Frequency‐Domain Analysis of External Signal Propagation Through Sliding Mode Control Systems With Dynamic Actuators

ABSTRACT The importance of frequency domain methods in analysis and design of sliding mode (SM) control systems is mostly associated with chattering, where the advantages of these methods over state‐space and Lyapunov's methods are quite obvious. Among the frequency domain methods that are prominent in the respect of the noted analysis are the describing function (DF) method, along with the harmonic balance (HB) principle, and the locus of a perturbed relay system (LPRS) method. However, both the DF and the LPRS methods are rarely used for the analysis of control inputs and disturbance propagation. The respective functionality of these methods remains underutilized, and the problem of input signal or disturbance propagation remains just superficially addressed. The current research aims to address the propagation problem through the development of bias function analysis. A new introduction to the ideas of the LPRS method and the bias function analysis is also presented.