A. Background for First 7"wo Examples
The major objective of this research is to develop a design procedure for compensating networks which takes cognizance of the possibility that certain components of a physical network may impose limitations because of their finite ranges of linearity. Up to the present time network synthesis theory usually has presupposed components which are linear over infinite ranges. It was left to the application engineer to select physical parts with sufficiently wide ranges of linearity so that the designed system would not operate with any part in the saturation region. For much engineering work this is a satisfactory procedure. However, in certain applications, particularly in automatic-control applications, this procedure could result in requiring excessively large components, since component operating range is allowed to play little part in establishing the design. In certain situations it would seem possible to reduce linear range requirements by permitting the system error to increase slightly from the minimum value possible with linear range considerations excluded from the system determination. One can conceive of a "trading curve" for system design which governs the exchange of reduction of linear range requirements for increase in system error. If specifications are such that the "trading curve" permits a large reduction of linear range for a small increase in error, one is inclined to make use of this fact in making his design. This is particularly * This paper is abstracted from the theoretical portion of a thesis presented to the Masssachusetts Institute of Technology in partial fulfillment of the requirements for the degree of Doctor of Science in Electrical Engineering. The basic problem of dealing with saturation in feedback-control systems has arisen repeatedly in the author's experience in the automatic control field.