SUMMARY 



149 



precision is necessary for each of the three 

 techniques. 



Next we will consider the same task with 

 a constant speed course. This is another 

 common experimental design. Errors in 

 rate and position develop. Perfect correc- 

 tion of both types of error simultaneously 

 will bring the reticle and target back into 

 alignment. Just as in the other case, cor- 

 rections are made by acceleration adjust- 

 ments of the reticle movement. However, 

 the development of error is now suppressed 

 by the maintenance of the correct rate. 

 The center column in Table III indicates 

 for each tracking technique the handle 

 movement dimensions in which precision is 

 required. 



A brief comment on error correction will 

 serve to illustrate another aspect of the op- 

 erator's role. In the constant-speed track- 

 ing task just considered, the reduction of a 

 position error is necessarily accompanied by 

 a temporary rate error. The continuous 

 change in target position requires that the 

 operator reduce both position and rate errors 

 simultaneously in order to achieve perfect 

 tracking. However, experimental observa- 

 tions indicate that the two types of error are 

 corrected alternately. A number of investi- 

 gators using constant speed courses note a 

 tendency for operators to "tolerate" small 

 constant errors in position rather than aban- 

 don their successful rate adjustment. 



Operational Analysis and System Variables 



Operational analysis is a well worked out, 

 mathematical technique for analyzing the 

 characteristics of physical transmission sys- 

 tems. It is widely used by engineers to pre- 

 dict the response of servomechanisms and 

 electrical networks which are too complex to 

 allow the computation of the performance of 

 the whole from performance of individual 

 components. The relationships between in- 

 put and output are the basic functions, and 

 they may be investigated without reference 

 to intervening mechanisms. 



Perhaps unfortunately, the power of these 

 methods is restricted, for the present at 



least, to the analysis of linear systems only. 

 The application of these methods, therefore, 

 to the analysis and synthesis of closed cycle 

 systems containing a human operator as one 

 of the elements will be fruitful to the extent 

 that these systems are linear or can be made 

 Imear and to the extent that the human op- 

 erator is linear or can be made linear. 



The concept of linearity as applied to 

 transmission systems includes three funda- 

 mental properties. These are: 



1 . The normal response is a linear function 

 of the input, in the mathematical sense. 



2. The normal response at any time de- 

 pends only on the past values of the input. 



3. The normal response is independent of 

 the time origin. 



The application of operational analysis to 

 human motor responses has been discussed 

 by Ellson (9) . Using this technique, experi- 

 mental investigation of the linearity of sys- 

 tems containing human elements is now in 

 progress at several different laboratories (11, 

 20, 23). The test for hnearity rests on the 

 fact that in the case of truly linear systems, 

 if the response of the system to certain char- 

 acteristic inputs is known, the response to 

 any other arbitrary input can be determined. 

 The test inputs consist of either a step func- 

 tion input (the sudden displacement of the 

 variable preceded and followed by a steady 

 state) or sine wave inputs over a limited 

 range of frequencies. Successful prediction 

 of the output of the system to a complex in- 

 put from a knowledge of the system output 

 to each of its simple components constitutes 

 an important indication that the system is 

 linear. The preceding discussion of system 

 variables is directly related to the determina- 

 tion of the effective input in such tests and 

 to the establishment of similarities between a 

 system which has been tested and other sys- 

 tems about which information is desired. 



Summary 



An examination of the literature on studies 

 related to the problems of control design 

 yields a heterogeneous mass of unrelated 

 facts that have been gleaned from experience 



