Probability Criterion for the Design of Servomechanisms

摘要

Of the criteria that are used in the design of servomechanisms, the so‐called ``minimum mean‐square'' error criterion is used quite widely in cases where the undesirability of the error increases with its magnitude. There is, however, an important class of applications, particularly in the field of ballistics, where a more appropriate criterion can be defined as the probability that the error be less than some prescribed tolerance. The problem of maximization of this probability is shown to reduce to a number of implicit equations whose solution in practice must be carried out by cut and trial. It is further shown that under certain conditions the maximization of probability yields the same values for the design constants as the minimization of mean‐square error. These conditions are discussed for the general case as well as for certain specific cases which are important in practice.