Method is described for reduction of error components in numerical integration, sampling with zero hold order, and execution time delay

Alford, C. O.

Hammond, J. L., Jr.

English

NASA Technical Reports Server

1972	 B72-10141 
NASA TECH BRIEF 
Marshall Space Flight Center 
NASA Tech Briefs announce new technology derived from the U.S. space program. They are issued to encourage 
commercial application. Tech Briefs are available on a subscription basis from the National Technical Information 
Service, Springfield, Virginia 22151. Requests for individual copies or questions relating to the Tech Brief program may 
be directed to the Technology Utilization Office, NASA, Code KT, Washington, D.C. 20546. 
Errors in Hybrid Computers 
The problem: 
In any hybrid computer there exist inherent system 
sampling errors. 
The solution: 
A method has been devised for the reduction of a 
particular group of error components, namely in: 
(1) numerical integration 
(2) sampling with zero hold order 
(3) execution time delay. 
How it's done: 
In any numerical integration method which produces 
solutions to differential equations at discrete values, the 
step size is the difference between successive values at 
which solutions are produced. This is usually a constant 
figure. There exists a principal error function of any 
numerical method used in conjunction with hybrid com-
puters caused by truncation and analog sampling errors. 
The choice of optimum numerical integration method 
depends on analog to digital (AID) and digital to analog 
(D/A) timing requirements, required data conversion 
storage, and execution time. 
Digitally generated functions coupled to analog com-
puters through zero hold (D/A) converters produce errors 
directly related to the sampling period ( 6 ). In order to
effect a reduction in error, the error must be made 
dependent on powers of 6 higher than the first. This is 
done by replacing the zero order hold devices with first 
order hold devices. The sampling period is not changed. 
Execution time delays of digital computations for 
use by the analog computer is another source of error. 
By proper sequencing, extrapolation, and estimation, 
this error component can be reduced. 
Note: 
Requests for further information may be directed to: 
Technology Utilization Officer 
Marshall Space Flight Center 
Code A & TS-TU 
Huntsville, Alabama 35812 
Reference: B72-10141 
Patent Status: 
No patent action is contemplated by NASA. 
Source: C. 0. Alford and J. L. Hammond of 
Georgia Institute of Technology

under contract to
Marshall Space Flight Center
(MFS-21289) 
is
Category 02 
This document was prepared under the sponsorship of the National 	 Government assumes any liability resulting from the use of the 
Aeronautics and Space Administration. Neither the United States 	 information contained in this document, or warrants that such use 
Government nor any person acting on behalf of the United States	 will be free from privately owned rights.
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Errors in hybrid computers

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