Patent GB-1224871-A (GB)
Title: Apparatus for the solution of simultaneous equations and inequalities by electrical analogue means
Inventor: WALTON JOHN HUGH DAVEY
IPC: G06G7/122
Filed: 1966-11-10
Abstract: 1,224,871. Analogue solution of simultaneous equations or inequalities. J. H. D. WALTON. 9 Feb., 1968 [10 Nov., 1966], No. 50448/66. Heading G4G. An apparatus for solving arrays of simultaneous equations or inequalities applicable to the optimization of manufacturing processes, and business or economic problems, comprises a multiterminal network in which each of a first set of terminals is individually connected to each of a second set of terminals over resistance elements; the elements connected to a terminal of the first set being respectively inversely proportional to the coefficients in the first column of a set of simultaneous equations or inequalities; the elements connected to another such terminal being respectively inversely proportional to the coefficients in the second column, and so on for the remaining columns of coefficients, and for the column of constant terms; so that all the coefficients of a given equation are represented by elements converted to a specific terminal of the second set. Variable voltage generators are connected between individual first set terminals and earth, and current meters are connected between all terminals and earth. The voltage generator energizing the elements representing the column of constant terms is adjusted to an arbitrary value representing unity, and the remaining generators are adjusted to zeroize the meters connected to the second set of network terminals; at which the equations are solved and the voltmeters connected to the first set of network terminals read the analogues of the independent variables. For inequality solution, adjustment is made for the meters of the second set of terminals to indicate a predetermined polarity or phase sense. In operation, the terminals 5 of the first set of a network 1 are respectively energized from generators of a first type 3, wherein a first reference frequency source 10 energizes a modulator 9 whose output is amplified at 7 and applied to terminal 5 over a filter 6; the signals emergent from the terminal at a second frequency being extracted by the filter, amplified at 8 and applied to the modulator 9 over a rectifier and smoothing circuit (not shown) to control the amplitude of the signal fed into terminal 5. The output at the corresponding output terminal of the second set is applied to a generator of a second type, wherein it is extracted by filter 13, amplified at 14 and similarly applied to modulator 11 energized from a second reference frequency source 12 to produce an output at a second frequency representing the amplitude of the first frequency signal at the terminal, which output is applied to the terminal through the filter; passes through the network, and controls the input to terminal 5, so that the corresponding terminal output is zeroized to solve the equation, or adjusted to solve the inequality. The remaining network input and output terminals may be energized from similar generating circuits energized in common from sources 10, 12, and the input to terminal 5 may be zero frequency (i.e. D.C.). In a modification (Fig. 2, not shown) of a network of the kind described in Specification 1,173,900 wherein the first and second sets of network terminals are respectively connected to sets of row and column conductors, diode ring modulators are utilized, fed from centretapped transformers; and the filter circuits comprise coupling transformers and by-pass capacitors; the inputs to the first set of terminals being D.C. and the inputs to the second set being A.C. at the frequency of a single source, while the amplifiers have critical frequency responses. Edge reading alternating and direct voltmeters are connected to the first and second terminal sets. The network elements may be directly variable by external parameters, e.g. strain; or may comprise mechanical, optical, hydraulic or like equivalent elements linked to the network by transducers.