Singular perturbation margin and generalised gain margin for linear time-invariant systems

In this paper, we propose a singular perturbation margin (SPM) and a generalised gain margin (GGM) as stability metrics for single input-single output (SISO) linear time-invariant (LTI) systems from the view of singular perturbations and regular perturbations, which have bijective correspondences wi...

Full description

Saved in:
Bibliographic Details
Published in:International journal of control 2015-01, Vol.88 (1), p.11-29
Main Authors: Yang, Xiaojing, Zhu, J. Jim, Hodel, A. Scottedward
Format: Article
Language:English
Subjects:
Assessments
Dynamical systems
Gain
Mathematical analysis
Mathematical models
Perturbation methods
regular perturbation
Singular perturbation
Stability
stability margin
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we propose a singular perturbation margin (SPM) and a generalised gain margin (GGM) as stability metrics for single input-single output (SISO) linear time-invariant (LTI) systems from the view of singular perturbations and regular perturbations, which have bijective correspondences with the classical phase margin (PM) and the gain margin (GM), respectively. Both of the numerical and analytical time-domain SPM and GGM assessment methods are provided, and relationships between the singular perturbation parameter, PM of the perturbed system, PM and SPM of the nominal system, and the (monotonically increasing) phase of the fast system are also revealed. These results make it possible to assess the PM of the nominal system in the time domain for SISO LTI systems using the SPM with a standardised testing system called 'PM-gauge,' as demonstrated by examples. The concepts of SPM and GGM can be used as metrics of stability margins for linear time-varying systems and nonlinear systems.
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2014.936511