Abstract
There is a class of systems that can only be stabilized by unstable compensators. However, for most practical systems suitable for use with linear regulators, this is possible with stable ones. To avoid exponentially unstable results in the design of pole placing PI-compensators it is of crucial importance to consider the position of the transmission zeros. This also has a favourable effect on the disturbance rejection. In multi-input multi-output (MIMO) systems, however, not only the zero position but also the zero direction is of importance. In this paper, a design method for multivariable PI-controllers in the time- and in the frequency-domains is presented which helps to avoid the occurrence of exponentially unstable controllers. A modified design method for multivariable PI-controllers, recently published in this journal, facilitates the procedure.
Zusammenfassung
Es gibt Systeme, die sich nur mit Hilfe instabiler Regler stabilisieren lassen. Bei den meisten praktischen Systemen, die sich für den Einsatz von linearen Reglern eignen, ist dies jedoch mit stabilen möglich. Wenn man beobachterbasierte PI-Zustandsregler so entwerfen möchte, dass sie nicht exponentiell instabil sind, muss man die Nullstellen-Lagen der Systeme berücksichtigen. Dies wirkt sich auch günstig auf das Störverhalten aus. In Mehrgrössensystemen sind aber nicht nur die Nullstellen-Lagen, sondern auch die Nullstellen-Richtungen von Bedeutung. In diesem Beitrag wird eine Entwurfsmethode für Mehrgrössen PI-Regler im Zeit- und im Frequenzbereich vorgestellt, welche hilft, das Auftreten von exponentiell instabilen Reglern zu vermeiden. Als günstig erweist sich dabei eine modifizierte Entwurfsmethode für Mehrgrössen PI-Regler, die kürzlich in dieser Zeitschrift erschienen ist.
About the author
Peter Hippe worked as Akademischer Direktor at Lehrstuhl für Regelungstechnik of the Universität Erlangen-Nürnberg till September 2006. Main fields of interest: Control systems with plant input restrictions, design of state controllers and of MIMO compensators in the frequency domain.
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Research ethics: Not applicable.
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Author contributions: The author has accepted responsibility for the entire content of this manuscript and approved its submission.
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Competing interests: The author states no conflict of interest.
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Research funding: None declared.
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Data availability: Not applicable.
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