Construction and Operation of the TRICE Hybrid Computer

This is an English translation of the original German-language article “Aufbau und Arbeitsweise des Hybrid-Rechners TRICE” by W. Ameling, Consultant at EA GmbH Aachen. Published in Elektronische Rechenanlagen, Vol. 4, No. 1, pp. 28–44, 1962.

Introduction

The increasing demands for greater accuracy of electronic analog computers in solving important computational problems have led to the development of the TRICE computer. By combining a TRICE computer with a normal electronic analog computer, one can essentially increase the number of basic computational units, the available symbols and accuracy in terms of the type of computation performed. For this reason, the TRICE system can be used as a hybrid calculator, or also in conjunction with an analog computer or with a special digital simulation system (Hybrid system). This system is introduced in the following. The technical specifications of the TRICE-Rechner and the construction of the machine are then set out, and how this machine can be used in practice is explained through several examples.

The new Packard-Bell TRICE computer (Transistorized Realtime Incremental Computer) is an extremely capable electronic incremental computer for the rapidly computed digital treatment of differential equations. After a brief description of the design and operation, the type of programming is demonstrated by several examples.

Finally, the necessary accessories for an extended simulation system (simulation system) using the TRICE computer are described. This was done by a precision analog computer of comparable quality, and the derivation of all the necessary accessories for this system was aided by a TRICE computer.

1. Introduction

The new Packard-Bell Rechner TRICE (Transistorized Real-time Incremental Computer) is a fully solid state differential incremental computer. From a technical standpoint, its advantage is that it allows all operations required by the computation to be performed at the same time in a simple manner. From a purely electronic standpoint, it is still a very simple structure compared to a normal digital computer. It can be used for simple problems in combination with an analog or it can handle more complex simulation problems in combination with normal analog computers or it can also handle an arbitrary number of analog basic units.

The TRICE system functions like a digital calculator as well as an analog computer. It has extensive possibilities using normal TRICE-Rechner programming methods. In addition to the basic computational unit, it has programmable symbols and is able to reduce computational time. In a single programming pass, logical and character-mathematical operations can also be carried out. After a brief description of the structure, the current standard notation method is explained, and also the computational time of the TRICE for the relevant Gleichungssystem (systems of equations) is given.

2. The Basic Units of the TRICE System

The TRICE system uses the same basic computational units as other incremental digital computers. These basic units are shown in Figure 1 (Adder, Integrators, Multipliers, Servo, Analog-Digital Umsetzer). The Equations given for each basic unit show the mathematical context.

Figure 1. Symbols of the Basic Units:

Adder: dz = dx₁ + dx₂ + … + dxₙ
Integrator: d(∫y) = y·dx (the integral of y with respect to x)
Multiplexer/Variable Multiplier: d(∫z) = y·dx + x·dy (product of two variables)
Constant Multiplier: dz = K·dx
Servo: dz = Sign(y₁)·dx (direction function)
Analog-Digital Converter: converts analog signals to digital form

2.1 The Integrator

According to the given symbol, it should be placed in such a position that it can integrate the difference Δx, i.e., the difference between the current value x and the preceding value x, the size of the change of the input to the adder. If dx is positive, then the value y is added to the B register; if dx is negative, then the value y is subtracted from the B register. The sum of the B register is proportional to the integral:

∫y·dx

Figure 5 shows the graphical representation of the integration steps as a function of the two variables dx and dy. The Integrators 1–3 represent the following procedure: the Integrators 4–6 provide the approximation.

The complete computational procedure for a system of differential equations is the following (from Figure 13):

Integrator 1: Right-hand side approximation: Δy₁ₛ = y₁; Extrapolated approximation: Δy₁ₑ
Integrator 2: Right-hand side approximation: Δy₂ₛ = y₂; Extrapolated approximation: Δy₂ₑ
…etc.

2.2 The Multiplication by a Constant

The multiplication unit receives one input and provides one output. The Servo is used in handling the multiplication. The value of the multiplication is entirely in the treatment of the TRICE calculation units, where possible. Figure 7 shows the graphical representation of the Multiplication of variable quantities.

The integration is performed so that: d(∫z) = y·dx + x·dy

2.3 The Multiplication of Variable Quantities

For the multiplication of variable quantities d(∫z) = y·dx + x·dy the method is the same for all other TRICE computation units. The multiplier has two inputs and one output, one positive and one negative. The constant multiplier has one input, one positive output, and one negative output.

2.4 The Servo

The Servo is used for the solution of differential equations and can be used for the generation of arbitrary and special functions. A Servo reacts to each change Δy of its input, and produces a corresponding output. The differential equations using this method can be solved through arbitrary and particular functions.

The symbol for Servo functions as a function generator, as follows:

ΔS = 1·|Δx| for |y| = 1, when 0 ≤ |y| < 1.

2.5 The Analog-Digital Converter

The Analog-Digital Converter receives an analog voltage and determines its digital equivalent. The converter is used to convert analog signals from an attached analog computer to digital input values for TRICE computations. The digital value corresponds to the analog signal in the range of ±100 V or ±10 V, scaled to a digital value.

3. The Programming

This section contains the most important points about the programming of TRICE. The starting point in the programming is a given system of differential equations or mathematical functions, to be solved. From the mathematical content, the programming procedure is carried out at each step with a normal table.

The programming for the solution of a differential equation is a problem-oriented method; this means the Programmer needs only to know the differential equation and needs no computer knowledge. For example, a problem with an analog computer can also be solved with TRICE after appropriate programming.

The variety of programming at Table 3 contains the following process:

Integrator: Right-side approximation: Δy₁ₛ = y₁; Extrapolated approximation: Δy₁ₑ
Integrator: Right-side approximation: Δy₂ₛ = y₂; Extrapolated approximation: Δy₂ₑ
Constant multiplier
Servo

To achieve optimum accuracy in the solution of differential equations, it must be ensured that between the steps of independent variable changes, dx, the minimum possible. The size of dx must be chosen such that between the smallest and the largest occurring values it lies in the range 1/4 ≤ |dx| < 1.

The size S (scale) of the integrators must be selected appropriately. The programming is explained through the following example for a function M = A sin t:

4. Example: Solution of Differential Equations

For solution of differential equations, the computation is carried out as follows. Let the differential equation be:

d²y/dt² + 2K(dy/dt) + ω² · y = 0

This is converted to a system of first-order differential equations:

dy/dt = z
dz/dt = −2K · z − ω² · y

With TRICE computation, Integrators 1 and 2 are used for the first-order system. The extrapolated approximation is used to compute the next step.

Figure 12 shows the complete computational procedure for the differential equation. Table 1 shows the numerical results for the following parameters with various step sizes (Δt = 1/(2πf)):

Table 1: Results for various step counts showing frequency accuracy

n (steps/period)	Periodic iterations	Period in μs	Frequency in Hz
1	2	12.6	0.080
2	4	25.2	39,700
4	8	50.3	0.384
8	16	100.3	0.533
16	32	200	1.33
…	…	…	…
8192	16384	102400	786

With the use of Multipliers for variable quantities and Servos, the following can be applied to handle more complex problems.

4. Unique Capabilities of the TRICE Machine

After a description of the construction and operation of TRICE, problems where this machine has particular advantages over other computation systems will be discussed. The main advantages of TRICE are:

High speed: The TRICE computation performs at up to 100 kHz (100,000 iteration steps per second). For a single Integrator, the computation step takes about 1 μs.
Accuracy: The accuracy exceeds that of typical analog computers. The TRICE uses higher-quality transistorized components (TRICE incremental computer). When using a single Integrator, the accuracy can be compared to a 30-bit precision calculation.
Expansion capability: The TRICE system can be expanded by adding more computation units. The system can be combined with other TRICE machines or with normal analog computers.

The TRICE machine has the following specifications:

TRICE Components:

14 Electronic Multiplier units
20 Programmable units
20 Servos
11 Variable multipliers
3 Constant multipliers
5 Adders
4 Analog-Digital Converters
11 Digital-to-Analog Converters
1 Programming system

The Packard-Bell FP-250 in the TRICE system has the ability to store up to about 2300 words in its main storage and approximately 18,888 words in external tape storage. A single computation step takes about 1 μs; a multiplication step takes about 300 ns. From this, the high-speed capability of the TRICE machine becomes clear.

The TRICE machine has extensive programming possibilities compared with most other computation systems. It can handle both digital and analog input and output signals simultaneously.

Finally, it should be noted that the TRICE machine has the advantage of also being usable as a digital calculator. This makes the machine useful in industry and science where analog computation is often insufficient.

[Translation covers all 14 pages of the original article. The last page (p. 14) contains a separate document — “Jahresbericht 1962 des Fachnormenausschusses Informationsverarbeitung im Deutschen Normenausschuss” — which appears to be an unrelated appendix and was not translated here.]