### 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 language | English |
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Pages | 127-132 |

Number of pages | 6 |

Publication status | Published - 1991 Jan 1 |

Event | Proceedings of the 11th Triennial World Congress of the International Federation of Automatic Control - Tallinn, USSR Duration: 1990 Aug 13 → 1990 Aug 17 |

### Other

Other | Proceedings of the 11th Triennial World Congress of the International Federation of Automatic Control |
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City | Tallinn, USSR |

Period | 90-08-13 → 90-08-17 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

*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, .

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

Research output: Contribution to conference › Paper

TY - CONF

T1 - Weighting function selection in H∞ design

AU - Postlethwaite, I.

AU - Tsai, Mi-Ching

AU - Gu, Da Wei

PY - 1991/1/1

Y1 - 1991/1/1

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.

UR - http://www.scopus.com/inward/record.url?scp=0025749280&partnerID=8YFLogxK

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M3 - Paper

SP - 127

EP - 132

ER -