Linearization of Time-Independent Nonlinearities by Use of an Extra Signal and Extra Nonlinearity

Abstract

The technique of signal stabilization is that of introducing an extra signal at the input to a nonlinearity to improve or otherwise alter its performance. In this paper this technique is extended to the introduction of both an extra signal and a nonlinear element to improve performance. Here a method is given for linearizing time-independent non-linearities in the sense of time averages by the introduction of a high frequency sawtooth wave and an ideal relay. The technique of pulse width modulation, employed in the communications field, is applied here. The method developed is applicable to feedback systems with a time-independent nonlinearity in the loop. The method is illustrated by applications to nonlinear systems with first and second-order lags. The concept of equivalent gain is used to simplify the mathematical approach so that the technique can be readily employed in engineering analysis and design. Good agreement is obtained between precise theory and approximations.