Analog Machines Research Articles

Mathematical Modelling Techniques in Guided Weapons

At BAC Filton the use of computers in missile work began early in the 1950s, much as elsewhere no doubt, by the company manufacturing its own analogue machines. The utilisation of computers was brought about by the need to develop the theoretical approach of design beyond the stage of hand computed calculations. Linear calculations could be long and tedious, and although ingenious exposure of the basic principles of missiles were often very instructive, they remained too simple to give complete reassurance.As the development of missiles proceeded, the realisation of the complexity and extent of the non-linearities became more evident, casting doubt on the likely success of the missiles under design and manufacture. Typically with Bloodhound there was the fear that a twist/steer missile would not work, most missiles of the day being tail controlled cartesians. Would one be able to keep the body movements down to an acceptable minimum for the sake of aberration or ramjet extinction? Just what were the cross coupling effects from pitch and roll into yaw? Later, when what one might call the purely mechanical reliability aspects of trials were over, the need to understand the interaction of the various phenomena of missile flight began to dominate design thought.

Memory versus logic: two models of organizing information and their influences on web retrieval strategies

We can find the first anticipation of the World Wide Web hypertextual structure in Bush paper of 1945, where he described a “selection” and storage machine called the Memex, capable of keeping the useful information of a user and connecting it to other relevant material present in the machine or added by other users. We will argue that Vannevar Bush, who conceived this type of machine, did it because its involvement with analogical devices. During the 1930s, in fact, he invented and built the Differential Analyzer, a powerful analogue machine, used to calculate various relevant mathematical functions. The model of the Memex is not the digital one, because it relies on another form of data representation that emulates more the procedures of memory than the attitude of the logic used by the intellect. Memory seems to select and arrange information according to association strategies, i.e., using analogies and connections that are very often arbitrary, sometimes even chaotic and completely subjective. The organization of information and the knowledge creation process suggested by logic and symbolic formal representation of data is deeply different from the former one, though the logic approach is at the core of the birth of computer science (i.e., the Turing Machine and the Von Neumann Machine). We will discuss the issues raised by these two “visions” of information management and the influences of the philosophical tradition of the theory of knowledge on the hypertextual organization of content. We will also analyze all the consequences of these different attitudes with respect to information retrieval techniques in a hypertextual environment, as the web. Our position is that it necessary to take into accounts the nature and the dynamic social topology of the network when we choose information retrieval methods for the network; otherwise, we risk creating a misleading service for the end user of web search tools (i.e., search engines).

Memory versus logic: two models of organizing information and their influences on web retrieval strategies

We can find the first anticipation of the World Wide Web hypertextual structure in Bush paper of 1945, where he described a “selection” and storage machine called the Memex, capable of keeping the useful information of a user and connecting it to other relevant material present in the machine or added by other users. We will argue that Vannevar Bush, who conceived this type of machine, did it because its involvement with analogical devices. During the 1930s, in fact, he invented and built the Differential Analyzer, a powerful analogue machine, used to calculate various relevant mathematical functions. The model of the Memex is not the digital one, because it relies on another form of data representation that emulates more the procedures of memory than the attitude of the logic used by the intellect. Memory seems to select and arrange information according to association strategies, i.e., using analogies and connections that are very often arbitrary, sometimes even chaotic and completely subjective. The organization of information and the knowledge creation process suggested by logic and symbolic formal representation of data is deeply different from the former one, though the logic approach is at the core of the birth of computer science (i.e., the Turing Machine and the Von Neumann Machine). We will discuss the issues raised by these two “visions” of information management and the influences of the philosophical tradition of the theory of knowledge on the hypertextual organization of content. We will also analyze all the consequences of these different attitudes with respect to information retrieval techniques in a hypertextual environment, as the web. Our position is that it necessary to take into accounts the nature and the dynamic social topology of the network when we choose information retrieval methods for the network; otherwise, we risk creating a misleading service for the end user of web search tools (i.e., search engines).

Analogue solution of 2nd-order hyperbolic partial differential equations by method of continuous characteristics

Hybrid methods based on the method of characteristics are developed for the solution of three different forms of hyperbolic differential equations. The techniques developed extend the early work of Hartree. It is shown that linear equations may be solved by a conventional analogue machine with iterative logic. Nonlinear problems require, in addition, the use of generalised integrators. Solutions obtained are compared with digital-computer solutions, and indicate thesignificant advantage of the hybrid machine in respect of computing time. The technique described provides a rapid method for modelling distributed-parameter systems which is of particular relevance to online-control applications.

Switch using bipolar transistors for use in analogue computing

In this paper, a transistor switch for use in analogue-computing circuits is described, and the essential steps in its design are given. The switch is then applied, in a feedback configuration, to produce a fast, accurate method of resetting the initial conditions of an integrating computing amplifier. An assessment of the steady-state errors is provided, and a detailed transient analysis leads to the prediction of reset transients for both transistor and valve operational amplifiers. These transients are confirmed experimentally. It is shown that the switch leads to a cheap and accurate way of resetting integrators, which will allow solid-state analogue machines to be operated repetitively at rates of over 1 kHz.

Microprogrammed Control in Problem-Oriented Languages

The application of microprogramming to problem-oriented languages is described in terms of a simulated analog system on a digital computer. Microprogramming facilitates the development of a problem-oriented machine code, which can be simply generated from the problem-oriented source language by simple translation. In the system described a problem defined by differential equations is drawn up in the form of an analog diagram. The diagram is coded into an analog-oriented source language which is converted by translation into the analog machine code. The system also allows the machine assembly code to be freely used with the analog input in coding the supervisory and interrupt facilities that are incorporated in the overall system design.

Finite approximants of compact totally disconnected machines

O. It is classical that compact totally disconnected algebraic structures are approximable by finite algebraic structures of the same genus. Thus compact totally disconnected groups, rings, semigroups, lattices, and so on, are projective (inverse) limits of finite groups, rings, etc. Here we are concerned with similar propositions for simple "automata", and are particularly interested in the approximants having two-element state spaces. Except for results contained in papers on topological semigroups, there seems to exist little in the literature on topological automata, in the sense to be used here, though there are a couple of papers in press. (The papers of Day and Wallace [4] and Wallace [ 17] have been submitted for publication, and a dissertation by David Stadtlander (under the direction of L. W. Anderson) has been completed. Closely related ideas appear in the instance of relative ideals in which consideration is given to a subsemigroup acting on a semigroup ([2], [15] and [16]). There is, however, the wellknown problem of Seymour Ginsburg [5] as to the possibility of topologizing automata to simulate analog machines. The difficulty here is, apparently, that appropriate mathematical models of analog computers still lack definition. This paper deviates somewhat from what might be regarded as the norm for contributions to machine-theory, not only in the use of topology, but in the assumption that the input semigroup is compact, rather than, for example, freely generated by an alphabet. It may be observed, however, that (i) in proving existence theorems involving topology, some sort of com*The authors are grateful to the National Science Foundation (GP 3623) for its support. 2O9

Analog simulation of satellite times-in-view

During the planning stages of any communication or com mand/control system utilizing satellites, it is necessary to examine the ground-terminal/satellite geometry for many proposed configurations in order to find the one most suitable. By "most suitable," I mean the configuration exhibiting the greatest ground-terminal-to-satellite acces sibility as demonstrated by a maximum time-in-view. The procedures I describe in this paper provide a means for rapidly generating ground terminal/satellite visibility records via an analog computer simulation of the Earth's surface/satellite orbit geometry. The analog simulation has several significant advantages relative to similar digital computer approaches-(1) it is significantly faster (easily 15,000 times real-time) and less expensive to operate; (2) the output, ink-on-paper strip-chart recordings, is directly interpretable without further data reduction; (3) system parameter changes are readily introduced while a simula tion is in progress; (4) the Systems Analyst can maintain a decidedly greater rapport with his configuration analysis. The disadvantages are: (1) diminished accuracy, and (2) exclusion of Earth/orbit non-linearities and anomalies—in a real-time tracking or scheduling simulation, these dis advantages are serious; in a systems analysis tool such as this time-in-view simulation, they are not of great con sequence. I have devoted the first five sections of this paper to a description of the development of the vector-matrix model underlying the simulation. The sixth section describes the mechanization of the model using an electronic analog computer. The equations from which the computer potentiometer settings are derived are quite tedious to manipulate man ually—even aided by a desk calculator. In an appendix, I describe the simple digital computer (in my case, a RE- COMP II) program used to obtain the desired potentiom eter settings. It strikes me that, while lack of simultaneity in the usage of the analog and digital machines precludes the use of the word hybrid, we may validly coin the expression "syner getic computing" to describe this simulation.

The analogue computer simulation of an alloy junction transistor wide band equivalent circuit

The paper reviews and develops an accurate equivalent circuit of a junction transistor which is valid over a wide band of frequencies; the parameters of the circuit themselves emphasizing the physical mechanisms of the device. It is then shown that the equations governing the equivalent may be solved by a general purpose analogue machine. After establishing the accuracy of the analogue by comparing its results with those from a digital machine. The problem of adjusting the parameters of the analogue so as to obtain accurate transistor representation is discussed briefly.

Resonance behavior of a dynamical system with collisions

In this article forced vibrations of a two-mass dynamical system with collisions are investigated. The simplest periodic motion of the system under consideration has been studied previously in a number of papers [1 to 3]. It has been established that, in a fairly narrow range of variation of the parameters, collisions lead to a considerable decrease in the vibrations. However, similar nonlinear systems exhibit various types of forced vibrations [4] which can occur in other ranges of values of the parameters and which do not exclude the appearance of significantly different behavior of the system. Therefore, the investigation of the effect of changes of the parameters on the character of the motion is of some interest. The present problem is solved in this paper by reducing the equations of ions of motion to certain point transformations of four-dimensional surfaces, and solving these on the computer. Since by its very nature a digital computer is, generally speaking, well adapted to carrying out point transformations regardless of the character of the non-linearities, its use seems to be more effective than solving the system under study with an analogue machine [5]. As a result of the study of the behavior of the phase trajectories (whose structure may become more and more complex as the time of solution increases), a region of values of the parameters is singled out, for which sharply defined resonances occur. Therefore, under some conditions, damping by impact (acceleration damping) can lead to a pronounced increase in the vibrations of the system.

Study of the dynamic characteristics of the first unit of the I. V. Kurchatov Beloyarsk Atomic-Power Station

Results of a study of nonstationary processes in the I. V. Kurchatov Beloyarsk Atomic-Power Station, using an electrical analog machine together with the actually-operating control apparatus, are presented. This enabled the dynamic characteristics of the power unit to be obtained and the optimum parameters for setting the main controls of the station to be selected. The theoretical characteristics of the reactor were also compared with experimental results measured directly.

The Parallel Digital Differential Analyzer and its Application as a Hybrid Computing System Element

TRICE hybrid computing systems are currently in volved in aerospace simulations that are interesting and sophisticated. Indeed it would seem that these applications are so successful that an increasing wave of interest can be expected in such DDA applications. Unlike earlier DDA's, the parallel digital differential analyzer, we believe, combines more of the best fea tures of analog and digital machines: It boasts speed, accuracy, and ease of programming. Because the machine itself is entirely digital, it couples naturally and inexpensively with convention al digital computers. Unlike other digital machines with central memory and sequential operation, all elements of this DDA operate simultaneously, thus providing rapid solutions to nonlinear differential equations characteristic of analog computers. And like its analog cousin, our DDA is programmed read ily via a patchboard, by connecting its computing elements in direct correspondence to the elements of differential equations. In one sense, TRICE is more properly a hybrid— a unique combination of analog and digital machine characteristics—than are the combinations of analog and digital computers currently being interfaced. Yet it can also be connected with analog and/or digital computers. Here we would like to explain how TRICE works, compare its advantages as a hybrid element, and con clude with a review of some current applications.

An Electrical Analogue for the Study of Tissue Saturation Processes with Oxygen and Inert Gases

A resistance-capacity analogue machine for the study of the saturation and desaturation of tissues with oxygen and inert gases is described. Two types of deviation from saturation time courses of exponential form are found, and the occurrence of these depends upon the blood flow rate in relation to the geometrical arrangement of capillaries in the tissue. The difference between the effects of parallel and antiparallel blood flow in adjacent capillaries upon the saturation time course is shown. The relevance of the results to the estimation of regional blood flow in tissues from saturation time courses is discussed.

The code Apache intended for the programming of an analogue problem by means of a digital computer

This paper describes the working of the APACHE (Analog Programming And CHEcking) system for the production of computer programs using a digital computer, which has been developed jointly by digital and analog programmers at the computation center of EURATOM in Ispra, Italy. The language which has been formulated for the writing of analog problems is discussed and its rules are set out in the appendix, while the processes involved in the utilization of the program are described and illustrated by an example of the listing of the digital computer input and output for a range of equation types. Finally, the significance of this new programming system in terms of economic exploitation of the analog machine, the use of trained personnel, and the design of new computers, are considered briefly.

Evaluation of Transport Costs for Alternative Factory Sites — A Case Study

The problem of siting one or more factories so as to minimize transport costs is considered in the context of other factors of interest to management. The method of solution is described. This involved the solution of simple transportation problems, the determination of rules by which costs could be computed, the construction of an analogue machine to assist with the problem of site selection and the writing of a programme for a digital computer to cope with the heavy load of calculation. The way in which the work of the operational research team was organized to meet a deadline is described and a number of technical difficulties are discussed. The solution consisted of the presentation of minimum transport costs for each of a large number of possible combinations of factories so that management could assess the relative importance of transport costs together with other factors when deciding where to build factories for the manufacture of a new product.

APACHE-A Breakthrough in Analog Computing

This paper describes the working of the APACHE (Analog Programing And CHEcking) system for the production of analog computer programs using a digital computer, which has been developed jointly by digital and analog programers at the computation center of EURATOM in Ispra, Italy. The language which has been formulated for the writing of analog problems is discussed and its rules are set out in the Appendix, while the processes involved in the utilization of the program are described and illustrated by an example of the listing of the digital computer input and output for a range of equation types. Finally, the significance of this new programing system in terms of economic exploitation of the analog machine, the use of trained personnel, and the design of new computers, are considered briefly.

Design of an accurate simulator for sampled-data systems

A detailed consideration is given of certain specialized units by means of which an analogue machine, normally used for simulation of continuous systems, may be adapted to allow also simulation of sampled-data systems. Emphasis is mainly on those circuits and methods which achieve best accuracy, the order of 0.1% being possible when valve circuits are employed.

A universal non-linear filter, predictor and simulator which optimizes itself by a learning process

A machine is described consisting of a universal non-linear filter, which is a highly adaptable analogue computer, together with a training device. The analogue machine has 18 input quantities from which it can compute in about 2 millisec 94 terms of a polynomial, each term containing products and powers of the input quantities, with adjustable coefficients, and can form their sum. The input quantities may be, for instance, 18 past samples of the values of a stochastic variable which is fed into the machine, and the result of the computation is an output function which contains 94 free variables. The training device optimizes the output by successive adjustment of the variable coefficients, until it has approached a target function as closely as can be achieved with a polynomial of 94 terms, by the criterion of the least mean-square error. This is done by repeatedly feeding into the machine a record of the stochastic process, long enough to be representative, and adjusting the variable coefficients, one at a time after each run, by a strategy which ensures that the error will monotonically decrease from run to run.In order to make the machine an optimum filter it is trained on a record of a noisy process, together with a target record which contains the signal only. It is taught as a predictor by taking as the target function a value of the stochastic process advanced by a certain time interval beyond the last value which goes into the input. It is trained as a simulator, for instance of an unknown mechanism, by feeding it with the input of the mechanism to be simulated at one end and presenting it at the other with its output as target function. The machine will then make itself into a model of the device to be simulated and the non-linear transfer function of the device can be read off from the final setting of the coefficients, as nearly as it can be represented by a 94-term polynomial. The machine is not confined to single-input systems.The machine incorporates 80 analogue multipliers of a novel ‘piezomagnetic’ type which, in its present form, can perform over 1000 multiplications per second with an error of 0.5% or less.A few examples of the first test applications of the machine are described.

AYDAR, Special Purpose Analog Machine for Raw Data Reduction

article Free AccessAYDAR, Special Purpose Analog Machine for Raw Data Reduction Authors: Serge J. Zaroodny Aberdeen Proving Ground, Maryland Aberdeen Proving Ground, MarylandView Profile , Tadeusz Leser Aberdeen Proving Ground, Maryland Aberdeen Proving Ground, MarylandView Profile Authors Info & Claims Journal of the ACMVolume 5Issue 1Jan. 1958 pp 89–99https://doi.org/10.1145/320911.320922Published:01 January 1958Publication History 0citation317DownloadsMetricsTotal Citations0Total Downloads317Last 12 Months5Last 6 weeks0 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

Computing applications where analogue methods appear to be superior to digital

In solving scientific engineering problems and design studies the first step consists of formulating the mathematical analogue of the problem which is to be studied. It is then a matter of convenience which means are employed to realize this mathematical model—analogue or digital. There are therefore no a priori reasons why either method is to be preferred and the choice will be dictated by the exigencies of the problem and the equipment in existence.Some advantages of analogue machines are quoted and three particular problems are studied for which analogue methods appear to be superior, namely the computation of non-linear heat flow, noise analysis, and the Monte Carlo method for solving neutron collision problems.