Weighting function selection in H∞ design

I. Postlethwaite, Mi-Ching Tsai, Da Wei Gu

Research output: Contribution to conferencePaper

18 Citations (Scopus)

Abstract

We examine an H$ mixed sensitivity design problem formulated to achieve good disturbance rejection and tracking properties as well as robust stability. A two degree-of-freedom controller is used, then, as is well known, the tracking objectives can be considered separately. A major concern in H design is the selection of weighting functions to satisfy the design specifications. In this paper we give conditions on the weights which guarantee the optimization problem is well-defined; describe how a constrained optimization can be posed so that improper and unstable weights can be used; describe the effect the weights have on various design objectives; show how an appropriate selection of weights can reduce a 2-block optimization problem (requiring an iterative solution) to a 1-block problem (with a closed-form solution); give an illustrative example. In particular we show how the pole-zero cancellation phenomenon in H design can be exploited or prevented by a suitable choice of weight, and how an optimal controller with a given frequency roll-off can be obtained.

Original languageEnglish
Pages127-132
Number of pages6
Publication statusPublished - 1991 Jan 1
EventProceedings of the 11th Triennial World Congress of the International Federation of Automatic Control - Tallinn, USSR
Duration: 1990 Aug 131990 Aug 17

Other

OtherProceedings of the 11th Triennial World Congress of the International Federation of Automatic Control
CityTallinn, USSR
Period90-08-1390-08-17

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Controllers
Disturbance rejection
Constrained optimization
Poles
Specifications
Robust stability

All Science Journal Classification (ASJC) codes

  • Engineering(all)

Cite this

Postlethwaite, I., Tsai, M-C., & Gu, D. W. (1991). Weighting function selection in H∞ design. 127-132. Paper presented at Proceedings of the 11th Triennial World Congress of the International Federation of Automatic Control, Tallinn, USSR, .
Postlethwaite, I. ; Tsai, Mi-Ching ; Gu, Da Wei. / Weighting function selection in H∞ design. Paper presented at Proceedings of the 11th Triennial World Congress of the International Federation of Automatic Control, Tallinn, USSR, .6 p.
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Postlethwaite, I, Tsai, M-C & Gu, DW 1991, 'Weighting function selection in H∞ design' Paper presented at Proceedings of the 11th Triennial World Congress of the International Federation of Automatic Control, Tallinn, USSR, 90-08-13 - 90-08-17, pp. 127-132.

Weighting function selection in H∞ design. / Postlethwaite, I.; Tsai, Mi-Ching; Gu, Da Wei.

1991. 127-132 Paper presented at Proceedings of the 11th Triennial World Congress of the International Federation of Automatic Control, Tallinn, USSR, .

Research output: Contribution to conferencePaper

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N2 - We examine an H$∞ mixed sensitivity design problem formulated to achieve good disturbance rejection and tracking properties as well as robust stability. A two degree-of-freedom controller is used, then, as is well known, the tracking objectives can be considered separately. A major concern in H∞ design is the selection of weighting functions to satisfy the design specifications. In this paper we give conditions on the weights which guarantee the optimization problem is well-defined; describe how a constrained optimization can be posed so that improper and unstable weights can be used; describe the effect the weights have on various design objectives; show how an appropriate selection of weights can reduce a 2-block optimization problem (requiring an iterative solution) to a 1-block problem (with a closed-form solution); give an illustrative example. In particular we show how the pole-zero cancellation phenomenon in H∞ design can be exploited or prevented by a suitable choice of weight, and how an optimal controller with a given frequency roll-off can be obtained.

AB - We examine an H$∞ mixed sensitivity design problem formulated to achieve good disturbance rejection and tracking properties as well as robust stability. A two degree-of-freedom controller is used, then, as is well known, the tracking objectives can be considered separately. A major concern in H∞ design is the selection of weighting functions to satisfy the design specifications. In this paper we give conditions on the weights which guarantee the optimization problem is well-defined; describe how a constrained optimization can be posed so that improper and unstable weights can be used; describe the effect the weights have on various design objectives; show how an appropriate selection of weights can reduce a 2-block optimization problem (requiring an iterative solution) to a 1-block problem (with a closed-form solution); give an illustrative example. In particular we show how the pole-zero cancellation phenomenon in H∞ design can be exploited or prevented by a suitable choice of weight, and how an optimal controller with a given frequency roll-off can be obtained.

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Postlethwaite I, Tsai M-C, Gu DW. Weighting function selection in H∞ design. 1991. Paper presented at Proceedings of the 11th Triennial World Congress of the International Federation of Automatic Control, Tallinn, USSR, .