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The Method of Singular Frequencies for Robust Control Design in an Affine Parameter Space

Bajcinca, N. (2001) The Method of Singular Frequencies for Robust Control Design in an Affine Parameter Space. In: Proc. of MED'01, pp. 100-105. 9th Mediterranean Conference on Control and Automation, June 27-29, 2001. ISBN 953-6037-35-1.

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Abstract

The Method of Singular Frequencies is an elegant tool for design of controllers in an affine parameter space. The essential aspects of the method were already introduced in [4], [1] and [2]. In [4] stable PID controlleres are designed by making use of the Theorem of Hermite-Biehler. It was shown that for a fixed proportional-term kp, convex stable polygons result. In [1] it was shown that actually the singular frequencies reside behind this 'mystery', and the method was extended also for sigma stability. In [2] the linear transformation of parameters was introduced to extend the PID design also for circle-stability. In this paper we generalize this approach for controllers in an affine parameter space. The concept of a singular Gamma region is introduced. Particularly, PID-controllers are studied in a systematic approach, as the first step towards the generalization of the method. A symbolic method for detection of stable polygons is introduced. Subsequently robust control of time delay systems is discussed. Finally the method is generalized for design of the robust affine controllers in a three-parameter-space. Gamma-space and gamma-vectors are introduced to derive the set of all singular Gamma regions for a given structure of the affine controller. Presently the method is more suited for the design of controllers, especially for digital control.

Document Type:Conference or Workshop Item (Paper)
Additional Information: LIDO-Berichtsjahr=2002,
Title:The Method of Singular Frequencies for Robust Control Design in an Affine Parameter Space
Authors:
AuthorsInstitution or Email of Authors
Bajcinca, N.UNSPECIFIED
Date:2001
Journal or Publication Title:Proc. of MED'01
Page Range:pp. 100-105
ISBN:953-6037-35-1
Status:Published
Keywords:Singular frequency, singular Gamma region, parameter-space method, robust control.
Event Title:9th Mediterranean Conference on Control and Automation, June 27-29, 2001
HGF - Research field:Aeronautics, Space and Transport (old)
HGF - Program:Aeronautics
HGF - Program Themes:other
DLR - Research area:Aeronautics
DLR - Program:L ST - Starrflüglertechnologien
DLR - Research theme (Project):UNSPECIFIED
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Robotics and Mechatronics
Deposited By: elib DLR-Beauftragter
Deposited On:16 Sep 2005
Last Modified:14 Jan 2010 18:00

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