Patent GB-897198-A (GB)
Title: Analog computer
IPC: G11B5/53
Filed: 1960-01-13
Abstract: 897,198. Electric analogue computers. SCOTT PAPER CO. Jan. 13, 1960 [Jan. 13, 1959], No. 1231/60. Class 37. An analogue computer for solution of linear simultaneous equations of the type representing the unidirectional transference of material at maximum efficiency from despatching points to receiving points along a plurality of routes having coefficients representing the respective route costs of transference without the use of iterative steps, compriees a simulating network having input terminals, output terminals and intermediate terminals all constituting nodes of an internal network; analogue flow paths connecting predetermined input terminals to predetermined output terminals with predetermined intermediate terminals lying in said flow paths, which together constitute the internal portion of the network between the input and output terminals; potential producing elements representing the respective coefficients in the equations being inserted in the parts of the flow paths between the input and intermediate and between the intermediate and output terminals in opposition to the normal directions of the analogue flow in each such paths representing a respective variable of the equations; flow rectifying elements inserted in sufficient flow paths to prevent circulatory flow within any loop internal of the input and output terminals which might otherwise arise from the potential producing elements, and at least one flow path connected externally of the internal network between the output and input terminals thereof containing a constant analogue flow generator; the flow in each path being measured by suitable means ascertaining the value of the analogue thereof as a solution of the respective equation variable. Fig. 4 shows an electrical computing network having input nodes 1, 2, output nodes 4, N; and intermediate nodes 2, 3, 4, 5 wherein nodes 1, 2; 1, 3; 2, 3; 2, 4; 2, 5; 3, 4; 4, 5; 4, N; and 5, N are interconnected over flow paths 45, 48, 51, 46, 53, 54, 52, 47, 50 respectively containing series connected half-wave rectifiers 62, current limiters 63, and opposition voltage sources 61; the network being fed with currents i1 and i2 from generators 42, 43 at input nodes 1, 2 and currents i3, i4, being withdrawn from nodes 4 and N by generators 44 and 42 to represent a system of distribution, wherein a large number of trucks carries goods from supply points 1, 2 over plural routes through various cities represented by network nodes 2, 3, 4, 5 to delivery points 4, N. In the distribution system Si = number of trucks required at supply point i per unit time Dn = number of trucks required at delivery point n per unit time Xij + number of trucks moving from i to j over link Lij per unit time |Xij | max = maximum allowable value of Xij Cij = cost per truck moved from i to j T = total cost of delivery It is shown that (1) T = # CijXij ij (2) # Si = # Dn i n (3) S1+S2 = D3+D4 and by electrical analogy with a proportionality constant of unity, (4) Si = ii the current into the ith supply point (5) Dn = in the current out of the nth delivery point (6) Xij = iij the current between nodes i, j (7) IXijlmax = |iij|max the maximum permissible current between i, j (8) Cij = eij the opposition voltage 61 between nodes i, j (9) T = P the total power dissipated internally of the network so that (10) # CijXij = #eij iij ij ij (11) i1+i2 = i3+i4 and if the opposition voltages of the respective internodal branches are adjusted to represent the respective transportation costs over corresponding channels, and the input and output currents are adjusted to represent the numbers of trucks arriving at the supply points and leaving the delivery points per unit time, it is shown with reference to Specification 869,856 that the power dissipation in the network attains an equilibrium value at which it is a minimum. The total cost is thus also minimized and the density of truck movement over the various routes for maximum economy of operation is analogously obtained by measuring the currents in the corresponding network paths by instruments inserted therein. Rectifiers 62 are inserted to prevent recirculating currents by limiting current flow to a single direction. In Fig. 5 (not shown), a more complex network for solving the transit problem comprises flow paths permitting bi-directional currents between predetermined pairs of intermediate nodes, and including flow limiting devices set to operate at different levels whereby the traffic capacities of different routes are simulated. Fig. 6 shows a flow limiting device wherein a normally closed relay 67 short-circuits limiting resistor 66 series connected in a flow path with resistor 68; the voltage drop across which is amplified and compared with a reference at comparator 70 to open relay 67 and insert the limiting resistor when the current in the path exceeds a predetermined level. The device may operate to insert alternative limiting resistors at different critical current levels, using multiple relays and comparators. Intermediate nodes may be split to introduce additional resistors, current limiters and voltage sources into the network (Figs. 7a, 7b, 7c, not shown), to represent traffic bottlenecks, load limitations, or additional transit costs. Simpler forms of computing networks are described (Figs. 1, 2, 3, not shown). It is stated that the analogue network may be A.C. operated, or may be a mechanical, pneumatic, or hydraulic network. Specification 869,856 is referred to.