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STANLEY ROGERS Analog Computer Laboratory, Convair Division, General Dynamics Corp., San Diego, Calif.
Analog Computers and Computing The 10 years of experience with a mammoth analog computer described here provide useful know-how for users or potential users of even the smallest equipment
T H E most popular types of largescale analog computers in use today are the “direct-analogy’’ analog computer and the electronic analog computer or differential analyzer (sometimes called a n “active element” analog computer because its basic component is the “operational” amplifier). The former is basically an electrical network consisting of inductors, capacitors, resistors, and transformers, plus current generators and forcing-function generators. A number of aircraft companies have direct-analogy computers, the largest of these machines having been installed a t Convair-Ft. Worth this year. Principal uses are the solution of static-stress problems in redundant structures and the solution of flutter, landing-load, and gust-load problems in aircraft. T o solve problems on these machines, structures are divided into cells, and the physical characteristics of each cell are simulated on a direct-analogy basis by capacitors (mass), inductors (springiness), resistors, and transformers (lever-arm lengths). While this seems simple, in practice it isn’t when it is necessary to represent a new type of structure adequately. Once this has been done by experts, variants are easily handled. Though digital computers have made inroads into the areas formerly regarded as the property of this type of computer, the directanalogy machine is the most efficient on
1A3A
flutter problems and in many cases is competitive in the other areas. This type of computer solves certain classes of partial differential equations. The term “analog computer” usually refers to the electronic analog computer. I t consists of a n assembly of operational amplifiers, potentiometers, multipliers, function generators, and decision elements, and means for interconnecting these to solve specific problems. The principal use of these computers is the solution of system of simultaneous ordinary differential equations, usually nonlinear. These equations occur widely in aircraft and missiles-in control systems, servos, aerodynamic stability, interception problems, guidance system dynamics-and analog computers are widely used to solve them. Long before a new airplane or missile has its first test flight, it is common practice to “test fly” the airframe and its critical subsystems on the analog computer. For example, the entire hydraulic control system is built on a test stand. The system is then connected to the analog computer (Figure 3), which simulates the balance of the complete airframe system and its aerodynamics and which can be extended to include radar system, fire-control system, and maneuvering target. Thus, the control system can be “debugged” to a large extent before the first airframe is built. I n the computer laboratory it is quite
INDUSTRIAL AND ENGINEERING CHEMISTRY
safe to explore flight maneuvers too dangerous to flight test and so learn how control system and airframe dynamics will behave in extreme maneuvers. The same computer-plus-control-system combination is used to familiarize pilots with the characteristics of new airplanes before they fly them for the first time. These uses of analog computers have resulted in large but undeterminable savings in life, time, money, and experimental aircraft. In addition, design of the first model of a new aircraft is a great deal better than it could have been without extensive use of analog computation a t all phases of design, development, and test. An extension of analog computer applications pioneered at the Naval Air Missile Test Center, Mugu, Calif., is postflight analysis. Here the computer’s coefficientsand, if necessary, hookup, are experimentally modified until the computer duplicates the actual flight of a test missile, which may not have flown as expected. I n this way insight into what caused unexpected behavior can often be gained. Fields of application for general-purpose electronic analog computers are growing. Just about to begin is their use in static-stress analysis of redundant structures. This application in its simpler forms uses many linear computing elements (amplifiers and potentiometers), leaving costly multipliers and function generators idle. For this reason, static-
stress analysis is economically attractive only if it does not displace problems that use the computer’s equipment more fully. Another new application is the solution of sets of simultaneous algebraic equations. This requires the use of special networks with the operational amplifiers to keep the computer from breaking into oscillation. As yet an upper limit on the size a set of equations has not been found, but it will probably depend on the number of potentiometers available. large-Scale Analog Computer
Historically, most computer facilities started small and grew rapidly. In 1948, when few people knew what an analog computer or “simulator” was, Convair-San Diego very nearly refused such a computer offered free by the Navy. When it arrived, nobody knew how to use it or what it was good for, but within two years a substantially expanded computer was running 24 hours a day. Because removable, storable problem boards were almost unknown to analog computers in those days, a crude system was built to make multishift operation possible. Demands for computing equipment quickly outstripped the small facility as the needs for the Terrier missile program -and the impending Tradewind, F-102, and Atlas programs were felt. Eventually machines of similar design were built for Convair-Pomona and Convair-San Diego. These were the first truly large-scale machines designed for around-the-clock operation and for maximum versatility. San Diego Computer. T o economize on ground area, the computer is built on two levels. The upper levei consists of operating consoles, equipment (mostly plotting boards, function generators, auxiliary linear computers) to which operators normally need access, and several “wiring tables” where operators wire the problem boards that interconnect computer elements to solve particular problems. The lower level houses the bulk of the computing equipment (amplifiers, servo-set potentiometers, multipliers, resolvers), There are some 50 racks of computing equipment on this floor, and 67 racks altogether. Thousands of wires run from the lower floor through openings in the ceiling into the operating consoles above. There are two control consoles on the upper level. Each has four operating stations. Each of these stations is a complete medium-size computer capable of independent operation, and each has ready access to all of the plotting boards, function generators, and other equipment in the entire facility. The control system makes it easy to “slave” any or all of the operating stations to any one of
them so that problems of various sizes can be efficiently handled. In addition, there are four linear computers on which small problems may be solved. These may be combined with each other as desired for solving problems too big for one of them. They may also be used to supplement any or all of the main-conerating stations. The whole r contains some 550 operational amplifiers, 840 electric servo motors, and 8500 vacuum tubes. I t cost about $1,500,000 and occupies 5000 square feet of floor space. For multishift operation it is generally to change the problems on the with each change of shift. his computer was designed for three-shift operation, it had to be possible to remove one group of problems and set up a new group of them in a short time. Problems can be removed in seconds by removing the problem boards (often called patchboards) from the consoles.
Figure
or he can punch the desired settings and potentiometer identifications into tabulating machine cards and feed these to a card reader. This is the faster method, and it eliminates one source of human error. With either method, the operator gets a visual digital verification of the setting. He can also get a printed record if he wants it. Only the largest problems require as much as an hour to set up. I n some current models of commercial computers, pots are set from punched paper tape. However, no matter how large a computer is, it usually lacks something needed to solve a problem. Hence the computer was designed to facilitate “borrowing” all kinds of computing equipment. For example, if rhore resolvers (or servos or amplifiers) are needed and if another operator is not using all of his, idle units can be borrowed and controlled without possibility of interference from him. The table on page 1638 shows the distribution of equipment on one typical main console station. There has been an increasing need for nonlinear equipment and for additional problem boards. About 95% of the “solutions” produced are graphs drawn by eight-channe1 strip-chart recorders as the solution progresses. To interpret these graphs, the engineer needs to know the sensitivity of each channel (usually in millimeters of deflection per volt), the offset in zero
1. Patchboard used on Convair-San Diego analog computer VOL. 50, NO. 11
NOVEMBER 1958
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position of the pen, and the initial condition (starting value) of each recorded variable. A feature (now in wide use) that was originated o n this computer is a sequencing device that automatically records this information a t the beginning of each run. It also starts each solution coincident with a timing marker pulse which occurs once per second. Because the operator usually makes numerous “runs” of the same basic problem, zero is recorded for a short distance after the end of each run. Between runs, he changes one of the initial conditions of the problem (such as the roll angle of a n airplane) or one of the parameters (such as the damping factor of a control) and runs a new solution. The computer consists of the consoles, a master control system built into them, and a variety of computing equipment bought at various times from several
a major advance in the analog art. The basic purpose of the problemcheck is to make it easy for the operator to be sure that his problem board is correctly wired, all his patchcords are properly in place and making good contact, all potentiometers are correctly set and statically everything is working correctly. If any fault is found on the check, an automatically printed record makes it easy to pinpoint the fault. While this check does not guarantee the absence of dynamic faults, it covers most of the ordinary troubles. The unique feature of the Convair problem-check is that the test data are stored in punched cards. This makes it possible to test a problem under two or more static conditions. No special wiring is required as the card sets u p the test conditions automatically and instantaneously.
centage could be raised to 95% or higher. The remaining failures would be limited to the unpredictable, random, “catastrophic” type. With the present checking program each typical computing element (such as amplifiers and servo multipliers) has a mean, trouble-free operating period of seven to nine months. As only 20% )f the failures occur during operating time, the mean trouble-free period, as seen by computer operators, is three to four years. Marginal checking would increase the mean trouble-free period many fold. The next modifications made on the computer will probably include marginal checking. Few companies need such a large computer. A popular size for computation centers is one tenth as large; this would be more nearly typical of chemical industry needs. Assuming that such a computer would have 100 major computing elements, about three failures per month would be expected during operating time without marginal checking. With it, an average of less than one failure a month during operating time would be expected. Many failures were concentrated in certain power-supply circuits. These were modified, and a substantial drop in power-supply failure rates resulted. Also “reliable” types of electron tubes generally are reliable, and they reduce both maintenance costs and failure rates. Vacuum tubes and most other electronic components have longer lives if they are kept cool. The Convair-San Diego computer is air-conditioned, but
Distribution of Equipment on One Typical Main Console Station of the Convair-San Diego Analog Computer
Figure 2. Hydraulic control system test stand. Most test stands do not resemble airplanes as closely as this one does. Note engineer in “cockpit” of test stand
manufacturers. Most of this equipment was bought “stripped”-that is, without the manufacturer’s customary controls and auxiliary equipment. All of this equipment was integrated into the single large computerjust described. Problem-Check. From time to time the computer is modified to keep it up to date. The latest such effort includes modifying most of the operational amplifiers, installing a new and improved system for setting potentiometers, and adding a new problem-check featurc-
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Reliability a n d Maintenance. Percentages of “up time” can be misleading because there is no generally accepted way of figuring them. Every morning there is a 2-hour maintenance check-out period. Nearly everything in the computer is tested under maximum specified operating conditions. Anything that fails to pass its tests is immediately replaced by a plug-in spare. Records show that about 80% of all “failures” are found by these daily tests. By using marginal checking techniques, this per-
INDUSTRIAL AND ENGINEERING CHEMISTRY
Component
Number
Summing/integrating amplifiers Inverting amplifiers Servo multipliers (each accepting up to six input variables and delivering up t o five output products; two are capable of generating total of six arbitrary functions of one variable) Servo resolvers (for coordinate transformations and for obtaising sines and cosines) Electronic multipliers Servo-set potentiometers Manual potentiometers Dual limiters Diode-bridge Cathode-follower feedback Comparators for switching when a voltage crosses a selected value “General network” connections for access to any type of network Noise generatorsa Function generators (for functions of one variable and up to 70 functions of two variables. Square-, triangular-, and sinewave generatorsa
42 16
Q
-4vailable over trunk-line system.
8 2 2 126 12 6 12 12 96 2 130
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COMPUTERS IN THE CHEMICAL WORLD Operate them far below maximum ratings. Design circuits to work with wide variations in parameters. Provide generous cooling. Keep dust out of the computer. Run the computer several hundred hours under adverse conditions to precipitate failures caused by manufacturing defects. Then put it into service. Build into the computer a thorough marginal-checking system and use it regularly. For utmost reliability, incorporate “redundant” circuits so designed that failure of one component will not cause a failure of the circuit’s function. N e w Developments
Combined Analog-Digital Computation. This development began in the spring of 1954 when Convair missile engineers anticipated having to solve a series of problems beyond the capability of any existing computer. Indeed, these problems demanded a computer that was both analog and digital at the same time. I n collaboration with engineers from a young Boston firm (EPSCO, Inc.), they worked out initial specifications for a machine named the Addaverter (for analog-to-digital and digital-to-
Figure 3. Main operating console of Convair-San Diego analog computer. Just out of photograph on right is a 40-foat row of multipliers, function generators, plotting boards, auxiliary computers, etc. Most of the computing equipment is on the floor below
not adequately for maximum tube life. Also “catastrophic” tube failures most often occur in the first 50 to 200 hours of tube life. Hence, “burning in” tubes for 200 hours before they are installed in the computer greatly reduces this type of failure. This is not done now but probably will be when other causes of failure have been substantially reduced. Maintaining the computer and checking it out every day take a staff of four engineers and 11 technicians. When a failure is found, the chassis containing the malfunction is removed from the computer and a stand-by replacement unit is put in its place. The computer is considered to be “down” from the time it gives a wrong solution because of equipment failure until the computer is again operating within its specifications. Down time has been averaging less then 9% per problem per shift of full usage. The number of spare chassis of any type needed for replacements depends on how often they fail on the average and on how long it takes to make repairs. Because there are so many operatiorial
amplifiers, the technicians are adept at repairing them, usually taking only half an hour per chassis (two amplifiers per chassis). Although 4% spares have been available, 5 or 6% would permit a few failures to accumulate before having to repair them. For the 16 resolvers, which are difficult to repair and expensive, there are two spares (12.5%), and this is inadequate. Down-time must be considered in the light of the mode of operation. People who want problems solved on the computer learn how to set up their own problems and how to operate the computer. Operators thus differ greatly in experience and skill. This reduced operating efficiency is more than offset by the greatly increased insight gained by solvblem on the computer. ility as is economically justified can be attained. If the need is for small, special-purpose analog cornPuters, it should be relatively to achieve extremely high reliability. The formula for such a computer is simple: Use highly reliable components.
Figure 4. Instrument
and pilot’s
controls in cockpit of test stand shown in Figure 2. For pilot familiarization with a new instrumentsdif. ferent from those in this photograph are mounted on the panel VOL. 50, NO, 11
NOVEMBER 1958
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analog converter). I t acts as a link between a large analog and a large digital computer so that the two may work as a team on a single problem. Specifications for the Addaverter were completed with the participation of Ramo-Wooldridge Corp. Both Convair-Astronautics and Ramo-Wooldridge ordered Addaverters and put them into service early this year. (Conversion equipment is now being offered by other firms under other trade names.) The purpose of tying large analog and digital machines together was to simulate successfully an airframe (essentially an “analog” system as its variables are continuous) with a digital control system. More accuracy was needed in analog computations and mole sp-eed in digital computation than was, and is, available in modern analog and digital computers, respectively. A combination analog and digital computer meets these needs in two ways: Computing tasks may be assigned to the computer best adapted for them. Thus, the analog computer carries out operations involving the higher frequencies in the problem, as these are difficult for the digital computer to handle. The digital computer carries out operations where drift is intolerable or where high accuracy is needed; the analog computer is inadequate for such computations. Where necessary, computed results are converted into the language of the other computer for use. For example, the digital computer can handle coordinate transformations and generate functions of three independent variables much better than the analog computer. Yet, these may be tasks logically belonging to the analog computer. The input data are converted to digital form, and the digital computer carries out the calculations and feeds the results to the digitalto-analog converters, which deliver the required analog signals to the proper points in the analog computer. Certain operations, such as driftless integration, are achieved by having the digital computer make a numerical approximation and having the analog computer operate on the error in the approximation. An excellent study of combined analog-digital computation has been made by Leger and Greenstein of ConvairAstronautics ( 2 ) . Convair-Astronautics is combining an IBM 704 digital computer with a largescale analog computer through a 25channel converter. Ramo-Wooldridge is using an ERA-I 103A computer and a 30-channel converter. These computers represent multimillion dollar investments, but Greenstein successfully set up a small problem requiring only one analog integrator, a small digital computer, two converters, and no complicated sychronizing system (7). Not having a small digital computer available, he was obliged to use a big one.
High-speed Parallel Digital Differential Analyzer. One of the most challenging developments of 1957-58 lies in an area half way between analog and digital computers. This is the area of the “digital differential analyzer,” a type of computer that is digital inside, but that looks very much like an analog machine to the outside world. All the older machines of this type have used magnetic drums and have operated serially (iteration rates are typically 60 to 100 per second). The drums have limited the size of problems they can handle, and serial operation has made them slow. Nevertheless, they have special virtues for solving ordinary differential equations, not the least of which is relatively low cost. They can be made very compact (the Litton 20) or com. bined with a general-purpose digital computer (Bendix Computer Division). Recently announced by Packard-Bell Computer Corp., Los Angeles, is a digital differential analyzer that uses separate registers instead of a drum memory, operates at 100,000 iterations per second, and is “fully parallel.” It is reported to have amazed its designers by generating an approximate sine wave of 2000 cycles per second without any decrement. The separate registers remove the limit on problem size that the drum imposed on older models. “Fully parallel operation” means that this type of computer solves all parts of a problem simultaneously, just as the electronic analog computer does. The integrators, multipliers, servos, and other parts are patched together to solve problems in much the same way (with patch cords) as are the amplifiers of the electronic analog computer. An embryonic cornputer of this type was to be delivered to Redstone Arsenal last spring. If this type of computer achieves in practice all that it appears to promise, it will be a major advance in the art. It could be used in place of an analog computer in combined analog-digital computation to eliminate the need for analog-digital converters for theoretical problems-i.e., problems in which no actual physical equipment is being tested. Or it could, in some cases, replace the digital computer in a “combined” computation. Because of its high speed, it could, no doubt, replace both the analog and digital computers in certain problems that would normally call for combined computation. For communication with an analog computer the same firm also offers a new converter that can accept both analog and digital inputs and can perform certain arithmetic operations such as multiplication and square root. These new machines conform to a growing trend-they are transistorized. A number of additional analog-todigital (and vice versa) converters have been developed, and the field of com-
1 640 INDUSTRIAL AND ENGINEERING CHEMISTRY
bined analog-digital computation should undergo rapid development in the near future. Analog Computer Developments. Developments in the pure analog field will doubtless provide increased reliability through transistorization of circuits and incorporating marginal checking in analog computers, ability to set up large numbers of potentiometers simultaneously, problem-check equipment that will indicate immediately whether there is an error and where it is: reduced bulkiness and cluttered “patching” of the problem boards now nearly universally used on large analog computers, and automatic conversion of equations into wiring and scaling instructions. Analog computers will find new applications as we learn more about using them and as new auxiliary equipment is developed for them. One important area which has been nearly closed to electronic differential analyzers of conventional design is the solution of partial differential equations. Lawrence Wainwright has proposed an ingenious use of a magnetic tape memory with a conventional analog computer to solve certain classes of partial differential equations, and ConvairAstronautics is building prototype equipment embodying his ideas. This may open new fields to analog computation. Three approaches to solving the partial differential equations of static-stress analysis in redundant structures have been worked out by T. M. Dannback in collaboration with W. J. Schart and S.T. Paine (all of Convair-San Diego). These approaches involve converting the original equations into sets of algebraic equations. One approach makes the computer a model of a direct-analogy analog computer and has the convenience of having one knob per parameter. The others lack this convenience, but have considerably more mathematical flexibility and power. Because the approaches involve solving simultaneous algebraic equations, it has been necessary to devise techniques for keeping the solutions and the computer stable. It appears likely that the advances outlined plus the many others in progress will widen the fields of usefulness of analog computers and make them easier to use and more reliable in operation.
literature Cited (1) ~, Greenstein. J. L.. Trans, Am. Inst. Elec. Engrs., in press. ( 2 ) Leger, R. M. Greenstein J. L., Control Eng. 3, No. 9, 145-53 (195b). ,
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RECEIVED for review April 16, 1958 .4CCEPTED July 29, 1958 Division of Industrial and Engineering Chemistry, Symposium on Computers in the Chemical World, 133rd Meeting, ACS, San Francisco, Calif., April 1958.
