Stability Margin and Spherical Uncertainty

Weinmann, Alexander

doi:10.1080/01969720600886949

Cited by 5 publications

(2 citation statements)

References 18 publications

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“…Spherical uncertainties were also addressed in combination with the stability margin related to the graph of the resolvent matrix in Weinmann (2006); the stability radius was addressed for a single-input single-output plant and controller in Weinmann (2007a); systems given by transfer functions based on polynomial matrices in Weinmann (2007b).…”

Section: Introductionmentioning

confidence: 99%

The Admissible Spherical Uncertainty for Dynamic Systems in State Space

Weinmann

2008

Cybernetics and Systems

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Among the family of additive-type uncertainties, the uncertainty with the exactly largest admissible Frobenius norm is derived which does not affect stability of a continuous-time linear dynamic system. Special emphasis is put on second-order systems. Selecting the monotonic and oscillatoric stability border, the admissible uncertainty is derived in explicit detail. Closed derivation for the uncertainties is feasible for linear and bilinear ones. The matrix-based results are also given for arbitrary order of the dynamic system. Minimum degree of stability and nice stability are also addressed.

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Section: Introductionmentioning

confidence: 99%

The Admissible Spherical Uncertainty for Dynamic Systems in State Space

Weinmann

2008

Cybernetics and Systems

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“…Whereas parasitic dynamics (with non-unity gain) do affect the loop gain, GM can be considered predominantly a regular perturbation margin. References [4]- [6] have discussed Nyquist robust stability margin, time-delay stability margin and so on, in the fields of robust control and L 1 adaptive control including regular and singular perturbation margins from the view of above classification.…”

Section: Introductionmentioning

confidence: 99%

A singular perturbation approach for time-domain assessment of Phase Margin

Zhu

Yang

Hodel

2010

Proceedings of the 2010 American Control Conference

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Abstract-This paper considers the problem of time-domain assessment of the Phase Margin (PM) of a Single Input Single Output (SISO) Linear Time-Invariant (LTI) system using a singular perturbation approach, where a SISO LTI fast loop system, whose phase lag increases monotonically with frequency, is introduced into the loop as a singular perturbation with a singular perturbation (time-scale separation) parameter ε. First, a bijective relationship between the Singular Perturbation Margin (SPM) ε max and the PM of the nominal (slow) system is established with an approximation error on the order of ε 2 . In proving this result, relationships between the singular perturbation parameter ε, 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 standardized testing system called "PM-gauge," as demonstrated by examples. PM is a widely used stability margin for LTI control system design and certification. Unfortunately, it is not applicable to Linear Time-Varying (LTV) and Nonlinear Time-Varying (NLTV) systems. The approach developed here can be used to establish a theoretical as well as practical metric of stability margin for LTV and NLTV systems using a standardized SPM that is backward compatible with PM.

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Duality-based robust polynomial matrix controller

Weinmann

2007

Elektrotech. Inftech.

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Complex dynamic processes partly contain unknown parameters (in the controller) and known parameters (in the process). The latter are frequently deteriorated by uncertainties. The inverse problem results from the challenge to find the unknown system parameters such that the over-all input output behaviour turns out close to some given performance. As the index of performance the stability margin is selected. In this paper, a computer-assisted gradient approach is presented which improves the stability margin of a multivariable control system in the presence of spherical uncertainties. Following the appropriate gradient and observing a heuristic stopping condition from the viewpoint of design engineering, the method provides a unified approach both for controller design and robustification. Dualitä tsbasierter robuster Polynommatrix-Regler.Komplexe dynamische Prozesse enthalten teilweise unbekannte Parameter (im Reglersystem) und bekannte (im Prozess). Letztere sind noch hä ufig mit Unsicherheiten belastet. Das inverse Problem resultiert aus der Herausforderung, die unbekannten Reglerparameter so zu finden, dass das Eingangs-Ausgangs-Verhalten nahe an der gewü nschten Zielvorstellung liegt. Als Gü teindex wird der Stabilitä tsrand gewä hlt. Vorgestellt wird eine computergestü tzte Gradientenmethode, die den Stabilitä tsrand eines multivariablen Automatisierungssystems in Gegenwart sphä rischer Unsicherheiten verbessert. Verfolgt man mit dem angepassten Gradientenverfahren ein heuristisches Abbruchkriterium unter technologischen Aspekten, so ist die Methode ein vereinheitlichtes Verfahren fü r Reglerentwurf und Robustifizierung.

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Stability Margin and Spherical Uncertainty

Cited by 5 publications

References 18 publications

The Admissible Spherical Uncertainty for Dynamic Systems in State Space

The Admissible Spherical Uncertainty for Dynamic Systems in State Space

A singular perturbation approach for time-domain assessment of Phase Margin

Duality-based robust polynomial matrix controller

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