Steady-state nonlinearity of open-loop reset systems

TL;DR

This paper introduces a new steady-state representation for open-loop reset systems, modeling reset integrators as a combination of linear systems and piece-wise constant nonlinearities, simplifying their frequency domain analysis.

Contribution

It presents a novel steady-state model for reset integrators and relates general reset system behavior to this nonlinearity, enhancing analysis methods.

Findings

Reset integrator modeled as linear system plus nonlinearity

Nonlinearity appears as a square wave for sinusoidal inputs

Simplifies frequency domain analysis of reset systems

Abstract

In this paper, we introduce a new representation for open-loop reset systems. We show that at steady-state a reset integrator can be modelled as a parallel interconnection of the base-linear system and piece-wise constant nonlinearity. For sinusoidal input signals, this nonlinearity takes a form of a square wave. Subsequently, we show how the behaviour of a general open-loop reset system is related to the nonlinearity of a reset integrator. The proposed approach simplifies the analysis of reset elements in the frequency domain and provides new insights into the behaviour of reset control systems.