Future Developments in Hybrid Computing

This document is an English translation of the original German article “Entwicklungstendenzen im hybriden Rechnen” by W. Giloi, published in Elektronik, vol. 17, no. 11, 1968, pp. 11–17.

Future Development in Hybrid Computation

by W. GILOI
Technische Universität Berlin
Lehrstuhl A, Institut für Informationsverarbeitung

[Editorial note: The present contribution is the German text of a lecture given by the author at the AFIPS-Conference (Computer Exposition, 28 Nov. to 2 Dec. 1967) in Anaheim, California. — The Editors.]

1. Where Are We Today?

Even before the AFIPS Conference in Detroit in 1963, the German term “Hybridrechner” (hybrid computer) had become established to describe hybrid computation. The term originated in the USA, was used in the paper “Computation possibilities of combined analog-digital systems” by D.W. MacNeal. He defined a hybrid computer as a combination of a digital and an analog computer. Up to this point the distinction between hybrid computers and ordinary analog computers is clear. The question is: to what extent must a digital computer complement an analog computer to justify the designation “hybrid”?

1.1 Dynamic Error Behavior of Analog and Digital Computers

An analysis of the error sources of analog computers — as shown in Figure 1 (error as a function of frequency for various error types) — leads to the conclusion that dynamic errors grow with increasing frequency of the solution, while static errors remain constant. At the same time, the dynamic characteristics of analog computing elements (amplifiers, multipliers, function generators) lead to specific frequency limitations. The figure shows the typical error behavior with Kirchhoff errors, amplifier errors, and function generator errors versus frequency, with an integration frequency range indicated.

For digital computers, on the other hand, precision is independent of the frequency of the computed function — within the range of feasible step widths — while computation time grows dramatically as higher precision is demanded. The precision is, in principle, unlimited.

As a result of these observations, an analog computer is well-suited to represent quickly varying processes with modest accuracy requirements. A digital computer is well-suited to handle processes requiring high accuracy but tolerating greater computation time. Hybrid computers combine both capabilities.

The state of the art in 1967 can be characterized as follows:

The digital computer in the hybrid combination takes over increasingly larger portions of the overall computation task.
The boundary between analog and digital portions is shifting increasingly in favor of digital computation.
The analog portion will eventually be limited to those tasks that cannot be economically performed by a digital computer.

1.2 Solution Comparison: Analog vs. Digital vs. Hybrid

For typical simulation problems, the computation time on an analog computer scales proportionally with the time constant of the process being modeled. On a digital computer, computation time grows roughly with the square of the number of state variables, or more precisely, with the stiffness ratio of the differential equation system.

For strongly nonlinear, high-dimensional systems, neither pure analog nor pure digital computation yields optimal results. The hybrid combination exploits the best characteristics of each type.

The solution diagram (shown in Figure 1 of the original) illustrates the relationship between digital frequency (Digitalfrequenz) and analog frequency (Analogfrequenz), with a region of optimal hybrid operation between the purely analog and purely digital domains.

2. Analog Part of the Hybrid System

The analog portion of a hybrid computer serves those computational tasks for which it is better suited than the digital portion, specifically:

Fast integration of differential equations (with limited precision requirements)
Generation of nonlinear functions (using diode function generators, multipliers)
Signal conditioning and scaling
Continuous physical process simulation

The precision requirements for the analog portion are typically limited to about 0.01% (4–5 decimal digits). The speed of the analog computation is constrained by the bandwidth of the operational amplifiers and other computing elements.

In a typical hybrid system, the analog portion contains:

High-speed operational amplifiers
Electronic analog memory (track-and-hold circuits)
Multipliers and function generators
Comparators (for mode control and event detection)

The importance of the ADC/DAC interface is paramount. The analog-to-digital converters (ADCs) must operate quickly enough not to become the bottleneck of the hybrid system. For real-time simulation, conversion times of 1–10 µs are typical. The digital-to-analog converters (DACs) are generally faster than ADCs and present less of a performance constraint.

3. Digital Part of the Hybrid System

The digital portion of the hybrid computer handles:

Parameter storage and iterative parameter optimization
Logical decision-making (mode control, switching)
High-precision or slowly-varying computations
Program control and sequencing
Output data logging and formatting

The digital computer controls the overall problem setup and the switching between operating modes (IC — Initial Conditions, OPERATE, HOLD, REPETITIVE OPERATION).

3.1 Interface Considerations

The interface between analog and digital portions of the hybrid system is the most critical design element. It includes:

Multiplexers (to share a single ADC among multiple analog variables)
Sample-and-hold circuits (to freeze analog values during ADC conversion)
ADC and DAC hardware
Control logic (for synchronization)

A key design challenge is that the analog computer operates continuously, while the digital computer operates in discrete time steps. The interface must bridge this fundamental difference.

4. System Structure of the Hybrid Computer

Figure 2 (Bild 2 in the original, showing the “Struktur des hybriden Rechners”) depicts the general system architecture. The hybrid computer consists of:

An analog computing unit (with integrators, summers, multipliers, etc.)
A digital computing unit (the digital computer proper)
The ADC/DAC interface
A hybrid controller (or mode control unit)
A programming panel (for analog patching)

The digital computer communicates with the analog portion through the interface, exchanging both data values (via ADC/DAC) and control signals (mode switching commands).

Modern hybrid systems (as of 1967–1968) include specialized hardware such as:

ADDER systems
Crosspoint switch matrices (for reconfiguring the analog patch without manual rewiring)

The crosspoint switch (shown in the diagrams for the ADDER system, Bilder 4 and 5 in the original) allows the digital computer to dynamically reconfigure the analog computing network — a significant step toward fully automated hybrid computation.

5. Programming of Hybrid Computers

Hybrid programming is substantially more complex than programming either an analog or a digital computer alone. The programmer must:

Identify which portions of the problem are best solved on the analog side, and which on the digital side
Scale the analog problem (time scaling and amplitude scaling)
Write the digital control program
Establish the patching (physical or via crosspoint switch) of the analog part
Verify the combined solution

5.1 Hybrid Programming Languages

A key development trend identified in the article is the emergence of hybrid programming systems. These include:

MIDAS (Modified Integration Digital Analog Simulation) — one of the earliest hybrid simulation languages
FODA (FORTRAN-Oriented Digital Analog Simulation)
APACHE — developed for use with the EAI 8400 hybrid system
HYBLOCK — a block-diagram-oriented language

These languages allow the programmer to specify the hybrid computation at a higher level of abstraction, with the compiler/translator generating the detailed patching list for the analog portion and the digital control program.

A key programming system mentioned is described in Bild 6 (page 6) of the original, which shows a “Basis-Programmiersystem für hybride Rechenanlagen” (basic programming system for hybrid computers). The system comprises:

Input description subsystem
Analog portion (Analogteil): for patching automation
Digital portion (Digitalteil): for computation and control
Specific programs (Spezifische Programme): for optimization, parameter studies, and special computations
Checking and monitoring subsystem (Prüfung der Analogprogrammierung / Überprüfung der digitalen Simulation / Problemüberprüfung)

The output of this system is:

Automatic patching (automatisches Verbinden) of the analog portion
Generation of the digital simulation program

This represents the state-of-the-art concept for hybrid computing centers ca. 1967–1968.

6. Development Trends (Outlook)

The article concludes with the author’s prognosis for future developments in hybrid computing:

Increasing automation of hybrid programming — The labor-intensive manual patching and scaling process will be increasingly automated. Programs like APACHE and HYBLOCK will evolve toward fully automated hybrid programming.
Larger crosspoint switch matrices — As digital control of analog patching becomes standard, crosspoint switches will grow larger, eventually enabling very large analog networks to be reconfigured under program control.
Better ADC/DAC performance — Conversion speed and precision will improve, reducing the interface bottleneck.
Shift of computational work to the digital side — As digital computers become faster and cheaper, more of the computation will migrate from analog to digital. The analog portion will shrink to those tasks that are truly irreplaceable (high-speed, real-time signal processing).
Real-time hybrid simulation — The ability to run human-in-the-loop simulations (flight simulation, process control training, etc.) in real time will become increasingly important and feasible.
Hybrid computing centers — The establishment of dedicated hybrid computing centers (Hybridrechenzentren), serving multiple users with shared hybrid facilities, is predicted.

The author (Giloi, TU Berlin) draws on his own research and on international developments, particularly in the USA, to support these predictions. The article is presented as a thorough survey of the field as of late 1967, with forward-looking analysis.

References cited in the original (selected):

D.W. MacNeal, “Computation possibilities of combined analog-digital systems” (AFIPS 1963)
Various AFIPS Conference proceedings (1963–1967)
EAI (Electronic Associates Inc.) hybrid system documentation

[Translation covers all 7 pages of the original article; the document is complete.]