Frequency domain‐based nonlinearity detection and compensation in Lur'e systems

Abstract

SUMMARYNonlinearities often lead to performance degradation in controlled dynamical systems. This paper provides a new, frequency domain‐based method, for detection and optimal compensation of performance degrading nonlinear effects in Lur'e‐type systems. It is shown that for such systems a sinusoidal response to a sinusoidal input is necessary and sufficient to show the existence of an equivalent linear and time invariant dynamical model that fully captures the systems’ dynamics for a well‐defined set of input signals and initial conditions. This allows to quantify nonlinear effects by using a frequency domain performance measure and yields a novel method to design optimized static compensator structures that minimize performance degrading nonlinear effects. Moverover, the methods discussed in this paper allow to quantify the performance of nonlinear systems on the basis of output measurements only while requiring little knowledge about the nonlinearity and other system dynamics, which yields a useful tool to optimize performance in practice without requiring advanced nonlinear modeling or identification techniques. Finally, the theoretical results are accompanied by examples that illustrate their application in practice.Copyright © 2013 John Wiley & Sons, Ltd.