GB1398842A - Analogue computers - Google Patents

Abstract

1398842 Solving simultaneous equations J H D WALTON 2 June 1972 [3 March 1971] 5877/71 Addition to 1224871 Heading G4G An analogue computer of the kind using two sets of conductors respectively provided with input and output terminals and connected together by impedances representing parameters of the problem (e.g. coefficients of simultaneous equations), utilizes negative feedback signals in time or frequency multiplex with the forward signals whereby self-balancing may be achieved, and further network conductors associated with a feedback path for an error signal depending upon the difference between the response from the further conductors and a desired response derived from a variable reference source. In the embodiment, the apparatus is used to determine the weight of two ingredients in a mixture having two constituents in a desired proportion, the proportions of the two constituents in the separate ingredients being known. The probelm may be stated in terms of three simultaneous equations in variables x 1 , x 2 , x 3 where x 1 is the weight of the mixture and x 2 , x 3 are the values sought. In the network columns 5, 6, 7 provide analogues of the equations, rows 2, 3, 4 are fed with inputs representing the variables and the various connecting impedances are inversely proportional to the coefficients of the equations as determined by the known properties of the ingredients. Column 7 is the analogue of x 1 = x 2 + x 3 (i.e. 41, 42, 44 are unit resistances), so that if a known -x 1 is fed from an inverting amplifier 34 to row 4, the required values of x 2 , x 3 are those which produce zero output signal simultaneously in all three columns. Self-balance in this conditions may be achieved by inverting the output signal of a column and using it as an input, interference between forward and feedback signals in the network being prevented by time or frequency multiplexing. For this purpose, columns 5, 6 and rows 2, 3 may be associated with time-multiplex TR devices. According to the invention, a TR device 37 has an input connected by resistances 35, 40 respectively to the source of signal -x 1 and to an adjustable source of reference voltage 38 whereby it responds to the difference between x 1 and the reference voltage. By means of a pulseoperated switch, this error signal is alternately stored and fed to column 7 and thence by resistances 41, 42 to the sources of inputs x 2 , x 3 . During the periods that TR device 37 is non-transmissive, switches 39, 49 close and the TR devices (not shown), associated with inputs x 2 , x 3 become transmissive, whereby revised values of these variables are fed to the circuit and a new error signal generated. The error tends to zero as x 1 approaches a value set by adjustment of the reference source 38. The output of column 7 is connected to the input of inverter amplifier 34 by a direct feedback path. The purpose of the comparison between the given x 1 and the reference voltage is to enable x 1 to be reduced to a feasible value when the network indicates an insoluble problem, or to increase it to a maximum when the network produces a solution for initial test values of x 2 , x 3 .