A theory for the design of compensating networks for feedback-control systems and filters is developed herein. The novel feature of this theory is its consideration of saturation and transient performance in addition to the usual steady-state behavior. This theory is essentially an extension of the researches of Wiener and Lee ii~ statistical methods for filter design. Saturation is handled by limiting the rms. signal levels at critical points in the linear model used as the design basis for the physical systeln. Transient performance is handled by limiting the integral-square errors to a set of transient tests signals.
I. BACKGROUND AND OBJECT
Modern feedback-control systems are usually designed by a combination of analysis and experiment. This paper is confined to certain of the analytical aspects. In order to reveal the object of the investigation herein reported, the important analytical methods in current use will first be reviewed.
Compared with an elementary filter, a continuous feedback-control system involves two additional complications: the first, a partially or completely specified output device (servomotor or process); and the second, one or more independent or semi-independent disturbing variables (load torque, for example). In common with the filter, the feedback-control system often is called upon to separate data from noise. However, because of the restrictions upon the output device, the designer of a feedback-control system has free choice of the remaining equipment only. For this reason, feedback-control designers often regard their problem as one of compensation design. * This paper is abstracted from the theoretical portion of a thesis presented to the Massachusetts Institute of Technology in partial fulfilhnent 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. A partial solution was obtained during work for the Fairchild Guided Missile Division, Fairchild Engine and Airplane Corp. under Navy Contract NOa(s) 9020. The more general solution contained in this paper was obtained iu the course of research conducted in the Servomechanisms Laboratory at M.I.T. under Air Force Contract W33-038ac-13969.
The author is indebted to Drs. G. S. Brown, A. C. Hall and Y. W. Lee of the Massachusetts Institute of Technology for their sponsorship of this research. He wishes to thank his colleagues at the Massachusetts Institute of Technology for their constructive criticism of the research and its reportings.