# analogue computer

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## analogue computer

(computer, hardware)For example, the turning of a wheel or changes in voltage can be used as input. Analogue computers are said to operate in real time and are used for research in design where many different shapes and speeds can be tried out quickly. A computer model of a car suspension allows the designer to see the effects of changing size, stiffness and damping.

## Analogue Computer

a computer in which there is for every instantaneous value of a variable quantity in the original relationships a corresponding instantaneous value of another (computer) quantity, often differing from the original in physical character and scale. For each elementary mathematical operation on the computer quantities there exists, as a rule, some corresponding physical law which determines the mathematical relation between the physical quantities at the output and input of the computing element (for instance, Ohm’s and Kirchhoff’s laws for electric circuits, the expression for the Hall effect, for Lorentz force, and so on).

The manner in which the original data are presented and the individual computing units are constructed predetermines, to a great extent, the relatively high operating rate of an analogue computer and the simplicity of programming and composing problems, but it limits the application and accuracy of the results obtained. An analogue computer is also notable for its low general-purpose utility (algorithmi-cally restricted); when shifting from solving one class of problem to another, it is necessary to change the structure of the computer and the number of computing elements.

The slide rule, which appeared around 1600, is generally considered the first analogue computer. Graphs and nomograms for determining functions of several variables were the next variety; they are first encountered in the navigation manuals of 1791. In 1814 the English scientist J. Hermann developed the planimeter, an analogue instrument used to measure an area bounded by a closed curve on a plane. The planimeter was improved in 1854 by the German scientist J. Amsler. His integrating instrument with a rolling wheel later led to the invention of the frictional integrator by the English physicist J. Thomson. In 1876 another English physicist, W. Thomson, used the frictional integrator in the design of a harmonic analyzer to analyze and predict the heights of tides in various ports. He demonstrated in principle the possibility of solving differential equations by coupling several integrators, but because of the low level of technology at the time the idea was not realized.

The first mechanical computer for solving the differential equations of ship design was constructed by A. N. Krylov in 1904. Based on this, the idea of an integraph, or analogue integrator, was proposed and developed by the Polish mathematician Abdank-Abakanowicz (1878) to obtain the integral of an arbitrary function traced on a plane graph.

Subsequent development of mechanical integrators is linked with the work of the American scientist V. Bush, under whose leadership a purely mechanical integrator was developed (1931), followed by its electromechanical variant (1942). In 1936 the Russian engineer N. Minorskii proposed the idea of an electrodynamic analogue. The evolution of the modern DC analogue computer was stimulated with the development of a computing amplifier by B. Russell (1942–44, USA).

The work of the Soviet mathematician S. A. Gershgorin (1927) was of great value in laying the foundation for the design of network analyzers. In the USSR in 1936 under the direction of I. S. Bruk a mechanical integrator and an electrical network analyzer were constructed to determine the steady-state conditions of power systems. In the 1940’s development was started on an electromechanical antiaircraft fire director using AC and on the first electron tube integrators (L. I. Gutenmakher). Carried on under the direction of Gutenmakher (1945—46), the work led to the creation of the first electronic analogue computers with recycling of the solution. Under the direction of V. B. Ushakov, V. A. Trapez-nikov, V. A. Kotel’nikov, and S. A. Lebedev a number of analogue computers using DC were designed in the USSR in 1949. These efforts mark the beginning of modern analogue computer development in the USSR.

An analogue computer is used primarily to solve the problems of monitoring and control, advance analysis, experimental investigation, analysis of control or regulation system dynamics, synthesis problems for control and regulating systems, and problems in the determination of disturbing or useful signals that act on a system.

In automatic monitoring and control systems an anologue computer is generally used to determine or formulate a control law and to calculate the composite parameters of the process (efficiency, power, performance, and others). If a mathematical expression is assigned which defines the association of the composite parameter or a control action with the coordinates of an object, the analogue computer serves to solve the corresponding equation. The computational results pass to either an actuator mechanism (a closed system) or an operator. In the latter case the analogue computer acts as an information device. For example, analogue computers are widely used to evaluate the economic efficiency of power systems, and the same analogue computers can control actuator mechanisms—that is, serve as automatic regulators. When the control law has not been determined beforehand but only some criteria of optimality and the limiting conditions are specified, analogue computers are used in optimum control search systems and serve as a mathematical model of the object.

Advance analysis, based on high speed, is another function of the analogue computer. By repeatedly solving the system of equations that describe a controlled process and by taking into account the current characteristics, an analogue computer “scans” in a short time a large number of alternative solutions using different values of the parameters that are subject to change during the control process. Well ahead of the progress of the process, its required quality can be ensured by control signals predicted by the analogue computer. The values determined by the computer are transmitted to a regulating device—in the form of control point settings, for example—after which the search for the best alternative is continued. In the advance analysis mode an analogue computer performs the functions either of a computer-adviser, where an operator uses the results of the computations performed by the computer for manual or semiautomatic control, or of a control computer that automatically considers the current characteristics of a process and controls them to optimize the criteria. Selecting the best mode for a technological process is also determined by self-adjusting mathematical machines in an advance analysis mode.

Experimental investigation of a system performance with control or regulation apparatus under laboratory conditions is handled by the analogue computer for that part of the system which for some reasons cannot be reproduced under laboratory conditions. Connection between an analogue computer and control or regulation apparatus is achieved mainly by converters which change the computer variables in scale and mode of presentation.

In analysis of control or regulation system dynamics, the equations specified for an object are solved on a time scale chosen to find the basic parameters that will provide the requisite course for the process. Of particular importance is the high-speed analogue computer, for its aid makes possible the solution on an accelerated time scale of certain iterative and optimization problems as well as the realization of the Monte Carlo method, which requires the repeated solution of stochastic differential equations. In this instance an analogue computer drastically reduces the calculation time and provides graphic results.

Solving synthesis problems for control and regulating systems is reduced to a selection in accord with prescribed technical conditions of a structure for the invariant part of the system, of functional relationships of the required form, and of fundamental parameter values. The final result is obtained by a multiple repetition of the solution and a comparison between it and the approximation criterion adopted. Problems of this type are often reduced to a search for the extremum of some functional.

In solving problems on the determination of disturbing or useful signals that act on a system, a determination is made of the magnitude of the disturbance or useful signal at the input using the differential equations describing the dynamic system, the values of the initial conditions and the changes determined by experiment in the character of the output coordinates and the statistical characteristics of the noise and signal being measured. An analogue computer can also be used to build instruments that automatically register disturbances and produce a control signal dependent on the character and amount of the disturbances.

An analogue computer consists of a certain number of computer elements which are classified according to the nature of the mathematical operations they perform—namely, linear, nonlinear, and logical. Linear computer elements perform the operations of summation, integration, changes of sign, multiplication by a constant, and others. The nonlinear (function generators) reproduce nonlinear relationships. There are computer elements designed to reproduce an assigned function from one, two, or more arguments. It is customary to distinguish in this class the devices for reproducing discontinuous functions of a single argument (typical non-linearities) and the multiplier-divider devices. Among the logic computer elements are analogue logic devices such as those designed to discriminate the largest or smallest of several quantities, discrete logic devices, relay switching circuits, and certain other special units. In order to combine analogue and discrete logic devices, extensive use is made of hybrid logic devices (such as comparators). All the logic devices are usually combined into one, called a parallel logic device. It is equipped with its own patch board for connecting the individual logic devices to each other and to the remaining analogue computer elements.

Depending on the physical embodiment of the computers’ variables, analogue computers can be classed as mechanical, pneumatic, hydraulic, electromechanical, and electronic. The most common are the electronic analogue computers, which have a substantially broader pass band and are convenient to link with other computers and with apparatus control elements. These computers are assembled from premanufactured radio engineering subassemblies and semifinished products. The design of the analogue computer elements is based on multistage DC electronic amplifiers having high gain in the open circuit mode and strong negative feedback. Depending on the structure and character of the input circuit and the feedback circuit, an operational amplifier performs a linear or a nonlinear mathematical operation or a combination of these operations.

Because of the nonideal operation of individual computer elements and inaccuracies in the transfer factors and initial conditions of the equipment, the solution obtained with an analogue computer has errors. The resultant error depends not only on the primary causes mentioned but also on the character and peculiarities of the problem being solved. As a rule the error increases with the number of computer elements (especially nonlinear) connected in tandem. It can be assumed in practice that, when stable nonlinear automatic control systems are being investigated, the error will not exceed several percent if the order of the set of differential equations is no higher than the tenth.

Analogue computers can be constructed with manual or automatic program control. In the first case, before beginning the solution, the computer elements are interconnected to correspond with the performance sequence for the mathematical operations defined by the original problem. In computers with program control the fulfillment of the individual mathematical operations is changed in the process of solving a problem according to the algorithm prescribed for the solution. During the solution of a problem, a change of the order in which individual operations are performed causes the computer operation to be intermittent; a solution period alternates with a stopping period (to perform the necessary switching). In this mode an analogue computer must be provided with an analogue memory device.

The existence of a memory and the discrete character of the computer operation make possible the multiple use of individual computer elements, allowing a reduction in the number of these components without restricting the class of problems that can be solved, although speed is reduced.

Of considerable interest are computers that have a high solution repetition rate (30 to 1,000 Hz) in connection with the design of the system of automatic control as well as with the necessity to provide a search for structures and parameters of control systems that are optimal in some respect.

The efficiency of analogue computers has been increased by supplementing analogue technology with digital methods, in particular with digital differential analyzers, where the separate computer elements perform mathematical operations on the increments of variables represented in one of the digital codes and the results are transferred from element to element using analogue computer principles. The use of digital differential analyzers, especially the sequential type, for special analogue computers not requiring high speed reduces the total amount of apparatus, although in other cases these computers are a poor second to digital computers with respect to all technical criteria and potentialities. The possibilities are much greater for hybrid computer systems in which the original quantities are represented simultaneously in digital and analogue form.

The so-called matrix models show promise for the complete automation of analogue computers. Their basic drawback is the large amount of apparatus, but with the appearance of integrated circuits this drawback is not of crucial importance.

The basic technical characteristics of some types of general-purpose electronic analogue computers in lot production in the USSR are given in Table 1.

The first five units are portable, small-sized desk systems. The IPT-5 is assembled from individual units of linear computer elements. The EMU-8 is also of unit construction, each unit consisting of four computer elements; these units do not require stabilized power supplies. The LMU-1 consists of separate sections; the IPT-5 and LMU-1 in combination with a set of nonlinear units can also solve nonlinear problems. The MN-7 (a desk type) has a limited, immobilized arrangement of computer elements which restricts its use. The MN-8, MN-14, MN-17, and EMU-10 multiple-section types are designed for the solution of complicated problems. Thus, the MN-8 has 80 operational amplifiers and 28 nonlinear computer elements, the MN-14 has 360 amplifiers and 92 nonlinear computer elements, and the EMU-10 has 48 operational amplifiers and 30 nonlinear computer elements. The MN-14 and EMU-10 outfits are supplied with interchangeable patch boards, digital voltmeters, and a control system that facilitates setting up problems and establishing initial conditions. In the MN-14 provision is made for control by means of punched tape. The EMU-10 is notable for the wide pass band of basic computer elements, and it has computer amplifiers with three amplifier channels in parallel.

### REFERENCES

Kriloff, A. “Sur un intégrateur des équations différentielles or-dinaires.”*Izv. Akademii nauk*, 1904, series 5, vol. 20, no. 1.

Gutenmakher, L. I.

*Elektricheskie modeli*. Moscow-Leningrad, 1949.

Tarasov, V. S.

*Osnovy teorii i konstruirovanie matematicheskikh mashin nepreryvnogo deistviia*, issue 1. Leningrad, 1961.

Kogan, B. Ia.

*Elektronnye modeliruiushchie ustroistva i ikh primenenie dlia issledovaniia sistem avtomaticheskogo regulirovaniia*, 2nd ed. Moscow, 1963.

Levin, L.

*Metody resheniia tekhnicheskikh zadach s ispoVzovaniem analogovykh vychisleteVnykh mashin*. Moscow, 1966. (Translated from English.)

Korn, G. A., and T. M. Korn.

*Elektronnye analogovye i analogo-tsifrovye vychislitel’nye mashiny*, parts 1 and 2. Moscow, 1967–68. (Translated from English.)

Bush, V. A. ‘The Differential Analyzer, a New Machine for Solving Differential Equations.”

*Journal of the Franklin Institute*, 1931, vol. 212, no. 10.

Fifer, S. T.

*Analogue Computation*. London, 1961.

B. IA. KOGAN

Table 1. Characteristics of some common Soviet analogue computers | ||||||
---|---|---|---|---|---|---|

Apparatus model | Type ol dillerential equations solved on the apparatus | Maximum order ol the dillerential equations or number ol lirst order equations in a system | Permissible duration ol a solution (sec) | Overall dimensions (mm) or area occupied by the apparatus (m^{2}) | Power consumption (kllovolts × amperes) | Power supply |

IPT-5 . . . . | Linear with constant and variable coefficients | 9 | 150 | 2,000×400 | 2.4 | Stabilized |

LMU-1 . . . . | Linear with constant and variable coefficients with typical nonlinearities | 6–9 | 200–400 | 622×476×1,230 | 2.1 | Stabilized |

MN-7 . . . . | Linear and nonlinear with a few nonlinear operations | 6 | 200 | 700×440×380 | 0.73 | Stabilized |

EMU-8 . . . . | Linear and nonlinear | Set of standard units, each designed for solving second order equations | 2,000 | Size of unit 350×300×300 | 0.06 | Unstabilized |

MN-11 . . . . | Linear and nonlinear with automatic search for solution per specified criterion | 6–9 | Solution repetition rate 100 solutions per second | 15 | 10 | Stabilized |

MN-8 . . . . | Linear and nonlinear with a large number of variable coefficients and nonlinear computer elements | 32 | 1,800 | 60 | 35 | Stabilized |

MN-14 .... | Linear and nonlinear with a large number of nonlinear computer elements | 30 | 10,000 | 40 | 15 | Stabilized |

EMU-10 . . . | Linear and nonlinear with variable delay—the solution of a problem of automatic optimization | 24 | 2,000 | 5 | 3.5 | Unstabilized with a low power auxiliary stabilizer |

MN-17 . . . | Linear and nonlinear with constant coefficients | 60 | From 0.1 to 1,000 | 7,520×2,390×1.024 | 5 | 3–phase AC line, 220/380 V, 50 Hz |