Automatic Regulators, Their Theory and Application
Authors: Smith Ed S. 
Published: February 2023

Abstract
The essential elements and characteristics of automatic regulators are considered in the present somewhat elementary paper which is intended to stimulate activity leading toward an A.S.M.E. research report. Attention is directed to the technical material in the paper rather than the terminology.
Sensitivity, speed, power, and stability are pertinent variables of automatic regulators. Their relations are mathematically treated herein. While it has been necessary to state a few definitions for clarity of treatment, such definitions are not offered as being universally applicable since different fields are accustomed to different terminologies.
An automatic regulator for a variable consists of a meter responsive to the variable, a controller for altering the variable, and governing means connecting the meter and controller to regulate the variable in a predetermined manner. These terms are used in a descriptive sense.
Since hunting generally results from a lag either of the variable (storage or process lag) or the response of the meter to changes of the variable (metering response lag), stability requires that the controller be properly damped, i.e., be made to approach gradually its proper position.
In this general treatment, the hunting of regulators is considered simply as a more or less damped harmonic function of time. This analysis directly relates the performance of typical regulators with their equations and, in particular, connects the stability of such regulators with their constants and those of the system controlled.
Twelve typical regulators and their characteristics are illustrated and briefly described. This is considerably fewer than the number of classes of regulators in common use.
Since the governing means determines the mode of regulation, it forms the principal subject of the paper. Only enough consideration is given the other means associated therewith to establish such of their characteristics as affect the regulation. The present material was selected as illustrating a practical and useful approach to a subject which may appear needlessly involved.
In one class of regulator (Class VII), the controller is prevented from overtraveling the meter even where considerable storage lag exists since the governing means comprises the following elements or their equivalents: A follow-up to prevent momentary swings; a dashpot to rapidly damp down such momentary swings as start due to sudden changes; and reset means to gradually restore the variable to the set point.
The speed of stable controller operation possible with this Class VII regulator provides a useful basis of comparison, in many applications, with other classes of regulators. Certain applications do not require nor justify the selection of such a complete regulator. While it may not be adequate for certain difficult services such as the automatic steering of large vessels, still it has had some use in industry. Class VII regulator has been given more space in the present treatment than possibly it deserves, because it serves to bring out the functions of the various elements involved.