Frequency Domain Stability Method for Reset Systems

TL;DR

This paper introduces a novel frequency-domain stability assessment method for reset control systems, overcoming limitations of existing techniques and enabling practical stability evaluation directly from frequency response measurements.

Contribution

It develops a new frequency-domain approach for stability analysis of first and second order reset elements, addressing complex assessment issues in high-dimensional plants.

Findings

The method effectively assesses stability using frequency response data.

It simplifies stability analysis for reset controllers in practical applications.

The approach is validated through practical examples demonstrating its effectiveness.

Abstract

Today, linear PID controllers cannot satisfy requirements of high-precision industry due to the development of technology. According to the literature, reset controllers can overcome this important barrier. However, similar to other non-linear controllers, stability analysis for these controllers is complex and needs parametric models of the systems. Consequently, the applicability of these controllers may diminish in industry. The well-known Hb method is one of the solutions of this significant problem. Nevertheless, assessing the Hb condition in the frequency-domain is complex, particularly for high dimensional plants. Furthermore, it cannot assess UBIBS stability of reset control systems in the case of reseting to non-zero values. In this paper, the aforementioned problems have been solved for the first and second order reset elements and a frequency-domain approach for assessing stability of reset control systems is developed. Finally, some practical examples are presented to demonstrate the effectiveness of the proposed approach to use the frequency response measurement directly to assess the stability.