STANLEY FIFER

Dian Laboratories, Inc.

New York, New York

6.1 INTRODUCTION

The purpose of this chapter is to familiarize the reader with the types and functions of analog computers, their components, and the manner in which these components are combined in the simulation of physical systems. Particular emphasis is placed on the general-purpose functional computer, in view of the great popularity enj oyed by· this type of analog. The basic components, e.g., the feedback amplifier, potentiometer, multiplier, passive network, diode, relay, function gen-erator, and recorder are described. Applications to linear and non-linear differential and algebraic equations are discussed, and the pro-gramming and mechanization of typical problems are illustrated. The scope of analog computer design and application is extremely broad;

this chapter is intended to serve only as a somewhat elementary intro-duction to this subj ect. An understanding of the basic characteristics and philosophy of analog computation given here is necessary if the reader is to appreciate and evaluate the manner in which analog com-puters are applied to more complicated and difficult problems, for example to those in automation and flight control, which constitute the subjects of later chapters. Here we can touch only lightly on what are believed to be the more significant aspects of analog computers as

132

ANALOG COMPUTERS 133 related to automation; the re'ader is referred to the bibliography for a more extensive treatment of the subjects that are of particular in-terest or importance to him,

The analog computer is distinguished, in general, by the fact that the equations which describe the relations between the computer vari-ables are the same as those goverriing the relation between the prob-lem variables whose solution is sought. The computer variables may, for example, be voltages, currents, or shaft rotations; the given physical variables may be displacements, velocities, accelerations, pressures, temperatures, or angles. In the course of the solution of a problem on an analog computer, we learn to interpret the computer configuration and the computer outputs in terms of the given physical situation itself, rather than as some abstract analog of it. It is this feature which endows the analog computer with its great value in design and analysis. The computer variables ;themselves are, in gen-eral, continuous quantities and are measured, rather than counted, as on a digital computer. This characteristic, of course, corresponds more closely with physical reality ^t There· is· such diversity among analog computers, however, that we cannot make too many generalizations about their characteristics. Moreover, ·there are some areas in which it is even difficult to effect a sharp delineation between analog and digital methods and components. For example, digital techniques are employed in some analog multipliers,· and digital devices are often used for read-out purposes on analog· computers. Analo~-to-digital

and digital-to-analog converters (Chapter 9), important elements in the field of automation, are examples of components in which the two.

forms of computation are brought together.

We may classify analog computers according to use. They may be employed as computers, simulators, trainers, and control devices. The computer, as the name implies, is employed to solve mathematical problems. The commercially available d-c machines, Beckman, Boeing, Electronic Associates, Goodyear, Mid-Century, Philbrick, and Reeves, are representative of this class. Virtually every engineering, reseatch, and aircraft firm of moderate size has an analog computer as a standard tool to solve problems arising in the course of its work that may be formulated in mathematical terms.

A simulator involves the combination of a. computer and actual physical hardware whose response is to be tested and optimized. For example, consider the problem of designing an autopilot, which is to roll-stabilize a missile in flight by means of a roll gyro. The gyro detects the missile angle of roll and feeds a signal proportional to this angle to the aileron surfaces which are caused to deflect so as to reduce

134 mechanization where the control surface deflection is generated. In the simulator, then, the actual hardware is subjected to realistic tests as it is in flight. Tremendous savings in time and money are effected.

Multiple-axis tables, loaders, and servojigs all play a role in this program.

The purpose of a trainer is to teach operating personnel in the laboratory how to guide some moving craft, such as an airplane, ship, submarine, or tank. The computer again solves the dynamic equations of motion of the body. Actual hardware is again employed; for ex-ample, in the case of a flight trainer, the cockpit, including the in-strument panel and the joy stick, is integrated with the computer and the pilot maneuvers the controls as he would in actual flight. Link and . Curtiss-Wright trainers for commercial and military aircraft are

ex-amples of this application. Take-off, cruise, landing, and emergency conditions are simulated.

Finally, analog computers serve as control devices, in industrial and military applications. Automatic pilots, for example, are analog com-puters designed to stabilize or guide an aircraft along a prescribed flight path. Analog computers are used in industrial control applica-tions, for example, to control the operation of lathes. personnel on the table experience these motions and· also observe in-struments which communicate such information as the forward speed u, the depth z, and the heading tf of the submarine. On the basis of these

ANALOG COMPUTERS 135 computer are the three components of velocity along the body axes of the submarine, u, v, and w, and the three angular rates of rotations about these axes, p, q, and r. These equations are extremely nonlinear in nature.

(3) Another analog computer accepts the angular and velocity rates and, on the basis of theoretical and experimental data, computes the hydrodynamic forces and moments acting on the

sub-Pitch

roll table Instructor

Personnel

0 Q W

Hydrodynamics

~ l

Force and u, v, w Euler