Abstract
This paper addresses the properties of externally positive systems and summarises existing conditions and design approaches that achieve externally positive closed-loop dynamics. The output variable of such systems is always nonnegative for any nonnegative input which is a very useful property in various control tasks. This paper investigates the problem of rendering control loops externally positive by an appropriate choice of a feedback. It shows that there is currently no general design procedure for that purpose and the question of when such a controller exists has not been clarified yet. It is also shown that there are plants for which there is no controller that leads to an externally positive control loop.
Zusammenfassung
Dieser Beitrag fasst bekannte Eigenschaften und existierende Entwurfsverfahren für extern positive Systeme und Regelkreise zusammen. Die Ausgangsgröße solcher Systeme ist für beliebige nichtnegative Eingangsgrößen stets nichtnegativ, was eine sehr nützliche Eigenschaft für viele Regelungsaufgaben ist. Dieser Beitrag untersucht das Problem, Regelkreise durch die geeignete Wahl einer Rückführung extern positiv zu machen. Er zeigt, dass es dafür derzeit noch kein allgemeines Entwurfsverfahren gibt und die Frage, wann ein solcher Regler existiert, auch noch nicht geklärt ist. Es wird gezeigt, dass es Regelstrecken gibt, für die es keinen Regler gibt, der auf einen extern positiven Regelkreis führt.
About the authors
Alexander Schwab is research assistant and doctoral candidate at the Institute of Automation and Computer Control at Ruhr-Universität Bochum, Germany. His interests include cooperative control of networked mobile systems.
Prof. Dr.-Ing. Jan Lunze is head of the Institute of Automation and Computer Control at Ruhr-Universität Bochum, Germany. His interests include networked control systems, hybrid systems, fault-tolerant control and discrete-event systems.
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