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Time-Invariant Control in LQ Optimal Tracking: An Alternative to Output Regulation

Bernhard, Sebastian (2021)
Time-Invariant Control in LQ Optimal Tracking: An Alternative to Output Regulation.
20th IFAC World Congress. Toulouse, France (09.-14.07.2017)
doi: 10.26083/tuprints-00019112
Konferenzveröffentlichung, Zweitveröffentlichung, Verlagsversion

Kurzbeschreibung (Abstract)

We propose a new time-invariant control for linear quadratic tracking problems with references and disturbances generated by linear exo-systems. The control consists of a static feedback and a static pre-filter similar as in output regulation theory (ORT). Instead of forcing the tracking error to converge to zero, a tolerated steady-state error is balanced against the necessary input-energy via a quadratic cost. For the first time in this context, we deduce a time-invariant control from algebraic equations such that necessary optimality conditions are satisfied on infinite horizons. Then, we prove strong optimality for bounded exo-system states. Hence, any other steady-state solution will lead to infinite additional cost. On finite horizons and for arbitrary exo-systems, we prove that our control is an agreeable plan as it approximates the computational expensive, time-varying optimal control of any suitably large horizon. Since our control applies for any initial conditions of the plant and the exo-system, it is well suited for a practical resource-efficient implementation. In this regard, a presented algorithm allows for an easy to carry out control design. Finally, an industrial application indicates the unified treatment of square, under- and over-actuated systems by our approach in contrast to ORT.

Typ des Eintrags: Konferenzveröffentlichung
Erschienen: 2021
Autor(en): Bernhard, Sebastian
Art des Eintrags: Zweitveröffentlichung
Titel: Time-Invariant Control in LQ Optimal Tracking: An Alternative to Output Regulation
Sprache: Englisch
Publikationsjahr: 2021
Ort: Darmstadt
Publikationsdatum der Erstveröffentlichung: 2017
Verlag: Elsevier
Veranstaltungstitel: 20th IFAC World Congress
Veranstaltungsort: Toulouse, France
Veranstaltungsdatum: 09.-14.07.2017
DOI: 10.26083/tuprints-00019112
URL / URN: https://tuprints.ulb.tu-darmstadt.de/19112
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Herkunft: Zweitveröffentlichungsservice
Kurzbeschreibung (Abstract):

We propose a new time-invariant control for linear quadratic tracking problems with references and disturbances generated by linear exo-systems. The control consists of a static feedback and a static pre-filter similar as in output regulation theory (ORT). Instead of forcing the tracking error to converge to zero, a tolerated steady-state error is balanced against the necessary input-energy via a quadratic cost. For the first time in this context, we deduce a time-invariant control from algebraic equations such that necessary optimality conditions are satisfied on infinite horizons. Then, we prove strong optimality for bounded exo-system states. Hence, any other steady-state solution will lead to infinite additional cost. On finite horizons and for arbitrary exo-systems, we prove that our control is an agreeable plan as it approximates the computational expensive, time-varying optimal control of any suitably large horizon. Since our control applies for any initial conditions of the plant and the exo-system, it is well suited for a practical resource-efficient implementation. In this regard, a presented algorithm allows for an easy to carry out control design. Finally, an industrial application indicates the unified treatment of square, under- and over-actuated systems by our approach in contrast to ORT.

Status: Verlagsversion
URN: urn:nbn:de:tuda-tuprints-191122
Zusätzliche Informationen:

Erscheint auch in: IFAC-PapersOnLine, Volume 50, Issue 1, Pages 4912-4919, ISSN: 2405-8963

Sachgruppe der Dewey Dezimalklassifikatin (DDC): 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften und Maschinenbau
Fachbereich(e)/-gebiet(e): 18 Fachbereich Elektrotechnik und Informationstechnik
18 Fachbereich Elektrotechnik und Informationstechnik > Institut für Automatisierungstechnik und Mechatronik
18 Fachbereich Elektrotechnik und Informationstechnik > Institut für Automatisierungstechnik und Mechatronik > Regelungsmethoden und Robotik (ab 01.08.2022 umbenannt in Regelungsmethoden und Intelligente Systeme)
Hinterlegungsdatum: 13 Jul 2021 12:07
Letzte Änderung: 27 Okt 2023 10:08
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