rise to an output variation at the outputofthe servo, and 15 the position of the shaft D2 and if this system is to be stable over the whole range of operation, the correspond in which a variation dependent upon the output varia ence'between I1 and the movements of the shaft D1 must tion is fed back to the input of the servo in such a be less accurate than would be desirable. . manner as to reduce the difference between the input and the potentiometer P1. output variations. 2 . ' I ~ ‘ ~ ~ 1 FIG. 2 differs from FIG. 1 ‘in that ,the ampli?er. A Such systems therefore comprise a servo and a feedback path between the output and input 20 of FIG. 1, assumed to be a multi-stage ampli?er, is shown divided into two parts AA, and BA1. The voltage ap- ~ of the servo. The-servo may be ofpany kind, such as electro-mechanical or hydraulic for example. ' plied from the output ofAA, to the input of BA, is ' controlled by a further potentiometer P3 on the shaft In such a servo system it is normally desirable to ar range that the loop gain around the system, that is the gain around the loop including the servo and, the, feed D2 and the potentiometer P3 is arranged to have an operating law that is as nearly as is practically con. venient the inverse of that of the potentiometer P2. It 25 back path, shall be a maximum consistent with stability. is, of course, not essential thatfthe two laws should be the exact‘inverse of one another andindeed‘it may. be impossible to make them so. In one example the poten ~ It is known, for the purpose of solving simultaneous equations, to provide two or. more closed-loop servo systems interconnected in such a way that the feedback variation of one system is a function of the output varia tion of the other system. The loop gain‘ around the ?rst tiometer P2 is the sine winding of a sine-cosine poten tiometer and the ideal law for the potentiometer P3 is named system is then, over at least part of the range then a cosecant whichtends to in?nity at 0°. Any ap~ of variation, less or more than the safemaximum.‘ If proximation to a cosecant law will give an improvement , the ?rst-named system be arranged to ‘be stable ‘through out its range of operation, the maximum departure from in. comparison with the arrangement of FIG. 1. The potentiometers P1, P2 and P3 can be regarded as voltage generators or electro-mechanical transducers each correspondence between the output and input variations generating a voltage dependent upon the movements of, of that system is greater than is desirable. This disad the mechanically driven member coupled thereto. vantage has‘sometimes led to the abandonment of such interconnected systems even when otherwise they might 40 ,Referring now to FIG. 3, the ampli?er within the broken line rectangle AA1 comprises two amplifying have been desirable. stages 10 and 11 and is connected through a potenti It is the object of the present invention to provide an ometer P3 to two valves 12 and 13 connected as a phase interconnected system in which the disadvantage referred splitter. The output of 12, 13 is applied to two valves to is substantially avoided or at least markedly reduced. According to the present invention there is provided 45 14 and 15 in push-pull arranged to feed one phaseof a a servo arrangement for the solution of simultaneous two-phase motor M1, the other phase of the motor being equations comprising at least two closed-loop servo sys tems each having an input at which variations represen connected to terminals 16 and 17. fed with an alternating current at 400 c./s. from a source ~ The valves 14, 15 are provided with negative feedback two outputs, and means for introducing into the loop 50 through a transformer 18 in order to provide the damp ing requisite in view of the high inductance of the Wind' of one system a control dependent upon variations in ing of the motor M1_ to which the valves are connected. one or more of the other systems and such as to render The motor M1 is shown as driving the wiper of ‘a po the loop gain around the ?rst-named system more nearly tentiometer P1 through, a' gear train 19 which also has constant than in the absence of the said control. The invention will be described by way of example with 55 an output shaft D1. The potentiometer P1 is centre tapped to earth and each of its end terminals 20, 20’ is reference to the accompanying drawings in which: tative of one of the equations can be applied, at least ' FIG. 1 is a block circuit diagram of a known arrange ment embodying two closed-loop electro-mechanical servo systems, ' I ' connected to an alternating current source at 400 c./s. The wiper of the potentiometer P1 is coupled through a cathode follower valve 21 and a transformer 22 to FIG. 2 is a modi?cation of the arrangement of FIG. 1 60 the terminals of a potentiometer P2 which is also centre .tapped to earth. The valve 21 is provided in order to in accordance with the present invention, and FIG. 3 is a practical circuit diagram of the circuit of FIG. 2. t . In the drawings electrical couplings are indicated by full lines and mechanical couplings by broken lines. In the known arrangement of FIG. 1 one electrical variation 1, is applied to the input of a ?rst servo com prising an ampli?er A, and an electro-mechanical trans ducer in the form of a motor M1 driving a potentiometer P1 and an output shaft D1 constituting the output of the ?rst servo. Another electrical variation I2 is applied to the input of a second servo comprisingan ampli?er prevent the current in P2 from loading P1 and thereby in?uencing its law. The ampli?er A2 may be identical with AA1 and BA, 65 withthe exception that the valve 11 is coupled to the valve 12 without the intermediary of the potentiometer P3. One phase of the two-phase motor M2 is connected to the output of the ampli?er A2, the other phase of the motor being fed with alternating current at 400 c./s. from terminals 23, 24 connected to a suitable source. The motor M2 drives a gear train 25 having one out put shaft D2, another driving the wiper of the potenti 3,021,071 3 4 ometer P2 and a third driving the Wiper of the potenti ometer P3. trically connecting said ?fth transducer between the out put of said ?rst ampli?er portion and the input of said second ampli?er portion. 2. An arrangement according to claim 1, comprising means electrically coupling said second transducer to the input of said third ampli?er portion. The wiper of the potentiometer P2 is connected to pro Vide the input P1. In the example shown in FIG. 3 the input variations I1 and I2 are alternatingcurrents at 400 c./s. varying in amplitude in accordance with some control parameter. 3. An electro-mechanical servo arrangement compris ing a ?rst servo system including ?rst and second ampli ?er portions each having an input and an output, a ?rst The ampli?er AA1, BA1 is therefore A.C.-coupled. The variations I1 and I2 may, however, be varying direct currents, in which case a D.C.-coupled ampli?er is used and the motors M1 and M2 are replaced by DC. motors. If desired, the ampli?er A2 may be divided into two electro-mechanical transducer electrically coupled to the output of said second ampli?er portion, a ?rst potenti ometer, means mechanically coupling said transducer to parts, corresponding to AA1 and BAI and the voltage applied from the ?rst part AA1 to the second part BAl may be controlled by a potentiometer corresponding to P3 driven by the shaft D1 and having a law which is an approximate inverse of that of the potentiometer P1. said potentiometer, a second servo system including a third ampli?er portion, a second electro-mechanical transducer electrically coupled to the output of said third ampli?er portion, second and third potentiometers, means mechanically coupling said second transducer to said second and third potentiometers, means electrically It Will also be evident that the invention can be applied when there are more than two interconnected servo sys tems. connecting said second potentiometerv to the input of . 20 said ampli?er portion, and means electrically connecting The way in which the invention can be applied to said third potentiometer between the output of said ?rst closed-loop servo systems other than electro-mechanical ampli?er portion and the input of said second ampli?er systems, for example to hydraulic systems, will be under portion. stood by those skilled in the art. 4. An arrangement according to claim 3, comprising I claim: 25 means electrically coupling said ?rst potentiometer to the 1. An electromechanical servo arrangement compris input of said third ampli?er portion. ing a ?rst servo system including ?rst and second ampli References Cited in the ?le of this patent ?er portions each having an input and an output, a ?rst electro-mechanical transducer electrically coupled to the UNITED STATES PATENTS output of said second ampli?er portion, a second electro 30 2,784,501 Stern et al ______ _-'- ____ __ Mar. 12, 1957 mechanical transducer mechanically coupled to said ?rst transducer, a second servo system including a third ampli ?er portion, a third electro-mechanical transducer elec trically coupled to the output of said third ampli?er portion, a fourth and a ?fth electro-mechanical trans 35 ducer mechanically coupled to said third transducer, means electrically connecting said fourth transducer to the input of said ?rst ampli?er portion and means elec ‘OTHER REFERENCES Electronic Computers (Shannon), Electronics, August 1946, PP. 110-113. An Automatic Simultaneous Equation Computer and its use in Solving Secular Equations (Adcock), The Re view of Scienti?c Instruments, vol. 19, No. 3, March 1948, pp. 181-187.