Parametric approach to computing stabilizing proportional-integral-derivative regions

This paper addresses the problem of determining the stabilizing proportional-integral-derivative controller regions for a general linear system with or without time delay in unity output feedback configuration. When such a problem is solved in the 3D space by a graphical method, it brings in the vis...

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Bibliographic Details
Published in:Transactions of the Institute of Measurement and Control 2019-01, Vol.41 (1), p.165-181
Main Authors: Le, Binh Nguyen, Nie, Zhuo-Yun, Wang, Qing-Guo
Format: Article
Language:English
Subjects:
Graphical methods
Intersections
Output feedback
Parametric statistics
Proportional integral derivative
Root locus
Stability tests
Time lag
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Summary:This paper addresses the problem of determining the stabilizing proportional-integral-derivative controller regions for a general linear system with or without time delay in unity output feedback configuration. When such a problem is solved in the 3D space by a graphical method, it brings in the visualizing difficulties. This paper proposes a new method by projecting the stability boundary in the 3D to the parameterized stability boundary band in the 2D plane of ( K p , K i ) while K d varies in an interval. The boundary band divides the plane to the regions for which simple and effective stability test is developed and the complete stabilizing regions in the 2D plane of ( K p , K i ) are determined for any given interval on K d . The rules are presented to find conditionally stable band portions, within which the corresponding stabilizing sub-interval for K d can be obtained from an analytical formula for the case of no band intersections and from the root locus on K d for the case of the band intersections. Several examples are designed to cover different cases and illustrate the method.
ISSN:0142-3312
1477-0369
DOI:10.1177/0142331218757863