Analog Computers

English translation

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Faszination Analogrechnen — Geschichte und Grundlagen elektronischer Analogrechner

Complete English translation of the original German-language document (45 pages).

Introduction — Mechanics — Electronics — Computing Elements — Programming — Systems — Hybrid Computers — DDAs — Simulation — Applications — Future

The Fascination of Analog Computing

[page 1: slide/title page]

Introduction — Mechanics — Electronics — Computing Elements — Programming — Systems — Hybrid Computers — DDAs — Simulation — Applications — Future

Terminology

The following terms are to be clarified first:

  • Analog computing
  • Stored-program digital computer
  • Direct analog(ue) computers
  • Indirect analog(ue) computers

[page 2]

Introduction — Mechanics — Electronics — Computing Elements — Programming — Systems — Hybrid Computers — DDAs — Simulation — Applications — Future

The Concept of Analog Computing

Analog computing does not necessarily mean working with continuous values, although this is often how it is portrayed.¹ Rather, analog computing means working with an analogy of the problem to be treated.

¹ Digital, i.e., discrete-value analog computers are not only theoretically possible but have also been successfully implemented.

[page 3]

Introduction — Mechanics — Electronics — Computing Elements — Programming — Systems — Hybrid Computers — DDAs — Simulation — Applications — Future

Analog Computers

Analog computers therefore operate by forming an analogy — that is, a problem is mapped by the interconnection (patching) of the computer (figure after [TRUITT60][p. 1-41]); there is no central control program.

[page 4: figure only — diagram showing analog computer architecture]

Introduction — Mechanics — Electronics — Computing Elements — Programming — Systems — Hybrid Computers — DDAs — Simulation — Applications — Future

Stored-Program Digital Computers

Whereas in analog computers the structure of the computer is adapted to the problem, stored-program digital computers have a fixed structure, while their control is adapted to the problem (figure see [TRUITT60][p. 1-40]).

[page 5: figure only — diagram showing stored-program digital computer architecture]

Introduction — Mechanics — Electronics — Computing Elements — Programming — Systems — Hybrid Computers — DDAs — Simulation — Applications — Future

Direct and Indirect Analog Computers

Direct analog computers: A true-to-scale model with a low degree of abstraction — special-purpose computers for narrowly defined problem classes.

Indirect analog computers: A high degree of abstraction — computers of this type are generally more versatile and can be used for more than one narrowly defined problem class.

[page 6]

Introduction — Mechanics — Electronics — Computing Elements — Programming — Systems — Hybrid Computers — DDAs — Simulation — Applications — Future

A Direct Analogy

Model of the roof of the Munich Olympic Stadium (see [DRESSLER72][p. 52]).

[page 7: figure only — photograph/illustration of the Munich Olympic Stadium roof model]

Introduction — Mechanics — Electronics — Computing Elements — Programming — Systems — Hybrid Computers — DDAs — Simulation — Applications — Future

An Indirect Analogy

Generation of a Joukowski profile with streamlines.

[page 8: figure only — illustration of a Joukowski aerofoil profile with streamlines]

Introduction — Mechanics — Electronics — Computing Elements — Programming — Systems — Hybrid Computers — DDAs — Simulation — Applications — Future

Mechanical Analog Computers

  • Antikythera mechanism
  • Slide rule
  • Planimeter
  • Kelvin’s tide predictor (harmonic synthesizer)
  • Fire-control computers
  • Differential analysers (Vannevar Bush et al.)

[page 9]

Introduction — Mechanics — Electronics — Computing Elements — Programming — Systems — Hybrid Computers — DDAs — Simulation — Applications — Future

Kelvin’s Tide Predictor

(Reproduced by kind permission of the Science Museum London.)

[page 10: figure only — photograph of Kelvin’s tide-predicting machine]

Introduction — Mechanics — Electronics — Computing Elements — Programming — Systems — Hybrid Computers — DDAs — Simulation — Applications — Future

Fire-Control Computer Mark 3

(Figure after [1][p. 150].)

[page 11: figure only — illustration of the Mark 3 fire-control computer]

Introduction — Mechanics — Electronics — Computing Elements — Programming — Systems — Hybrid Computers — DDAs — Simulation — Applications — Future

A Mechanical Differential Analyser

(Figure after [3][p. 190].)

[page 12: figure only — illustration of a mechanical differential analyser]

Introduction — Mechanics — Electronics — Computing Elements — Programming — Systems — Hybrid Computers — DDAs — Simulation — Applications — Future

Early Electronic Analog Computers

  • Fire-control computers
  • Helmut Hoelzer’s work
    • The Mischgerät (mixing device)
    • The first electronic analog computer
    • Solution of practical problems with the system

[page 13]

Introduction — Mechanics — Electronics — Computing Elements — Programming — Systems — Hybrid Computers — DDAs — Simulation — Applications — Future

Fire-Control Computer T-15

(Figure after [2][p. 154].)

[page 14: figure only — illustration of the T-15 fire-control computer]

Introduction — Mechanics — Electronics — Computing Elements — Programming — Systems — Hybrid Computers — DDAs — Simulation — Applications — Future

The Mischgerät (Mixing Device)

(Photo: Adri de Keijzer.)

[page 15: figure only — photograph of the Mischgerät]

Introduction — Mechanics — Electronics — Computing Elements — Programming — Systems — Hybrid Computers — DDAs — Simulation — Applications — Future

Helmut Hoelzer’s Electronic Analog Computer

[page 16: figure only — photograph/illustration of Hoelzer’s electronic analog computer]

Introduction — Mechanics — Electronics — Computing Elements — Programming — Systems — Hybrid Computers — DDAs — Simulation — Applications — Future

Fundamental Typical Computing Elements

  • Coefficient potentiometer
  • The idealized operational amplifier
  • Summing amplifier (summer)
  • Integrator
  • Operating modes: Pause (Initial Condition), Compute, Hold
  • Function generators
  • Multipliers
  • Division, square-root extraction
  • Comparators
  • Coordinate converters
  • Dead-time elements
  • Noise generators
  • Output devices

[page 17]

Introduction — Mechanics — Electronics — Computing Elements — Programming — Systems — Hybrid Computers — DDAs — Simulation — Applications — Future

Programming

  • Setting up computing plans (complete / partial feedback)
  • Partial differential equations
  • Scaling and time-scaling
  • Examples (all examples were implemented on historical installations):
    • Generation of a harmonic oscillation
    • Mass–spring–damper system
    • Predator–prey system
    • Bouncing ball in a box
    • Simulation of an automobile suspension
    • Projection of rotating bodies

[page 18]

Mass-Spring-Damper System: mÿ + dẏ + sy = 0

[page 19: equation/figure only — slide heading “Mass-Spring-Damper System mÿ + dẏ + sy = 0”; navigation bar lists: Introduction — Mechanics — Electronics — Computing Elements — Programming — Systems — Hybrid Computers — DDAs — Simulation — Applications — Future]

Analog Computer Setup for the MSD System

[page 20: figure only — slide shows the analog computer patch diagram (circuit schematic) implementing the mass-spring-damper differential equation; navigation bar as above]

Simulation Results

[page 21: figure only — slide shows two oscilloscope/plotter traces of simulation output:

  • s = 0.8 and d = 0.6 (underdamped case)
  • s = 0.8 and d = 1 (critically damped case) Navigation bar as above]

System Examples

  • Tube-based systems

    • Telefunken RA 1 and RA 463/2
    • EAI 231-R

  • Transistorized analog computers

    • Telefunken laboratory prototype
    • Telefunken RAT 700
    • Telefunken RA 800 and RA 800H
    • EAI TR-10
    • Telefunken RA 770
    • Telefunken RA 742
    • Dornier DO-80

[page 22: text slide listing the system examples above; navigation bar as above]

Telefunken RA 1

[page 23: figure only — photograph or illustration of the Telefunken RA 1 tube-based analog computer; navigation bar as above]

EAI 231R

(Figure after [EAI].)

[page 24: figure only — illustration of the EAI 231R analog computer, reproduced from the EAI source; navigation bar as above]

Telefunken RA 800

[page 25: figure only — photograph or illustration of the Telefunken RA 800 transistorized analog computer; navigation bar as above]

Telefunken RA 770

[page 26: figure only — photograph or illustration of the Telefunken RA 770 analog computer; navigation bar as above]

Hybrid Computers

  • The ADDAVERTER of Space Technology Laboratories (1956)
  • Hybrid computing installation Comcor-CDC
  • Telefunken HRS 860
  • Programming of hybrid computing installations

[page 27: text slide listing the hybrid computer topics above; navigation bar as above]

The ADDAVERTER

(Figure after [MCLEOD LEGER57], p. 1129.)

[page 28: figure only — illustration of the ADDAVERTER hybrid computer developed by Space Technology Laboratories (1956), reproduced from McLeod & Leger (1957), p. 1129; navigation bar as above]

Comcor-CDC Installation (Model)

(Figure after [BEKEY KARPLUS68], p. 166.)

[page 29: figure only — model/diagram of the Comcor-CDC hybrid computing installation, reproduced from Bekey & Karplus (1968), p. 166; navigation bar as above]

CI 5000 and SDS 9300

(Installation at the Department of Electrical Engineering, Naval Postgraduate School, late 1960s; figure reproduced with kind permission of Bob Limes.)

[page 30: figure only — photograph of the CI 5000 and SDS 9300 hybrid computer installation at the Naval Postgraduate School’s Department of Electrical Engineering, late 1960s; navigation bar as above]

Digital Differential Analyzers (DDA)

Digital implementation of an analog computer — after [MICHELS54], p. 2:

A digital differential analyzer is an electronic computer which solves differential equations by numerical integration.

Fundamental computing elements:

  • Integrator
  • Adder (summer)
  • Servo

[page 31: text slide; navigation bar as above]

Example Implementations

  • Guidance of the Snark cruise missile via celestial navigation
  • MADDIDA (from 1949)
  • Bendix D-12
  • TRICE

[page 32: text slide listing DDA example implementations; navigation bar as above]

MADDIDA

(With kind permission of Dag Spicer, Computer History Museum.)

[page 33: figure only — photograph of the MADDIDA (Magnetic Drum Digital Differential Analyzer), reproduced with permission of Dag Spicer, Computer History Museum; navigation bar as above]

TRICE

Figure after [AMELING63], p. 30.

[page 34: figure only — illustration of the TRICE digital differential analyzer, reproduced from Ameling (1963), p. 30; navigation bar as above]

Simulation of Analog Computers

  • Fundamentals
  • Examples
  • Mass-spring-damper system simulation in CSMP:

[page 35: slide heading with topic list and CSMP code or diagram for the mass-spring-damper system simulation; navigation bar as above]

Fields of Application

  • Mathematics — differential equations, boundary-value problems, zero-finding, conformal mappings, linear algebra, Fourier synthesis and analysis, stochastics, optimization problems, multi-dimensional representations
  • Physics — planetary orbits, particle trajectories and beam optics, optics, heat conduction, semiconductor physics
  • Chemistry — reaction kinetics, quantum chemistry
  • Mechanics and mechanical engineering — oscillations and vibrations, rotating systems, materials science, pneumatics and hydraulics, machine-tool control, servo systems
  • Nuclear engineering — research, training, reactor control

[page 36: text slide; navigation bar as above]

Fields of Application

Biology and Medicine — ecosystems and population dynamics, metabolic studies, circulatory systems, CO₂ regulation, pupillary control, neurophysiology, epidemiology, aerospace medicine, musculoskeletal systems

Geology and Oceanography — mineral deposit research, seismology, propagation of acoustic waves

Economics — Phillips’s hydraulic model of the economy

Energy Engineering — generators, transformers, AC and rectifier systems, transmission lines, power supply networks, power plant operation

Fields of Application (continued)

Electronics and Communications Engineering — circuit simulation, spectral analysis, resonance studies, filter design, (de-)modulators

Measurement, Control, and Automation Engineering — data acquisition and processing, control loops

Process Engineering — mixing tanks, heat exchangers, evaporators, columns, process simulation, adaptive control, parameter optimization

Transportation Systems — automotive engineering, traffic-flow simulation, rail vehicles, air-cushion vehicles and magnetic levitation trains, maritime engineering, torpedo development

Fields of Application (continued)

Aviation Engineering — flight tables, landing gear, arresting-cable systems, engine development, helicopter rotors, flight guidance systems, flight simulation, in-flight simulation

Rocket Engineering — rocket propulsion systems, flight behavior, rocket guidance

Spaceflight Engineering — launch vehicles and launch windows, trajectory computation, insertion of geostationary satellites, rendezvous maneuvers

Military Applications

Education and Training

Art, Music, and Entertainment — Heinrich Heidersberger, Herbert W. Franke, Hans Kulk, Cathode-Ray Tube Amusement Device, Tennis for Two

Analog Computing Centers

The Future and Prospects of Analog Computing

Some representative reasons for the decline of analog computing:

  • Low accuracy
  • Drift effects
  • High maintenance requirements
  • Generation of functions of several variables is very laborious
  • Partial differential equations can be handled by analog-electronic analog computers only with great difficulty
  • The speed advantage over stored-program digital computers became progressively smaller
  • No time-sharing possible; high overhead for program changes

The Future and Prospects of Analog Computing (continued)

The future of analog computing:

  • Close correspondence to the problem domain (teaching and education)
  • High interactivity
  • High parallelism of analog computers (potentially a very promising approach in conjunction with FPGAs or GPUs)

Current deployment already occurring in the field of neuroscience:

  • “Biological Inspired Neural and Dynamical Systems” (BINDS Labs), University of Massachusetts, Amherst
  • Analog VLSI and Neural Systems by Carver Mead
  • “Fast Analog Computing with Emergent Transient States” (FACETS), University of Heidelberg, etc.

Outlook

*The heritage of the past is the seed of the future.*²

² Inscription on the statue Heritage by James Earl Fraser, Federal Triangle, Constitution Ave. & 9th, Washington, DC.

Bibliography

[AMELUNG63] W. Amelung, “Aufbau und Arbeitsweise des Elektrischen Rechenanlages,” Elektronische Rechenanlagen 5 (1963), Heft 1, pp. 28–41

[BEKEY KARPLUS68] George A. Bekey, Walter J. Karplus, Hybrid Computation, John Wiley & Sons, Inc., 1968

Bureau of Ordnance Publication (ed.), Torpedo Data Computer, Mark 3, Mods. 5 to 12 inclusive, June 1944

[DRESSLER72] Fritz Dressler, “Das Dach,” in hobby — Das Magazin der Technik, Nr. 8/72, p. 50 ff.

M. D. Fagen (ed.), A History of Engineering and Science in the Bell System — National Service in War and Peace (1925–1975), Bell Telephone Laboratories, Inc., First Printing, 1978

Bibliography (continued)

Walter J. Karplus, Walter W. Soroka, Analog Methods — Computation and Simulation, McGraw-Hill Book Company, Inc., 1958

[MCLEOD LEGER57] John H. McLeod, Robert M. Leger, “Combined Analog and Digital Systems — Why, When, and How,” in Instruments and Automation, June 1957, pp. 1126–1130

[MICHELS54] Lowell S. Michels, Description of BENDIX D-12 DIGITAL DIFFERENTIAL ANALYZER, Bendix Computer Division, Bendix Aviation Corporation, 5630 Arbor Vitae Street, Los Angeles 45, California, March 13, 1954

[EAI] N. N., PACE 231R analog computer, Electronic Associates, Inc., Long Branch, New Jersey, Bulletin No. AC 6007

Bibliography (continued)

[TRUITT60] Thos. D. Truitt, A. E. Rogers, Basics of Analog Computers, John F. Rider Publisher, Inc., New York, December 1960