An analysis of control systems containing nonlinear elements and elements operating on discrete as well as continuous signals is described. When amplitude sensitive elements are involved in sampled-data systems, and provided certain restrictions are adhered to, it is shown that describing function techniques can be readily used to evaluate the stability and frequency response of such systems.
1. Introduction
THE FREQUENCY method has been extensively used in the study of intermittent or discretecontinuous "linear" systems, i.e. systems containing no amplitude sensitive elements. LINVILL [I] provided an extension to Nyquist's stability criterion to embrace these sampled= data systems and the absolute stability of such systems are well defined. Similar methods of analysis were developed by Ts~ras [2], RAGAZZINI and ZADEH [3] and others.
An extensive study of the sampling process in "linear" systems subjected to periodic signals has been made by WADDELL and MOR~S [4] who develop a linear transfer function for the sample and hold process which is applicable, subject to certain limitations, to input signals of all frequencies including multiples of half=sampling frequencies. The problem of stability and the presence of "sampling" oscillations are accounted for.
This paper applies the describing function technique to the work of WADDELL and MORRIS to provide an extension of their technique to systems containing amplitude dependent elements. Certain physical concepts useful in dealing with feedback systems involving both sampling and nonlinearity are included.
Close loop frequency responses of a particular configuration are predicted showing the presence of special phenomena of both nonlinear and sampled data systems.