Reset Controller Analysis and Design for Unstable Linear Plants using Scaled Relative Graphs

TL;DR

This paper introduces a graphical design method for reset controllers tailored for unstable linear time-invariant plants, leveraging Scaled Relative Graph analysis to ensure stability and performance bounds.

Contribution

It extends existing reset controller design techniques to unstable systems using a novel graphical approach based on Scaled Relative Graph analysis.

Findings

Design procedure for reset controllers for unstable plants

Provides $L_2$-gain performance bounds

Applicable to practical unstable system stabilization

Abstract

In this technical communique, we develop a graphical design procedure for reset controllers for unstable LTI plants based on recent developments on Scaled Relative Graph analysis, yielding an $L_2$-gain performance bound. The stabilizing controller consists of a second order reset element in parallel with a proportional gain. The proposed method goes beyond existing approaches that are limited to stable systems only, providing a well-applicable approach to design problems in practice where the plant is unstable.