Spurious predictions of limit cycles in a non-linear feedback system by the describing function method

Abstract

Abstract It is known that the describing function method can fail to predict limit cycles which do in fact exist. We wish to draw attention to a different mode of failure, where the method predicts limit cycles which do not exist. A surprising feature of the example we give is that the linear part of the system has excellent low-pass properties, unlike the linear parts used in examples of the other failure mode.