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## Details

Material Type: | Government publication, National government publication |
---|---|

Document Type: | Book |

All Authors / Contributors: |
Jerome I Elkind; David Marvin Green; United States. Air Force. Systems Command. Aeronautical Systems Division.; Bolt, Beranek, and Newman.; Wright-Patterson Air Force Base (Ohio) |

OCLC Number: | 436923031 |

Notes: | "December 1961." "Flight Control Laboratory, Contract Nr AF 33(616)-7397, Project Nr. 8219, Task Nr 82163." -- Title page AD0271948 (from http://www.dtic.mil). |

Description: | viii, 72 pages : illustrations ; 28 cm |

Series Title: | ASD technical report, 61-225. |

Responsibility: | Jerome I. Elkind, David M. Green. |

### Abstract:

A model matching or mimicking technique for measurement of linear time-varying dynamic systems and nonlinear dynamic systems is presented. The model used is composed of filters whose impulse responses are orthonormal. The filters were connected in parallel and their outputs weighted and added together. The weights are determined so that the mean-square difference between the output of the model and the output of the system is minimum. A model composed of a few filters can approximate with small error a large variety of systems, provided the impulse responses of the filters used in the model resemble the impulse response of the system. The use of orthogonalized exponential filters for measuring systems whose poles are real is discussed. The model weights are shown to be coefficients of regression of the system output on the filter outputs. When the residual error, the part of the system output that cannot be accounted for by the model, has a normal disribution, the weights also have a normal distribution. Relations for estimating the length of samples of the system input and output signals required to determine the weights with given confidence limits are derived. Time-varying systems are measured by determining successively the model weights from short samples of the input and output signals. Nonlinear systems are measured by combining the modeling technique with a piecewise linearization technique in which system input space is partitioned into regions and model weigts are determined for each region.

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