Analytical and experimental studies in signal stabilization of discrete systems

This paper describes the definition, development and application of a dual input discrete describing function (D.I.D.D.F.) for the analytical study of non-linear sampled-data systems. An analytical procedure is described which aims at deriving the actual D.I.D.D.F. for an ideal relay. The limit cycles that are ordinarily found in non-linear sampled-data systems can be completely quenched by injecting a high-frequency dither signal at the input to the non-linear element. By applying the D.I.D.D.F. technique, the magnitude of the dither signal required for complete suppression of the limit cycles can be obtained analytically. This technique can be applied to the study of a problem utilizing sinusoidal, triangular or square-wave dither signals. The latter half of the paper presents the results obtained from a comprehensive experimental study of the problem on a model built in our laboratory. © 1970 Taylor & Francis Group, LLC.