## Abstract

The design and implementation of control strategies for large, flexible smart structures presents challenging problems. One of these problem areas is the uncertainty of the natural frequencies of the structure. These uncertainties stem from control structure interaction, modelling errors, and parameter variations (such as fuel consumption). They are important because the natural frequencies of flexible structures tend to be lightly damped and closely spaced. Presently, neither the LQG/LTR controller algorithms nor the H_{∞} controller algorithms can account directly for natural frequency uncertainties and both algorithms suffer drastic performance degradation in the face of these uncertainties. In order to overcome this problem, we developed a new algorithm called H_{∞} robust control for natural frequency variations (H_{∞}/NF) that includes the knowledge of the natural frequency uncertainty bounds. In addition, we were successful in implementing this algorithm on a flexible smart structure in our laboratory. This smart structure was a cantilever beam that used NiTiNOL shape memory alloy (SMA) actuators. The performance of H_{∞}NF algorithm was compared with the modified LQG/LTR algorithm using a settling time specification. The H_{∞}/NF controller exhibited dramatically reduced sensitivity to natural frequency uncertainty as compared to the modified LQG/LTR controller. An additional problem area when dealing with smart structures is the limited control effort available from actuators. The standard LQG/LTR control algorithm produced controllers that saturated the NiTiNOL actuators used on the test article. To overcome this saturation problem, we used a modified LQG/LTR design algorithm. Because the initial H_{∞}/NF algorithm did not allow the designer to specify available controller effort, we extended the results by including a control effort cost penalty in the H_{∞}/NF algorithm. This algorithm couples a control effort penalty with the H_{∞}/NF algorithm allowing the designer a trade-off between natural frequency sensitivity and maximum controller effort. We successfully implemented the proposed algorithm on a simple cantilever beam test article.

Original language | English |
---|---|

Pages (from-to) | 156-167 |

Number of pages | 12 |

Journal | Proceedings of SPIE - The International Society for Optical Engineering |

Volume | 2192 |

DOIs | |

State | Published - May 1 1994 |

Event | Smart Structures and Materials 1994: Mathematics and Control in Smart Structures - Orlando, United States Duration: Feb 13 1994 → Feb 18 1994 |

## Fingerprint

Dive into the research topics of 'H_{∞}optimal control of smart structures'. Together they form a unique fingerprint.