bluuebunny/crossref_metadata_2025 huggingface dataset:
A hybrid computer technique for nonlinear function generation
Authors: Tutelman David M.
Published: March 2008

The simulation of a physical system on an analog computer often requires the use of one or more nonlinear function generators. This paper describes a means by which a dig ital computer can be used to simulate the diode function generators of the analog computer in a closed-loop system.

The digital computer program utilizes a table-lookup procedure to transform x into f(x). The table is previously prepared by the machine through linear interpolation be tween breakpoints. The breakpoints are the input data for the program.

Many simulation problems need a nonlinear function generator as an element in a feedback loop. The digital computer introduces delay into the loop, rendering the simulation inaccurate and perhaps even unstable. A phase- advancing network must be included to compensate for the delay in the hybrid system. A simple and inexpensive technique for accomplishing the phase advance is analyzed and experimentally verified; the derivative of the incom ing waveform is used to predict the wave's value at some later instant of time.

Advantages of the digital function generator include rapid setting, perfect reproducibility of functions, no limit on breakpoints, and an effective increase of the analog facility's nonlinear standby capability.
Toward a uniform simulation language
Authors: Augustin D.C.
Published: March 2008

Real progress has been made by the SCi Committee on Simulation Software in their attempt to specify a "stand ard" language for the digital simulation of continuous systems. Their success, as indicated by the discussion dur ing the Hybrid Software Standardization Seminar at the SNSCi Meeting in Boston, surprised many who thought that the Committee was attempting to satisfy everybody- a proverbially impossible task.

The SCi Committee on Simulation Software grew out of a general feeling that some sort of direction was needed in the area of "digital simulation languages". For many people, this feeling was crystallized by Brennan and Line barger's article "A survey of digital simulation ..." (Vol ume 3; Number 6, page 22, December 1964). The riot of invention duplicated effort and apparent neglect of good ideas indicated the need for some guidance and control!

Most of the developers of important simulation lan guages joined in the committee work. They met at rather frequent intervals, maintained effective communication through correspondence, and at length reached a con sensus on principles and concepts. The detailed specifica tion of a continuous system simulation language was then delegated to a working subcommittee.

They are now preparing a document, the subcommit tee's report, which will be modified and approved by the entire Committee on Simulation Software.
An analog model of conditioned responses
Authors: Steadman J.
Published: March 2008

This report describes the use of an analog computer in modeling of psychological conditioned responses. The model uses a simple track-hold circuit for an analog simu lation of a memory, with a constant input when the circuit is in the track condition. Consequently, the entire model is quite simple. The model is versatile, and produces a quantitative measure of the magnitude of the conditioned response. The data obtained from this simulation agrees well with psychological data. The results of Pavlov's famous experiments with dogs are given in this report for comparison with the results obtained from the model.
Analyzing networks containing diodes by analog computation
Authors: Hausner Arthur
Published: March 2008

Larrowe's direct simulation method of analyzing electrical networks with an analog computer is extended to include ideal diodes. The technique is somewhat artificial; each diode is replaced by a small inductance that passes cur rent in one direction. The limit as the value of the induct ance approaches zero is simply a high-gain limited ampli fier that introduces feedback to preserve all current and voltage equations at all times. The stability of the method is briefly discussed and an example is given to show its effectiveness.
Acoustic ray tracing on the general-purpose electronic-analog computer
Authors: Rubin A.I. , Graber G.F.
Published: March 2008

A simulation of the trajectory of underwater acoustic rays is implemented on a general-purpose electronic-analog computer. Equations defining the phenomena are sum marized, assumptions are listed, and a preferred form of the equations is developed to provide maximum attain able accuracy of solution. Included are considerations of the velocity of sound as an arbitrary function of both depth and range, and the effects of reflections from both the surface and an arbitrary bottom. A complete computer diagram is presented and special circuits are described. Typical results of depth versus range are shown for vary ing launch depths and launch angles. A method of ob taining the difference in time required for rays leaving a common emitter at various angles to reach a common receiver is also derived. By use of perturbations, Taylor series expansions, and the method of steepest descents to insert the constraint cos θ/c = constant, the overall error in this highly sensitive computation has been reduced to 0.01 per cent or better.
Simulation survey and literature review
Authors: Ross Lawrence W.
Published: March 2008

The Analog Computers Literature Review was produced on the Georgia Tech campus for many years as an awareness service for the analog computation laboratory there. Grad ually this service began to be known to computer scientists around the country, and in 1964 demand had grown suf ficiently for the ACLR to be offered publicly for subscrip tion. The ACLR has been distributed as far as Russia, where
Hybrid simulation of the Apollo guidance and navigation system
Authors: Sullivan Madeline M.
Published: March 2008

A hybrid simulation of the guidance and navigation system of the Apollo spacecraft is underway at the Massachusetts Institute of Technology Instrumentation Laboratory. The Apollo Guidance and Navigation equipment is digital, elec tronic, and electromechanical. The guidance and naviga tion analog and digital hardware is combined in simulation with analog and digital computers so that the hardware will be subjected to dynamic conditions approaching those found in a space environment.

The instrumentation of the Apollo Guidance and Navi gation System is described as well as its adaptation to the hybrid simulation. Software models are discussed to indi cate some of the varied problems considered. Digital pro cedures which are designed to support the operator and enhance the reliability of the simulation are described.

In conclusion, it becomes apparent that the judicious use of computers, together with guidance and navigation hardware and software, makes it possible to simulate in real time any part of the Apollo mission from lift-off to splash-down.
Simulating a jet gas turbine with an analog computer
Authors: Ahlbeck Donald R.
Published: March 2008

In the past several years heavy emphasis has been placed on all-digital or hybrid simulation techniques in the analy sis of dynamic systems. To some the unmodified analog computer might seem as anachronistic as the narrow-gauge steam locomotive. Often, however, the demon Economics steps in; at this time the analog computer presents a most satisfactory compromise between accuracy, flexibility and cost.

This article, Simulating a jet gas turbine with an analog computer, is a "case history" of such a dynamic system study. The prospect of an undetermined number of explo ratory runs, coupled with a limited foreknowledge of the system components, made the use of the analog computer (an EAI 31-R) attractive. With Battelle's current open-shop policy on analog computer use, the computer became, in effect, an extension of the engineer's slide rule. In spite of being Little Orphan Analog in a digital world, the machine performed admirably!
Methods of simulating structural dynamics
Authors: Ben Clymer A.
Published: March 2008

This tutorial article is intended to convey the capability of simulating dynamically almost any structure by means of mathematical models of several types. It is intended also for reference.

The article follows a building-block approach, starting with treatment of the basic structural elements: bars, straight beams, columns, curved beams, rods, plates, shells, and soil and foundations. Then methods of modeling an assembly of elements, as well as methods of assembling models of elements, are discussed.

The methods covered include lumping, finite differenc ing, normal modes, and assumed modes. A road map is presented which shows many analytical routes from one type of model to another. It is shown that these methods may be regarded as special cases of the Lagrange assumed- mode method. Realization of this fact enhances under standing of each method and its relationships with other methods, thus affording a unified outlook upon the methods.

Examples are given which point out both the impor tance of matching each assumed mode to every boundary condition and the remarkable accuracy of the resulting modal models.
Nonlinear system simulation
Authors: Howard Bernard E.
Published: March 2008

The ideas presented in this paper have evolved gradually over the past 10 to 15 years. Their genesis may be ob served in the three reports in the bibliography, covering work the author contributed to and directed. The approach has been used in many practical problems, including the simulation of guided missile systems at the large analog computer facility at Wright-Patterson Air Force Base, Ohio. The ideas have further evolved during the teaching of courses in numerical analysis at the University of Miami, a two week session at the EAI Princeton Computation Center in 1964, and extensive use of the Milgo Computa tion Center in Miami.

The paper itself was prepared specifically for the meet ing at which it was presented. It was couched in general phase-space terminology, but the examples were all two dimensional. The reviewer kindly suggested that either the discussion be directed toward the phase plane, or higher dimensional examples be included. Following his sug gestion, higher dimensional examples have been solved which will be presented as a sequel, to avoid making this paper too long. In addition, one of the author's graduate students, Mr. Alex Koler, has been producing some inter esting results on the global topology of the phase plane of quadratic systems, which will be presented separately. The field appears fruitful for further investigations.
Acoustical simulation of a randomly fading Communication channel
Authors: Manders A.M. , Wait J.V.
Published: March 2008

Experimental studies of fading RF communication chan nels are usually very difficult to perform under actual operating conditions. This paper describes a fading chan nel simulator which is easily constructed and flexible in operation. Using this simulator, modulation and coding techniques suitable for use in communication and ranging equipment can be tested and optimized for operation dur ing periods of severe fading. The simulator uses ultrasonic acoustical waves transmitted through water to achieve favorable changes in the space and time scales; typical fading rates are from 2 to 30 fades per second.

The paper also describes simple hybrid statistical mea surement equipment used in studying the probability dis tributions and correlation functions of the received signals.
Simulation of frequency tracking loops with complex targets
Authors: Engle J.O. , Nisson C.J.
Published: March 2008

This paper was written for the analog user to relate some of our experience in the area of signal processing (in this case signal processing by a radar receiver) to fit the theme of the Eastern Simulation Council meeting at which it was presented.

"In the paper we attempted to give a complete but simple picture; by describing the signals and system, de veloping the simulation models, instrumenting the models with available computing equipment and finally by dis cussing simulation difficulties. (We wish that we had more modern equipment so that the instrumentation, particu larly of the dc models, could be more significant relative to state-of-the-art.)"
An example program for the determination of chemical rate coefficients from experimental data
Authors: Nesbit Richard A. , Engel Robert D.
Published: March 2008

A program for matching experimental data to the com puted concentrations of various components of a dynamic chemical process is implemented. The digital subsection of the computer is programmed to execute a steepest descent search procedure. The analog section is programmed to solve the chemical rate equations which simulate the re action dynamics. These equations form a two-point bound ary value problem. The search procedure changes param eters in the rate equations, and it compares the computed concentrations to the experimental ones.

The squared error is summed over all data points, and this sum is minimized by the search. Significant speedup of the solution to this type of problem is possible with the hy brid system due to the fast solution of the differential equations on the analog and the automated search pro cedure on the digital.
Application of process simulation to operator training and startup of a high-speed paper machine
Authors: Rounsley Robert R.
Published: March 2008

Because of the complexity of operation of a paper machine, a simulation of operation would provide three avenues through which better startup and operation could be obtained: (1) engineering evaluation, (2) operator training, and (3) control-program evaluation.

Prior to the startup of a new high-speed paper machine, a simulation of the stock system where the suspended fibers are formed into a sheet of paper was undertaken. Basic information on the steady-state and dynamic be havior of such a system was obtained on a highly instru mented paper machine having components similar to those of the new machine. The system was analyzed one component at a time to fit available theoretical equations with minor modifications. This allowed reasonable extrap olation and reassembly of the system to describe the new machine.

An important factor in describing such a system was the transport lag in the pipelines. This facet of the simulation was accomplished with prewired Padé approximations of these lags. A second important characteristic in describing a paper machine in real time is the long time-constants involved in the rates of change. These may run as long as 10 minutes.

A replica of the main control panels was constructed for use as a training aid for the operating crews of the new machine. The panels were programmed on the computer to respond to upsets and grade changes as part of an inten sive training program for the operators.

Exploitation of the simulation system is still in progress. It is evident, however, that the smooth startup resulted from careful planning and effective operator training.
Calculation of temperature profile in ablator char using MIMIC
Authors: April Gary C. , Pike Ralph W. , Smith Cecil L.
Published: March 2008

The differential equation describing the temperature pro file in the carbon zone of a charring ablator was simulated on an IBM 7040 digital computer using MIMIC, a digital- analog simulator language. This differential equation de scribes a nonlinear, two-point boundary value problem, thus requiring an iterative procedure to converge to a solu tion. In order to handle the iterative procedure, the logical- control-variable feature of MIMIC was especially useful.
A reliable, straightforward technique for generating Bode and Nyquist diagrams
Authors: Gilly Willard A.
Published: March 2008

Several methods have been devised for generating Bode diagrams on an analog computer. All of them, or at least all of them that we are familiar with, are either imprecise or they are excessively laborious. And the method most commonly used by analog pro grammers -graphical comparison of variables on a strip chart recording-combines both disadvantages. These can be largely avoided by a method we have found quite convenient, using analog logic and memory equipment. Our method yields phase and gain information directly and requires no manual adjustments by the computer operator other than to change the frequency of the input signal and to adjust the abscissa of the X-Y plotter. The method can be used for both open-loop and closed-loop systems and is especially useful for obtaining the open-loop response of a closed-loop system, as in figure 1. Here is how it works:
Highlights of two and one-half years of simulation efforts for deep submergence vehicles
Authors: Noble Tom F.
Published: March 2008

This paper describes the highlights of two and one-half years of computer simulation effort on the deep submer gence vehicles Trieste II (Trieste), NR-1, and Deep Sub mergence Rescue Vehicle (DSRV). The work, which is still in progress, is being performed by Sperry Gyroscope Com pany under Navy and company-funded programs. Introductory material of the paper presents the simula tion program objectives, outlines the simulation facilities, and gives an overall simulation block diagram. The com puter simulations are being used in control-system, hull, and force-effector design efforts for the development of operational doctrine, as a tool for human engineering as sessment of displays, control input devices, and console layouts, and as a pilot training aid.

Basic computation equipment consists of a hybridiza tion between an Electronic Associates 231-R analog com puter and an Ambilog Model 200 digital computer. Major facilities used to supplement these computers are a two- degree-of-freedom cab containing console mockup, pilot's control station, and an electronic flying-spot-scanner tele vision display generator.

Major elements characterized in the simulations are six- degree-of-freedom boat dynamics; coordinate transforma tions for television display cues and real-world television pictures; various effectors, actuators, and sensors; and control computer equations.

The body of the paper gives details on the use of the computer simulation in deep submergence craft design work. The design stages are broken down as: statement of design criteria, analysis of system parts, analysis of com plete system, synthesis of system design, fabrication of system hardware, test and evaluation, and improvement of design. Unique hull, effector, actuator, and control-system design problems encountered during the two-and-one- half-year simulation study are outlined..

This paper on simulation is concluded with a summary which indicates the need for highly integrated displays, control input devices, and control computers for deep sea craft.
The stuttering problem considered from an automatic control point of view
Authors: Butler Blaine R. , Stanley Paul E.
Published: March 2008

The problem of stuttering in human speech is approached in this presentation on the premise that the speech mech anism is a feedback system. A simplified version of the human speech system is developed. Stuttering is assumed to be an instability which causes the system to become un stable or block. Various instabilities in the system are con sidered and their validity in the stuttering problem checked. This is accomplished by applying to the model clinically tested techniques which decrease or stop stutter ing in people. The assumption is that if the techniques which decrease or stop stuttering in people also return the model to a stable state, or normal speech, then this model instability is a possible cause of stuttering. This leads to the conclusion that a malfunction of the middle ear, a variable gain device, is a possible cause of stuttering. Investigating the speech system from an automatic control point of view is concluded to be a valid and fruitful approach.
Selected generalized integration techniques for analog computation
Authors: Hausner Arthur
Published: March 2008

Generalized integration is a technique for generating ex plicit functions on an analog computer by solving the appropriate differential equations they satisfy. Setting up the solution of differential equations using the parametric technique is first reviewed. Two theorems regarding the capability of linear equipment in generating sums and products are stated, and their usefulness is illustrated with examples. Applications of the technique to generating high-degree oscillatory polynomials and rational functions (which require nonlinear equipment) are also described.

The major advantage of the technique is achievement of great accuracy with minimum equipment in some cases. The major disadvantage is that, with time, errors may sometimes increase and may not be bounded.
Finite state control of quadruped locomotion
Authors: McGhee Robert B.
Published: March 2008

Previous work relating to the control of legged locomo tion systems has suggested that it might be possible to achieve stable locomotion in a machine using only on-off actuators at each joint. It has further been hypothesized that the coordination of joint motions could be accom plished by a simple finite algorithm implemented as an extremely small special-purpose digital computer. The re search reported in this paper establishes the validity of these conjectures by means of a successful experiment. A quadruped with four identical legs, each with a powered hip joint and knee joint, has been constructed and tested. The results obtained have significance both with respect to prosthetics and orthotics and with respect to the design of vehicles for off-the-road transportation.
Real time hardware-in-the-loop simulation verifies performance of Gemini computer and operational program
Authors: Gross Joseph L.
Published: March 2008

An IBM Gemini Mission Verification Simulation (MVS) facility exercises and verifies the performance of the actual Gemini digital computer and its operational programs through real time, hardware-in-the-loop simulations of Gemini missions. This paper gives a system-type functional description of MVS and describes the methodology used to verify performance of the actual computer through com parisons and analyses of mission profile data generated both by MVS and all-digital reference simulations. A de scription of the various types of mission profile data ob tained together with a discussion of its significance and use is included. The error analysis techniques used to establish the expected deviations between mission profile data generated by MVS and the reference all-digital simu lations are described.
Discussion of computer simulation techniques and comparison of languages
Authors: Tiechroew Daniel , Lubin John Francis , Truitt Thomas D.
Published: March 2008

A draft of this paper was prepared for the Workshop on Simu lation Languages, Graduate School of Business, Stanford Univer sity, March 6 and 7, 1964. The paper has benefited from sugges tions from participants at the Workshop, particularly Michael Montalbano, and from projects carried out by students in the Graduate School of Business: H. Barnett, H. Guichelaar, Lloyd Krause, John P. Seagel, Charles Turk, Victor Preisser. The paper has also benefited from discussions held in connection with the Workshop on Simulation Languages, University of Pennsylvania, March 17 and 18, 1966.

Characteristics of computer languages and software packages change rapidly. Some statements in the paper were originally intended for the situation current in March, 1964. Where signifi cant changes have occurred the text has been modified.
The Boeing integrated hybrid operating system
Authors: Wilson B.R.
Published: March 2008

A Hybrid Computing Complex must serve both experi enced and inexperienced users. It must handle both small and large engineering problems efficiently. It must be economical to use in all cases. The Operating System employed largely determines how well the Complex func tions. The Hybrid Operating System described here (de signed and implemented, under the supervision of the author, at The Boeing Company, Aerospace Group, Seattle, Washington) meets these requirements. It provides a hy brid form of compile-set-up-and-go operation. However, the quality of the man/machine "dialog" possible with analog computation is preserved. It includes all the system software; i.e., processors, monitors, executive systems, libraries and hybrid utilities. The system design minimizes resident memory size for any one mode of operation. Its modular control structure permits growth in several system dimensions. The system was designed for an SDS 9300 (with 24K core, four tapes and DES-1) coupled through an SDS interface (with extensive sense, control and interrupt structure) to a modified EASE 2100. The appendix provided discusses experience with the system to date, and some of its limitations.
A comparison of two digital methods of EEG simulation
Authors: Bower Edward K. , Dwyer Samuel J. , Lago Gladwyn V.
Published: March 2008

This article applies two very different approaches to the problem of digital simulation of a stationary time function, and compares their results. The first technique approxi mates the sampled time function by a Markov process of small order. The transition probabilities are estimated from samples of actual EEG, and a waveform is generated from these probabilities, using random number techniques.

The second technique treats a time function as the out put produced by a linear filter on some random input. The transfer function of the filter and the distribution of the in put signal are then calculated.

Graphs of the autocorrelation functions of actual EEG and both types of simulation are included for comparison. In the author's opinion, these graphs show the filtered- noise simulation to be somewhat superior to the Markov process simulation.
An example program for the determination of chemical rate coefficients from experimental data
Authors: Nesbit Richard A. , Engel Robert D.
Published: March 2008

A program for matching experimental data to the com puted concentrations of various components of a dynamic chemical process is implemented. The digital subsection of the computer is programmed to execute a steepest descent search procedure. The analog section is programmed to solve the chemical rate equations which simulate the re action dynamics. These equations form a two-point bound ary value problem. The search procedure changes param eters in the rate equations, and it compares the computed concentrations to the experimental ones.

The squared error is summed over all data points, and this sum is minimized by the search. Significant speedup of the solution to this type of problem is possible with the hybrid system due to the fast solution of the differential equations on the analog and the automated search pro cedure on the digital.
Computer representation of continuous vibratory systems using normal modes and bond graph techniques
Authors: Karnopp D.C.
Published: March 2008

The general features of normal-mode analysis are dis cussed using both equations and bond-graph representa tions. The problem of truncating the infinite series of normal modes in order to produce a finite-order model for analog or digital simulation purposes is discussed, and the notion of appending a residual compliance and a residual inertance to account for neglected modes is ex plained. Using the bond graphs, a number of questions concerning the choice of boundary conditions and the computing causality of the system forcing are studied.
A new high performance computer d-c amplifier
Authors: Naylor Jimmy Ray
Published: March 2008

A new computer d-c amplifier designed for very fast as well as for real-time analog/hybrid computation combines large bandwidth (30 MHz gain-bandwidth product) and high mid-band gain (68 dB at 10 KHz) with full ± 10V, 30mA output to 5.0 MHz, and low open-loop output im pedance (50 ohms at 10 KHz). High d-c gain (120 dB) and exceptionally low drift (50 pA/°C, 2.5 μV/°C ) is obtained with the aid of an inexpensive hot-substrate integrated- circuit preamplifier rather than with conventional chopper stabilization. A three-channel feedforward design employs an overcurrent-protected 30 mA class AB wideband output stage in the high-frequency channel, a feedback-equalized integrated-circuit operational amplifier as the intermedi ate-frequency channel, and the hot-substrate integrated differential amplifier stage as the low-frequency channel. Overcurrent protection makes the new amplifier short- circuit proof.

Table 1 shows the performance of the new d-c amplifier.
Fixed point versus floating point
Authors: Teitelbaum Leonard H.
Published: March 2008

This paper discusses the advantages of using fixed-point arithmetic in a hybrid environment. The particular ex ample used is that of a hybrid simulation system. The paper discusses the performance penalties which are paid in using floating-point arithmetic as opposed to fixed-point arithmetic. The paper points out the amount of digital- computer time used in fixed-point to floating-point con version. It also suggests a new hardware device, a floating point/fixed-point digital-to-analog converter. This paper points out one application in which this device could be useful.
Analog/hybrid solution of partial differential equations in the nuclear industry
Authors: Vichnevetsky R.
Published: March 2008

This article was presented at the AICA meeting in Versailles. It is printed here with the permission of Association interna tionale pour le Calcul Analogique.
Hybrid Simulation of a Variable Transport Lag
Authors: Nilsen R.N.
Published: March 2008

The object of this paper is to present a hybrid solution to the problem of simulating an ideal transport lag hav ing a variable time delay. The dynamic range over which the allowable time delay may be realized by this tech nique is limited on the low end by the sampling rate and execution time of the digital computer, and on the high end by the memory capacity of the digital computer. Experimental results using signals consisting of either sinusoidal waveforms or random noise are presented.
Sample sizes and confidence intervals associated with a Monte Carlo simulation model possessing a multinomial output
Authors: Hurtubise Rolland A.
Published: March 2008

A new classification of Monte Carlo digital computer simulations is suggested.

The body of this paper centers on the determination of sample sizes and confidence intervals associated with a simulation model which has a multinomially distributed output.

A brief description of a 'multinomial' Monte Carlo model is given. The theoretical considerations put forth are then verified on this model.
On the application of a variable transport lag
Authors: Nilsen R.N.
Published: March 2008

This paper discusses various hybrid applications of a variable transport lag. A specific example, the simulation of a thermally controlled environment, is presented. In it the transport lag is due to the delay caused by having to move a mass of heated air by pump from the heating element into the environment. Various forms of heater control and delay function are presented and their effects on the system are described.

Experimental results for various forms of heater con trol and transport lag variation are presented along with a discussion of the problems involved with this type of simulation. Finally, remarks as to possible methods of improvement and extensions are made.
Simulating low-concentration chemical reactions as in SMOG
Authors: Ulbrich E.A. , Jones R.A.
Published: March 2008

Air pollution is a fruitful subject for a wide range of simulations, varying from macroscale multizone flow models to microscale photochemical reactions. This article describes one of the latter type, a simulation of photochemical reactions similar to those which produce smog.
Implementation of hybrid integrators on a general-purpose analog/logic computer
Authors: Højberg K. Søe
Published: March 2008

Two types of continuously working hybrid integrators with analog input and digital output have been realized by means of standard analog computer equipment. The basic units are voltage-to-frequency converters. The in tegral is measured in quanta determined by the reference voltage and a pulse width (clock controlled) or the size of a capacitor.
Automatic patching for analog and hybrid computers
Authors: Hannauer George
Published: March 2008

This paper describes the results of an investigation into the feasibility of an automatic patching system for an analog or hybrid computer. The objective of the study is to reduce the number of switches required to a "rea sonable" number. Actual design of hardware is not con sidered. The final result is a "paper" design, which is evaluated by attempting to program several problems to see if enough paths exist.

The proposed design uses about 8,000 switches for an EAI-680-sized computer, which is far fewer switches than are required by any previously proposed system. The evaluation shows that this system is more than adequate and that, in fact, about 2,000 switches could be saved by modifying the design slightly.
Generalized finite-difference approximations f or the parallel solution of initial value problems
Authors: Vichnevetsky R.
Published: March 2008

Methods used in analog computation for the parallel- finite-differences solution of partial differential equations have been almost universally based on the "classical" derivation of finite-difference approximations. That is, the space-dependence of the approximate solution is lo cally assumed to be appropriately represented by a Tay lor (or polynomial) truncated series of low1, or higher7, order. Although known to introduce higher truncation errors than the use of other functional series2,3, this re striction has been mostly accepted for reasons of con venience because no simple method for obtaining more general approximations was available in practice.

We show in this paper that completely general finite- difference approximations of linear partial differential operators in space, based on functional (rather than, but including, polynomial) approximations, can be easily ob tained in a direct method involving only the inversion and multiplication of constant matrices.

One of the drawbacks of the analog computer imple mentation of equations obtained by application of the method presented here is that it requires more attenu ators than the classical low-order method. However, as suggested by Deiters and Nomura3, this is alleviated in a hybrid computer by introducing at discrete time inter vals the higher-order terms as digital corrections super imposed upon an analog low-order implementation.

Examples of the derivation of generalized finite-differ ence equations are shown for the representation of the Laplacian (diffusion) operator in circular (r, θ) and linear (x) coordinates.
Simulation of a pressure relief valve
Authors: Steber George R. , Romer I. Carl
Published: March 2008

An example is presented of the simulation of a hydraulic system involving transient fluid flow. Many approximate relationships are derived for the system, and the resulting equations are mechanized on an analog computer. Re sults are given which compare the simulation model to the actual system. The example clearly shows many of the advantages of simulation in problems of this type.
Padé approximations and analog computer simulations of time delays
Authors: Holst Per A.
Published: March 2008

The Padé approximations 1 of e- x are reviewed in con nection with their application in simulations of transpor tation delays (time delays) by analog computers. The approximation coefficients are specified in terms of the order of the approximations, and recurrence relation ships are established for the most common types. Analog computer circuits are given for general Padé approxima tions of any order and type, together with practical exam ples of both constant and variable transportation delay simulations. Special attention is paid to the zero-variable delay time constant, and circuits are given for this type of application.

The performance of the Padé approximation circuits is discussed in terms of phase error and amplitude char acteristics for sinusoidal signals, together with rate-of- change measures in connection with step-response analy ses. Conclusions are drawn as to the order and type of Padé approximation to be selected to meet given per formance requirements. A table of Padé approximations up to the 12th order is included.
Engineering applications of finite automata
Authors: Lutter Bernard E. , Huntsinger Ralph C.
Published: March 2008

The study of automata has been acquiring increasing im portance for engineers in many fields. For some time, the capabilities of these automata have been of the greatest interest to logicians and mathematicians. However, the expanding literature on the use of finite automata as probabilistic models demonstrates the growing interest in the application of these mechanisms to engineering phenomena.

We, the authors, became interested in these probabil istic models in an effort to develop a general self-adaptive control scheme based on the prediction of the future of the process to be controlled. Conceivably, an adequate model of a particular process could be generated by simply observing the process parameters. With this goal in mind we began an investigation of several different modeling techniques. The ability to model stochastic data was our primary concern. We feel that the results of several modeling experiments presented here may be of interest to our readers, and we hope to encourage the use of these techniques, especially in control applications.
Design of mechanical linkages using an analogue computer
Authors: Rea David P.
Published: March 2008

The application of the steepest descent technique to the solution of linkage problems is considered, using, as an example, a typical five-bar geared linkage. In a linkage design study it is necessary to be able to assess quickly the effects of changing linkage parameters on the motion of the linkage. The way in which the analogue computer can do this, using logical control and high-speed repeti tive operation, is fully discussed.
A disaster environmental simulator
Authors: Williams Lewis H. , Richie William C.
Published: March 2008

A Disaster Environmental Simulator (DES) has been developed for the study of resources allocation in a potential disaster locality and for the training of disaster managers. The DES is composed of four computer pro grams—Disaster Effects, Medical Inputs, Decision Cycle, and Mortality/Recovery. A potential disaster locality is divided into geographical areas. Within each geograph ical area, an inventory is established. The inventory con sists of people (nonmedical people, doctors, nurses, and medical technicians) and things (vehicles, medical sup plies, and hospital facilities).
An energy storage system
Authors: Easter Billy H.
Published: March 2008

To harness the energy contained in such unconventional sources as winds, tides, and sunlight, a power system must incorporate an energy storage device to act as a buffer between the source and the load. Since the size of the energy storage device depends upon the relative timing of the availability of energy and the load demand, a system simulation is a logical approach to the study and design of power systems using these unconventional en ergy sources. GPSS is presented as an excellent simula tion vehicle. The physical properties to be simulated are discussed and the resulting GPSS programs are presented. Some proposed applications for these power systems are presented.
Simulation and optimization of an electromechanical transducer
Authors: Stohler Phillip G. , Russell Christy H.
Published: March 2008

The design of a buzzer, one type of electromechanical transducer, has been improved by generating a mathe matical model of the device and simulating the model on an analog computer. A comparison of predicted cur rent responses to actual current responses verified the accuracy of the model and the computer program. The basic buzzer design was optimized by using the model to optimize the air gap, the spring, and the coil. Operat ing voltage ranges, the codes, and the coil adjustments for each code were also determined from the model. The new buzzer design resulted in improved efficiency, per formance, and cost.
An Error Function for Analog Curve Fitting
Authors: Bickel Rudolf G.
Published: March 2008

An error function to assist curve fitting of models to data points with an analog computer is described, and an ex ample of its usefulness in evaluating a biochemical model is given.
An integrated linear-transconductance analog multiplier
Authors: Free Maurice George
Published: March 2008

This paper describes a new solid-state, monolithic inte grated analog multiplier, based on the controlled-trans conductance principle that is designed for high speed, high accuracy, and excellent linearity. A novel differ ential amplifier circuit permits cancellation of undesired nonlinearities, and carefully matched device geometries account for the good accuracy of the new multiplier. With an inherent voltage gain of A v = 1/10, the multi plier will provide a ± 10 V output at ± 10 mA with linearity approaching 0.1 % at 100 Hz. The multiplier package may be used in conjunction with an external operational amplifier and external resistors, and offers the advantages of monolithic construction (low cost, ex cellent temperature tracking) with the precision of ad justable-parameter, discrete construction.
Determination of the time-domain equivalents of higher-order Laplace transfer functions by analog computation
Authors: León Jesús , Herrero Emilio E.
Published: March 2008

In the theory of optimal inventory control, a class of com plex Laplace transforms arises for which the theoretist needs to know the form and shape of the time domain equivalents.

Several methods have been used to obtain these time domain equivalents. In this paper simulation by analog computer has been used, and a low-order approximation of higher-order transfer functions has been simulated. The accuracy of this low-order approximation has been de termined by use of time domain plots.
Real-time simulation of a helicopter rotor on an analog computer
Authors: Schramm Milton
Published: March 2008

An accurate real-time simulation of a helicopter rotor can be achieved on a high-speed analog computer. By using repetitive operation and integrating along each blade every 2.5 milliseconds, the double integration required to determine rotor torque, thrust, moment, and rearward and sideward rotor forces is accomplished. The lift and drag coefficients are continuously calculated at all points along the blade. The same analog equipment used to calculate quantities for one blade is used for other blades by chang ing appropriate initial conditions. This analysis provides a transient rotor solution in which integration out the blade is accomplished every five rotor azimuth degrees. One console of a Hybrid Systems, Inc., SS-100 Analog/Hybrid Computer is used for the rotor solution.
A user specifies software for hybrid computing
Authors: Krasno L.
Published: March 2008

The article discusses a subject about which much is said and little is written—the writing of specifications for hybrid software. The basis for the article is an Aerospace Corpora tion Hybrid Computing Center study of the upgrading of the digital portion of our hybrid system.

In the process of discussing the study, a philosophy for writing specifications for hybrid software is presented. The philosophy, herein called "Functional Specifications," can be used by any facility regardless of its requirements. With Functional Specifications, a facility states only its require ments and leaves the designing of the system to the vendor.
Continuous Flow Charts
Authors: Gieszl Louis R. , Rieman Frank C.
Published: March 2008

The current concept of the flow chart for documenting a computer program seems to be more heavily influenced by its business data processing background than by its mathematically oriented inception. The result of this is a loss of definition which inhibits further developments in program documentation.

This paper proceeds from an analysis of the structure of a program and how this structure is represented by a flow chart to derive an extension of this: continuous flow charts.

A continuous flow chart, which may be constructed from a conventional flow chart by removing its points of (flow) discontinuity, is shown to be a form of docu mentation ideally suited for large-scale programs that by their nature involve complex logic (such as a war-game simulation).

The motivation for continuous flow charting is the pos sibility of dynamic documentation arising from a set of such flow charts. That is, the requirements suggested in this paper for a flow chart to be called continuous pro vide an inductive definition for the members of a set of levels of documentation of a simulation (such that the ease of a user's level to level transition of understanding [the logic depicted] is maintained). Such a set would have, at its highest level, a flow chart picturing the overall logic of the entire simulation, and, at successively lower levels it would contain flow charts describing smaller portions of the program in greater detail. An actual machine-language program would constitute the lowest level of documentation in this set.

Since the creation of such a set of continuous flow charts can be started from either the highest level or the lowest level, then this procedure should serve equally well for either developing a complex program from its most basic logical conception, or for documenting such a program as has already been written.
The lunar module simulator
Authors: Brown Malcolm O. , Waters John G.
Published: March 2008

The Lunar Module Simulators (LMS) in Houston and at Cape Kennedy are highly complex devices used for flight crew training and systems engineering evaluations to support the Apollo missions.

Each of the two simulators consists of a three-machine digital computer complex, associated digital conversion electronics, a crew station that is an accurate replica of the Lunar Module cockpit, an infinity-optics visual display system, and an instructor-operator control con sole.
Applications of analog and hybrid computers in electric power research
Authors: Krause P.C.
Published: March 2008

Recent applications of analog and hybrid computation techniques in research in variable-frequency drive systems and dc power systems are discussed. Although simulation techniques are not presented explicitly, publications are cited wherein the methods of analysis are set forth in de tail. Several new areas of electric power research which offer interesting and challenging applications of hybrid computation are briefly described.
System identification- an introduction and a survey
Authors: Bekey George A.
Published: March 2008

This paper presents a survey of a number of techniques for the identification of dynamic systems using computer techniques. The techniques discussed are particularly suited to digital or hybrid computer implementation. It is not intended to be a complete survey of the vast field of system identification, nor even the area of parameter estimation. Rather, it presents a discussion and compari son of several techniques which appear particularly use ful at the present time, including spectral analysis, search and gradient methods, quasi-linearization, and stochas tic approximation. Other related methods are discussed briefly.
Modal simulation of a distributed parameter system
Authors: Gilles Ernst D. , Zeitz Michael , Schiesser W.E.
Published: March 2008

This paper presents an analog/hybrid simulation method for linear and nonlinear distributed para meter systems. The modal method is based on a functional approximation for the computer solution of initial value partial differential equation prob lems using eigenfunctions. First, the mathematical foundations are reviewed; then the questions concerning the technical realiza tion on an analog/hybrid computer are treated. The simulation results for two examples of chemical processes are discussed.