Frequency Domain Stability and Convergence Analysis for General Reset Control Systems Architecture

TL;DR

This paper extends frequency domain stability analysis to general reset control systems, addressing industrial implementation challenges and examining the effects of time delay on stability.

Contribution

It develops a generalized $H_\beta$ stability method for reset control systems and analyzes reset elements' stability with time delays.

Findings

Frequency domain stability analysis is feasible for general reset control structures.

Time delay impacts the stability of reset elements.

Industrial application examples demonstrate practical relevance.

Abstract

A key factor that generates significant interest in reset control systems, especially within industrial contexts, is their potential to be designed using a frequency-domain loop-shaping procedure. On the other hand, formulating and assessing stability analysis for these nonlinear elements often depends on access to parametric models and numerically solving linear matrix inequalities. These specific factors could present challenges to the successful implementation of reset control within industrial settings. Moreover, one of the most effective structures for implementing reset elements is to use them in parallel with a linear element. Therefore, this article presents the development of the frequency domain-based $H_\beta$ stability method from a series to a more general structure of reset control systems. Additionally, it investigates the behavior of different reset elements in terms of the feasibility of stability in the presence of time delay. To illustrate the research findings, two examples are provided, including one from an industrial application.