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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. (Publisher's Version)
Darmstadt, Elsevier, 20th IFAC World Congress, Toulouse, France, 09.-14.07.2017, DOI: 10.26083/tuprints-00019112,
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Item Type: Conference or Workshop Item
Origin: Secondary publication service
Status: Publisher's Version
Title: Time-Invariant Control in LQ Optimal Tracking: An Alternative to Output Regulation
Language: English

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.

Place of Publication: Darmstadt
Publisher: Elsevier
Classification DDC: 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften
Divisions: 18 Department of Electrical Engineering and Information Technology > Institut für Automatisierungstechnik und Mechatronik > Control Methods and Robotics
Event Title: 20th IFAC World Congress
Event Location: Toulouse, France
Event Dates: 09.-14.07.2017
Date Deposited: 13 Jul 2021 12:07
Last Modified: 12 Sep 2021 20:16
DOI: 10.26083/tuprints-00019112
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-191122
Additional Information:

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

URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/19112
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