The increasing use of digital computers in the simulation of dynamic systems presents a number of new problems. In particular, the inclusion of a digital computer in a predominantly analog environment introduces time base problems. The digital computer appears to the analog circuitry to be a particular pulsed filter. Time delays due to sampling, computation, and output appear dynamically as ideal transportation delays.

The effects of time delays¹ can be compensated for at the digital-to-analog or analog-to-digital interfaces by either analog² or digital lead filters. Considerations with respect to problem constraints and the available equip ment dictate where and by what means the compensation is to be mechanized. Problem constraints involve the num ber of variables to be interfaced, the characteristics of the variables to be predicted (i.e., not highly nonlinear or dis continuous) and the effects of prediction errors on the variables. Digital simulation of a system of equations usu ally results in a higher order system of difference equations. The attendant problem of stability and attenuation or am plification of prediction errors may make compensation at the D/A interface more desirable. Equipment availability in terms of amplifiers, computation time and the number and type, sequential or parallel, of converter channels in fluence the choice of analog or digital filters.

The purpose of this paper is to apply both classical numerical analysis methods and phase and gain error cri teria to the problem of digital time prediction. A modified maximally flat phase criterion is applied to prediction co efficients to illustrate a filter used in a common simulation problem. Finally, phase and amplitude curves are included to show the advantages of the derived filters for simulation purposes as compared to classical polynomial extrapola tion.

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Communication P Systems with Channel States Working in Flat Maximally Parallel Manner

Pulsed prediction filters applied to digital and hybrid simulation