Continuation for stability domain determination: a case study

TL;DR

This paper introduces a continuation-based method to determine the stability domain of controlled dynamical systems, demonstrated on a 3-cable robot with linear controllers, offering an alternative to robustness analysis.

Contribution

It proposes a novel continuation approach for stability domain determination, implemented in MatCont, applied to a complex robotic system with linear controllers.

Findings

Successful application to a 3-cable robot system

Effective border detection of stability domain

Complementary to robustness analysis methods

Abstract

Determining a stability domain, i.e. a set of equilibria for which a dynamical system remains stable, is a core problem in control. When dealing with controlled systems, the problem is generally transformed into a robustness analysis problem: considering a set of uncertain parameters (generally chosen as polytopic), one seeks for guaranties that the system remains stable for this given set or some dilatation or contraction of this set. Thanks to the development of formal methods based on continuation, another approach is proposed in this paper to determine the border of the stability domain. The proposed developments were made with MatCont, a package to be used with Matlab, and the considered system is a 3-cable robot with linear PD and PID controllers.