US3191016A - Analog computer - Google Patents

Description

June 22, 1965 Filed Jan. 13, 1959 FIGI FIG. 2.

FIG3.

w. D. HOLAK ETAL 3,191,016

ANALOG COMPUTER 2 Sheets-Sheet 1 INVENTORS CLIFFORD E. MCCARTY ERKKI K. HYYPOLAINEN ATTYS.

WILLIAM D. HOLAK June 22, 1965 Filed Jan. 13, 19 59 FIGS w. D. HOLAK ETAL ANALOG COMPUTER 2 Sheets-Sheet 2 INVENTORSZ United States Patent 3,191,016 ANALOG COMPUTER William D. Holak, Crum Lynne, Clitiord E. McQa'rty,

Ridiey Park, and Erlrki K. Hyypolainen, Chester, Pa,

assignors to Scott Paper Company, Chester, Pa, a corporation of Pennsylvania Filed Jan. 13, 1%), Ser. No. 786,564 14 Claims. (Cl. 235-185) This invention relates to a simple analog computer for solving problems having to do with the change, exchange or flow in a manner which is most efficient and/ or least costly and particularly with reference to determining maximum flow under given sets of conditions.

Generally speaking, and with the exception of certain internal limitations, the computer is capable of solution of problems of this general sort by selection of power as the analog of the quantity to be minimized, and selection of other parameters according to their relative natures, if the problem can be set up as linear simultaneous equations within specified limits.

In its most general form, the analog computer of the present invention consists of a network having three types of terminals which represent input, output and intermediate terminals and which provide network nodes. The internal network is defined as that part of the network between the input and output terminals and consists of flow paths connecting together various terminals including intermediate terminals. All of the terminals are not necessarily connected to one another but each terminal is connected into the network in such a way as to provide, by means of its various flow paths, a continuous flow route between input and output terminals. Each flow path has a potential producing element arranged to oppose the general direction of fiow. Ordinarily, but not necessarily, each flow path will also have a flow rectifying means to insure unidirectional flow in that path. The individual flow paths are preferably to this extent similar to those described in the copending applications of William C. Elmore and Clifford E. McCarty, now US. Patent No. 2,934,273, and Clifford E. McCarty and William D. Holak, now U.S. Patent No. 3,017,104. Additionally the flow paths may have means for limiting the total amount of flow to represent a specified load capacity. External of the internal network at least one conductive connection between output and the input terminals and including a flow generator, is provided.

The present invention diiiers from the two abovespecified inventions because of the provision for internal terminals or nodes. The provision of these internal terminals permits complex internal networks not possible in the computers considered in the aforesaid applications. The terminals or nodes in the contemplation of the present invention may be more than a junction point. They may be energy-consuming points, energy producing points, flow-limiting points, or combinations thereof, in any of which cases the node is no longer a simple node in a usual sense but a split node effectively having an input terminal and an output terminal with the energy-consuming element and/or energy producing element and/ or flowlirniting element and/ or potential producing element in the flow path between the terminals. Such terminals or nodes enable the solution of problems of greater complexity and details than the two above-mentioned computers .which are designed to handle more general problems. The present computer may find wide application in analysis of detailed information in order to obtain more general information for use in other computers, such as the two above mentioned.

The present invention also introduces the concept of the split node whereby not only the flow paths between tints Patented June 22, 1965 nodes have some effect upon the current but the nodes themselves may have an effect upon the current. The split node is nothing more than a node which is divided so that it effectively has an internal tic-w path from one part of the node to the other in which various'types of flow-resisting elements, limiting elements and/ or potential producing elements may be introduced. In this arrangement the current flows to one part of the split node and away from the other part of the split node. At the present time it is contemplated that a maximum capacity flow limiter may be used in this location or a resistive element may be used between the divided parts of the split node but other applications may call for additional elements such as a potential producing element between the parts of the split node.

The flow-limiting device may have a variety of forms, one of which will be specifically described herein. The flow-limiting device will find wider application than strictly in a computer having internal network nodes and there is no intention to limit it to the specific form of computer described herein although it is useful with such a com puter.

The computer of the present invention will find wide use as a general transportation computer. It is useful,

' for example, to determine the manner in which freight should be routed in order to permit it to reach its destination most efficiently and probably leastexpensively. In the usual problem, the nodes may be numbered from 1 to N, and the flow paths described in terms of the nodes which they link, the how path linking nodes i and 1' being designated by L This general type of problem might be described as the network utilization problem which can be stated as follows:

Where X,,- denotes the rate of flow of product through link L find a set of flowsrthrough the links which maximize the total flow in the node N.

The problem may be subject to certain restraints. F or example, X in many cases must be positive and must not exceed a certain maximum load capacity.

Many possibilities exist with the computer of the present invention. A better understanding of the present invention may be had by reference to the following drawings in which:

.FIG. 1 shows a network having internal terminals arranged in parallel flow routes;

FIG. 2 illustrates a computer having plural internal terminals arranged in series in a single flow route;

PEG. 3 shows a computer in accordance with the present invention having a composite arrangement;

FIG. 4 schematically shows a computer of the present invention including cross link flow paths, the fiow paths of which have flow-limiting means;

FIG. 5 is a computer according to the present invention similar to FiG. 4 but having separate flow paths for travel in both directions between certain terminals;

FIG. 6 is a detailed showing of one form of flow-limiting device in accordance with the present invention;

FIG. 7a shows one form of split node;

FIG. 7b shows another form of split node; and

FIG. shows still another form of split node.

Referring first to FIG. 1, there is shown a computer network having an input terminal 10, an output terminal 11 and two intermediate terminals 12 and 13. The network between input and output terminals 19 and 11 including the intermediate terminals 12 and 13 represents the internal network. Each of the flow paths 14 connecting terminals 19 and 12, 12 and 11, 16 and 13, and 13 and 11 includes potential-producing means 15. Means insuring the flow only in opposition to the potential-producing means need not be used in this arrangement since there is no alternative provided that the current fiow externally generated is not reversed. As shown, there is connected to the input terminal 16 a constant flow generator 16, which in turn is connected in series within an external flow path 17 connecting terminals 11 and 19 together. In the circuit of FIG. 1, current divides at terminal .10 and flows partially through node 12 and partially through node 13 to terminal 11.

Referring to FIG.'2, an arrangement is shown in which there is an input terminal 20, an output terminal 21 and two intermediate terminals 22 and 23. In this case, the terminals 22 and 23 are connected in series with one another and the input andoutput terminals by series flow paths 24 to provide a single continuous flow route from terminal to terminal 21 comprising the internal network. Each of the flow paths 24 have potential-producing means 25 and may contain flow-rectifying means as well, although such rectifying means are unnecessary because of the simplicity of this particular network and in view of the fact that flow generator 26 at output node 21 produces flow in a proper direction at all times. An external connection 27 completes the circuit between output terminal 21, flow generator 26 and input terminal 20.

Referring now to FIG. 3, there is shown schematically a computer which has an internal network which is a composite of the networks of internal networks of FIGS. 1 and 2. Between an input terminal 30 and an output terminal31 are intermediate terminals 32, 33 and 34. Terminals 32 and 33 are connected in series with'the terminals 30 and 31 by their intermediate flow paths 35 to provide a continuous flow route. A parallel continuous flow route is provided through terminal 34 from terminal 30 to terminal 31 through similar intermediate flow paths 35. Each of the flow paths in this instance has a potential-producing means 36 plus means for producing a unidirectional fiow 37. Flow is induced by aconstant fiow generator 38 at the input terminal 30 and constant flow generator 39 at the output terminal. These generators are in turn connected together by external connection 40. If preferred, the rectifier means 37 may be omitted in this particular form.

Referring next to FIG. 4, a much more complex array is illustrated. The nodes which in the general problem are numbered from 1 to 10 are here numbered 1, 2, 3, 4 and 5, and N where 1 is the basic input terminal and N is the basic output terminal. Terminal 2 may also be considered an input terminal, and terminal 4 may also be considered an output terminal, although .by another viewpoint they may be considered special effect nodes in accordance with the needs of a particular problem.

In FIG. 4flow generator 41 produces a flow into node 1, and flow generator 42 produces a flow out of node N. Flowgenerator 43 produces flow into node 2, and flow generator 44 produces a flow out of node 4. Nodes 1 and 2 are connected together by flow path 45. Nodes 2 and 4 are connected by flow path 46. Nodes 4- and N areconnected by flow path 47. Flow paths 45, 46 and 47, and nodes 1, 2, 4 and N thereby provide a series ilow route. Similarly, nodes 1, 3, 5 and N are linked by flow paths 43, 49 and 50 in a series flow route. The two paths thus described are parallel flow paths'which might be thought of as alternate routes along which trucks may move through various cities represented by nodes. Interconnecting routes from 2 to 3 or from 4 to 5 are provided by flow paths 51 and 52. Additionally, other flow paths 53 and 54 interconnect nodes 2 and 5 and 3 and 4, respectively. Under certain circumstances it may be desirable for detours to be'taken.

FIG. 5 shows a similar arrangement to FIG. 4 wherein similar parts are indicated by similar numbers having the same designator with the addition of primes thereto. FIG. 5. provides, however, for travel in either direction between intermediate nodes, or at least some of them. Thus, 'in addition to flow from terminal 2' to terminal 3' along route 51', there can be a flow from terminal 3'. to terminal 2 along flow path 55. Between terminals 4' 4;, and 5 flow proceeds in one direction over flow path 52' and in the other direction over flow path 56. Alternate flow paths between terminals 2' and 5', 3' and 4' are provided by flow paths 57 and 58. Additionally, alternate flow paths are provided between terminals 2 and 4', 3' and 5 by flow paths 59 and 60.

Within the flow paths, as illustrated, are potential producing devices 61 arranged to oppose the flow of cur.- rent which is limited to flow in one direction through the flow path by rectifying means 62. Additionally, flow capacity limiting devices 63' are provided and may be set at dilferent levels to restrict a particular capacity in accordance with the analog of the problem undergoing solution. 7

' Referring to FIG. 6, there is shown schematically one arrangement for a flow limiting device of an electrical type. In this arrangement a normally closed relay switch 65 normally shorts out a flow limiting resistor 66 intended to limit current flow through the series circuit branch which is placed in series in the flow path. The relay 67 is arranged to open the switch 65 upon the attainment of a certain current level through to the device. This may be determined by resistor 68 in series with the switch 65, the voltage across which is amplified by amplifying means 69 and fed to a comparison means 70 such that, when the, voltage corresponding to the capacity of the device is reached, the relay 67 is actuated opening the switch 65 and there opposing the resistance 66 to limit current flow. Preferably, the flow limiting device is a multi-step switching arrangement not as simple as described above but one (not shown) which includes a plurality of switches 65, relays 67 and comparison means 76 appropriately arranged to provide a maximum cur-v rent restriction for the flow path.

Many other types of current limiting arrangements are available, and the one shown in FIG. 6 is by way of illustration rather than by way of limitation.

The present invention also contemplates the splitting of internal nodes. For example, in a particular instance a node like node 4 of'FIG. 4 might be split to introduce a resistor element '73 between the parts of the node 4a and 4b, as shown in FIG. 7a. At another point, for example, node 5 whichmight be split into node portions 5a and 5b, a current limiting element (such as that shown in FIG. 6) might be introduced as element 71 in series between the terminals 5a and 5b as shown in FIG. 7b. In FIG. 70 there is shown a split node consisting of parts 3a and 3b, between which is placed a potential producing element 72. Combinations of such elements (not shown) may be introduced in such split nodes.

Considering a network like that of FIG. 5, by eliminating different portions of the network, it can be visualized how problems of different form can be set up on a computer. For example, eliminate flow generators 43' and 44 and any external circuit which they may include so that nodes 2' and 4 are clearly internal nodes and a typical single supply, single demand situation is achieved. The potential producing means may be set to represent cost, the time to travel a particular flow path link, or whatever other limiting factor applies. As shown in FIG. 4, at most, one link joins any two nodes, node 1 is a source of some product and node N is the only demand point for this product. In order to simplify, it can be assumed that the product can be shipped homogen-i ously in a sense that it can flow in a continuous fashion through links rather than only in discrete truck loads or train loads. With each link or flow path L there is associated a non-negative load capacity limiting element. This load capacity is to be interpreted as the maximum sustained rate of one-way flow which the link is capable of bearing for one reason or another and dimensionally.

may be described in terms of tons per day, for example.

The limitations of the general network utilization problem described above apply and if X denotes the rate of flow of the product through flow path L then it is possible,

to find a set of flows through the various links which maximize the total flow in node N subject to the following restraints or limitations: (1) X must be non-negative and must not exceed C (determined by the load capacity limiting means) and (2) the total flow into any intermediate node, i.e., nodes 2, 3, to N1, must equal the total flow out of that node. The last restraint is to the efiect that none of the product is consumed or absorbed except at N and it follows that the effect of the problem is to maximize the total flow out of node 1.

The problem stated can be changed by conditions within the nodes which represent cities oifering general bottlenecks to the flow of traflic, for example. Thus, by use of the split node technique described above, it is possible to put a load capacity limitation or a handling or transfer cost at a node whereby regardless of the capacities of the individual flow paths or links leading into the node, the node imposes a separate limitation upon the flow.

Whenever a flow generator, such as 43 or 44 is introduced at a node, a new limitation is imposed in place of the second limitation above stated. Thus, for example, the total flow into the node 2 must exceed the total flow out of the node, considering only flow paths, by the amount of flow added to the node by flow generator 43. The converse of this is true if the flow is out of the node, as at node 4.

The physical interpretation of the arrangement of the flow generators at the nodes 2 and 4 may be that these nodes are points of limited constant production or consumption of the product. The objective remains that of maximizing flow to N. This need not be the case, however, and both flow generators 41 and 43 may supply nodes 1 and 2, respectively, as input nodes which are sources of the product and flow generators 42 and 44 may be connected to output terminals 4 and N so that they both may represent points of demands. In such case, the problem becomes one of maximizing the flow from all sources of supply to all demand points. Some circumstances may require the introduction of artificial nodes which have no physical significance in order to set up a problem of this type but no limitation is placed upon the physical significance or lack thereof of the nodes and flow paths or other portions of the computer.

The computer has been described for the most part in general terminology, even though the networks illustrated have been D.C. electrical systems. In such systems, the constant flow devices are constant flow generators, the flow paths are conductors, and the nodes are junction points of several conductors, except in the special case of split nodes, where they are two junction points separated by a conductive path including some element; The potential-producing means in this case is a battery, and the rectifying means is preferably a diode rectifier.

In other embodiments, the computer of the present invention may appear as an AC. network, a mechanical network or as a fluid network either employing hydraulic or pneumatic components. All modifications within the scope of the claims are intended to be within the spirit of the invention.

We claim:

1. In an analog computer, a network having a plurality of terminals including at least one input terminal, one output terminals, one of which flows routes includes said stituting network nodes in an internal network, said internal network having at least two flow routes each comprising at least one flow path connecting said input and output terminals, one of which flow routes includes said intermediate terminal dividing such flow route into two flow paths, at least one potential source element in at east one of the flow paths in the internal network and rectifiers in enough of the flow paths to eliminate circulating flow in the internal network, and at least one flow path including a constant flow generator between the output and input terminals external of the internal network, the improvement comprising at least one element in at least one of said routes of the internal network to limit flow through said route to a predetermined maximum which element consumes essentially no energy in the process until a predetermined current level is exceeded.

2. The analog computer of claim 1 in which there are intermediate terminals connected in series as well as intermediate terminals in parallel flow paths.

3. The analog computer of claim 2 in which terminals in parallel flow paths are connected together by cross flow paths.

4. The analog computer of claim 1 in which there is a constant flow generator at the input and output terminal of the network.

5. The analog computer of claim 1 in which there are a plurality of input terminals each having a constant flow generator associated with it and each input terminal having a continuous flow route to an output terminal.

6. The analog computer of claim 1 in which there are a plurality of output terminals each having an associated constant flow generator, and each input terminal having a continuous flow route through the fiow paths to an output terminal.

7. The analog computer of claim 1 in which some of the terminals have two paths between them, each limiting flow to the opposite direction from the other.

8. The analog computer of claim 1 in which there are at least two intermediate terminals serially disposed in a single flow route dividing such flow route into three flow paths.

9. The analog computer of claim 1 in which there are at least two intermediate terminals each in a diiferent flow route.

10. The analog computer of claim 8 in which atleast some of the intermediate terminals have two paths between them, each limiting flow to the opposite direction from the other.

11. The analog computer of claim 1 in which at least one of the terminals is a split node wherein the node is split into two separated terminal points between which is introduced an electrical element having some analog significance corresponding to a condition occurring at the analog of a nodal point.

12. The analog computer of claim 11 in which between the split nodal portions there is introduced a resistor element.

13. The analog computer of claim 11 in which between the split nodal portions there is introduced a flow limiting element.

14. The analog computer of claim 11 in which between the split nodal portions there is introduced a potential producing element.

References Cited by the Examiner UNITED STATES PATENTS 2,569,646 10/51 Wade et al. 235180 XR 2,608,770 9/52 Hansford 235--184 XR 2,639,089 5/53 Gleyzal 235-180 2,639,357 5/53 Kesselring 323--96 2,884,193 4/59 Liebmann 235184 2,934,273 4/60 Elmore et al. 235185 2,960,646 11/60 Malsbury 323- 3,053,453 9/62 Bock et al. 235l MALCOLM A. MORRISON, Primary Examiner. LEO SMILOW, WALTER W. BURNS, 111., Examiners.

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No, 3,191,016 June 22, 1965 William D. Holak et a1 It is hereby certified that error appears in the above numbered patent requiring correction and that the said Letters Patent should read as corrected below Column 5, lines 64 and 65, strike out "output terminals, one of which flows routes includes said stituting network nodes in an internal network, said in" and insert instead output terminal, and one intermediate terminal constituting network nodes in an internal network, said in- Signed and sealed this 21st day of December 1965.

(SEAL) Attest:

ERNEST W. SWIDER EDWARD J. BRENNER Attesting Officer Commissioner of Patents

Claims (1)

1. IN AN ANALOG COMPUTER, A NETWORK HAVING A PLURALITY OF TERMINALS INCLUDING AT LEAST ONE INPUT TERMINAL, ONE OUTPUT TERMINALS, ONE OF WHICH FLOWS ROUTES INCLUDES SAID STITUTING NETWORK NODES IN AN INTERNAL NETWORK, SAID INTERNAL NETWORK HAVING AT LEAST TWO FLOW ROUTES EACH COMPRISING AT LEAST ONE FLOW PATH CONNECTING SAID INPUT AND OUTPUT TERMINALS, ONE OF WHICH FLOW ROUTES INCLUDES SAID INTERMEDIATE TERMINAL DIVIDING SUCH FLOW ROUTE INTO TWO FLOW PATHS, AT LEAST ONE POTENTIAL SOURCE ELEMENT IN AT LEAST ONE OF THE FLOW PATHS IN THE INTERNAL NETWORK AND RECTIFIERS IN ENOUGH OF THE FLOW PATHS TO ELIMINATE CIRCULATING FLOW IN THE INTERNAL NETWORK, AND AT LEAST ONE FLOW PATH INCLUDING A CONSTANT FLOW GENERATOR BETWEEN THE OUTPUT AND INPUT TERMINALS EXTERNAL OF THE INTERNAL NETWORK, THE IMPROVEMENT COMPRISING AT LEAST ONE ELEMENT IN AT LEAST ONE OF SAID ROUTES OF THE INTERNAL NETWORK TO LIMIT FLOW THROUGH SAID ROUTE TO A PREDETERMINED MAXIMUM WHICH ELEMENT CONSUMES ESSENTIALLY NO ENERGY IN THE PROCESS UNTIL A PREDETERMINED CURRENT LEVEL IS EXCEEDED.

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