### Abstract

The target approximation method (TAM) and H_{∞} control theory are used to design robust vibration control of a flexible beam. The beam dynamics are approximated by a few lower order vibration modes of the beam. The remaining modes are treated as a modeling error. In the closed-loop system the uncontrolled and controlled modes interact through the control and observation spillovers, which cause a degraded system performance. The TAM solves the problem in the time domain by designing gains and actuator and sensor locations such that the closed-loop system imitates a target which has no spillovers. The H_{∞} approach tackles the problem in the frequency domain by designing a controller which attenuates a class of disturbing signals, including the disturbance generated by the uncontrolled modes. The TAM always gives a lower order controller than the H_{∞} approach. The H_{∞} approach might not be a good solution for the spillover effect minimization problem when the controller can only have a low-order estimator. The H_{∞} gains are much greater than the TAM gains. This implies that the H_{∞} controller consumes more power than the TAM controller.

Original language | English |
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Pages (from-to) | 2060-2061 |

Number of pages | 2 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 4 |

Publication status | Published - 1 Dec 1990 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Control and Systems Engineering
- Modelling and Simulation
- Control and Optimization

### Cite this

_{∞}approaches: A flexible beam case study.

*Proceedings of the IEEE Conference on Decision and Control*,

*4*, 2060-2061.