Loop Shaping with Scaled Relative Graphs

TL;DR

This paper introduces techniques for shaping the Scaled Relative Graph (SRG) of nonlinear operators to enhance robustness margins, extending classical Nyquist-based methods to nonlinear systems.

Contribution

It presents novel methods for manipulating the SRG of nonlinear operators to improve robustness margins, generalizing Nyquist diagram concepts.

Findings

SRG can be used to visualize nonlinear robustness margins

Shaping the SRG improves system robustness

New techniques extend Nyquist-based analysis to nonlinear operators

Abstract

The Scaled Relative Graph (SRG) is a generalization of the Nyquist diagram that may be plotted for nonlinear operators, and allows nonlinear robustness margins to be defined graphically. This abstract explores techniques for shaping the SRG of an operator in order to maximize these robustness margins.