Combined Analog-Digital Techniques in Simulation

Abstract

One of the most common types of problems to which computers have been applied is the study of complex nonlinear dynamic systems subjected to external disturbances. Such systems are represented mathematically by nonlinear systems of differential equations with time as the independent variable. The comparative characteristics of analog and digital computers when applied to the solution of dynamic systems problems are presented in this chapter. Many simulation type problems may be solved almost equally well on either an analog or a digital computer. Many types of problems are not handled well and consideration has been given to the advantages to be derived from interconnecting analog and digital machines through appropriate analog-to-digital and digital-to-analog converter equipment. In such a system, part of the problem can be solved on the digital computer and part on the analog computer, with exchange of data taking place through interconnecting data channels. An example of a combined solution is given here. Combined analog-digital techniques have been devised to perform the arithmetic operations in a digital computer. A digital-to-analog converter is inherently a multiplier and the analog-to-digital converter a divider. A different method of combining analog and digital techniques is by representing quantities not by numbers—as in the digital computer—or by electrical voltages—as in the electronic analog but by the sum of a number and an electrical voltage, where full scale on the electrical voltage is equivalent to one in the least significant digit of the digital part of the number. The usefulness of such a combined system would be on simulation problems where the precision required is greater than that obtainable by analog methods and that requires the real-time speed of the analog computer.