A general H∞/LTR design problem

Hans Henrik Niemann; Jakob Stoustrup

A general H∞/LTR design problem

Hans Henrik Niemann^*, Jakob Stoustrup

^*Corresponding author for this work

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › peer-review

4 Citations (Scopus)

Abstract

An alternative approach to the loop transfer recovery (LTR) design problem based on H_∞ optimization is considered. An H_∞/LTR design problem is formulated as an H_∞ optimization of the weighted recovery matrix (RM). This general recovery formulation includes the indirect H_∞/LTR design problem (equivalent to LQG/LTR), the H_∞/LTR sensitivity, and the input-output recovery problem as special cases. The weight matrix is also used for obtaining robustness in the final design. The control problem corresponding to the general H_∞/LTR design problem is formulated as a standard H_∞ state-space problem. The state-space solution to the H_∞ problem is derived and the corresponding H_∞/LTR controller is implemented as a Luenberger observer of order at most n + n_w (n_w is the order of the weight on the RM). The proposed H_∞/LTR method handles both minimum phase and nonminimum phase systems in the same framework.

Original language	English
Title of host publication	Proceedings of the IEEE Conference on Decision and Control
Number of pages	7
Volume	2
Publisher	IEEE
Publication date	1 Dec 1991
Pages	1920-1926
ISBN (Print)	0780304500
Publication status	Published - 1 Dec 1991
Event	Proceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3) - Brighton, Engl Duration: 11 Dec 1991 → 13 Dec 1991

Conference

Conference	Proceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3)
City	Brighton, Engl
Period	11/12/1991 → 13/12/1991
Sponsor	IEEE Control Systems Soc

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title = "A general H∞/LTR design problem",

abstract = "An alternative approach to the loop transfer recovery (LTR) design problem based on H∞ optimization is considered. An H∞/LTR design problem is formulated as an H∞ optimization of the weighted recovery matrix (RM). This general recovery formulation includes the indirect H∞/LTR design problem (equivalent to LQG/LTR), the H∞/LTR sensitivity, and the input-output recovery problem as special cases. The weight matrix is also used for obtaining robustness in the final design. The control problem corresponding to the general H∞/LTR design problem is formulated as a standard H∞ state-space problem. The state-space solution to the H∞ problem is derived and the corresponding H∞/LTR controller is implemented as a Luenberger observer of order at most n + nw (nw is the order of the weight on the RM). The proposed H∞/LTR method handles both minimum phase and nonminimum phase systems in the same framework.",

author = "Niemann, {Hans Henrik} and Jakob Stoustrup",

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note = "Proceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3) ; Conference date: 11-12-1991 Through 13-12-1991",

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T1 - A general H∞/LTR design problem

AU - Niemann, Hans Henrik

AU - Stoustrup, Jakob

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N2 - An alternative approach to the loop transfer recovery (LTR) design problem based on H∞ optimization is considered. An H∞/LTR design problem is formulated as an H∞ optimization of the weighted recovery matrix (RM). This general recovery formulation includes the indirect H∞/LTR design problem (equivalent to LQG/LTR), the H∞/LTR sensitivity, and the input-output recovery problem as special cases. The weight matrix is also used for obtaining robustness in the final design. The control problem corresponding to the general H∞/LTR design problem is formulated as a standard H∞ state-space problem. The state-space solution to the H∞ problem is derived and the corresponding H∞/LTR controller is implemented as a Luenberger observer of order at most n + nw (nw is the order of the weight on the RM). The proposed H∞/LTR method handles both minimum phase and nonminimum phase systems in the same framework.

AB - An alternative approach to the loop transfer recovery (LTR) design problem based on H∞ optimization is considered. An H∞/LTR design problem is formulated as an H∞ optimization of the weighted recovery matrix (RM). This general recovery formulation includes the indirect H∞/LTR design problem (equivalent to LQG/LTR), the H∞/LTR sensitivity, and the input-output recovery problem as special cases. The weight matrix is also used for obtaining robustness in the final design. The control problem corresponding to the general H∞/LTR design problem is formulated as a standard H∞ state-space problem. The state-space solution to the H∞ problem is derived and the corresponding H∞/LTR controller is implemented as a Luenberger observer of order at most n + nw (nw is the order of the weight on the RM). The proposed H∞/LTR method handles both minimum phase and nonminimum phase systems in the same framework.

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M3 - Article in proceeding

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T2 - Proceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3)

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A general H∞/LTR design problem

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