APPLICATION OF THE VOLTERRA SERIES TO THE ANALYSIS AND DESIGN OF AN ANGLE TRACKING LOOP

摘要

The subject of this report is the analysis and design of a nonlinear feedback control system, called an "angle tracking loop". A typical function of an angle tracking loop is to keep a radar antenna pointed at a target. The departure of the antenna from the target is the tracking error. This error is directly related to successful operation of the tracking device;therefore, its behavior is of interest. In this research, functional analysis techniques, namely methods associated with the Volterra series, are used to approach the angle tracking problem. For the tracker with a general polynomial nonlinearity, an arbitrary initial error and a bounded deterministic input, a method is developed for finding upper bounds on the magnitude of the tracking error (after expressing it in a Volterra series). Convergence regions of the Volterra series are also obtained. For the tracker with a general polynomial nonlinearity, a zero initial error and an input consisting of a random process (with bounded sample functions or bounded moments) in addition to a bounded, deterministic function, a method is developed for finding upper bounds oh the magnitude of the mean of the tracking error (after expressing it in a Volterra series). Convergence regions of the Volterra series in this case are also obtained.