### Abstract

When identifying continuous-time systems in the Laplace domain, it is indispensable to scale the frequency axis to guarantee the numerical stability of the normal equations. Without scaling, identification in the Laplace domain is often impossible even for modest model orders of the transfer function. Although the optimal scaling depends on the system, the model, and the excitation signal, the arithmetic mean of the maximum and minimum angular frequencies in the frequency band of interest is commonly used as a good compromise. In this paper we show (i) that the optimal frequency scaling also strongly depends on the estimation algorithm, and (ii) that the median of the angular frequencies is a better compromise for improving the numerical stability than the arithmetic mean.

Original language | English |
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Title of host publication | Conference Record - IEEE Instrumentation and Measurement Technology Conference |

Editors | S. Demidenko, R. Ottoboni, D. Petri, V. Piuri, D.C.T. Weng |

Pages | 1586-1589 |

Number of pages | 4 |

Volume | 3 |

Publication status | Published - 2004 |

Event | Proceedings of the 21st IEEE Instrumentation and Measurement Technology Conference, IMTC/04 - Como, Italy Duration: May 18 2004 → May 20 2004 |

### Other

Other | Proceedings of the 21st IEEE Instrumentation and Measurement Technology Conference, IMTC/04 |
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Country | Italy |

City | Como |

Period | 5/18/04 → 5/20/04 |

### Fingerprint

### Keywords

- Continuous-time
- Frequency domain identification
- Frequency scaling
- Numerical conditioning

### ASJC Scopus subject areas

- Instrumentation

### Cite this

*Conference Record - IEEE Instrumentation and Measurement Technology Conference*(Vol. 3, pp. 1586-1589)

**On the frequency scaling in continuous-time modeling.** / Pintelon, R.; Kollár, I.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Conference Record - IEEE Instrumentation and Measurement Technology Conference.*vol. 3, pp. 1586-1589, Proceedings of the 21st IEEE Instrumentation and Measurement Technology Conference, IMTC/04, Como, Italy, 5/18/04.

}

TY - GEN

T1 - On the frequency scaling in continuous-time modeling

AU - Pintelon, R.

AU - Kollár, I.

PY - 2004

Y1 - 2004

N2 - When identifying continuous-time systems in the Laplace domain, it is indispensable to scale the frequency axis to guarantee the numerical stability of the normal equations. Without scaling, identification in the Laplace domain is often impossible even for modest model orders of the transfer function. Although the optimal scaling depends on the system, the model, and the excitation signal, the arithmetic mean of the maximum and minimum angular frequencies in the frequency band of interest is commonly used as a good compromise. In this paper we show (i) that the optimal frequency scaling also strongly depends on the estimation algorithm, and (ii) that the median of the angular frequencies is a better compromise for improving the numerical stability than the arithmetic mean.

AB - When identifying continuous-time systems in the Laplace domain, it is indispensable to scale the frequency axis to guarantee the numerical stability of the normal equations. Without scaling, identification in the Laplace domain is often impossible even for modest model orders of the transfer function. Although the optimal scaling depends on the system, the model, and the excitation signal, the arithmetic mean of the maximum and minimum angular frequencies in the frequency band of interest is commonly used as a good compromise. In this paper we show (i) that the optimal frequency scaling also strongly depends on the estimation algorithm, and (ii) that the median of the angular frequencies is a better compromise for improving the numerical stability than the arithmetic mean.

KW - Continuous-time

KW - Frequency domain identification

KW - Frequency scaling

KW - Numerical conditioning

UR - http://www.scopus.com/inward/record.url?scp=4644265668&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4644265668&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:4644265668

VL - 3

SP - 1586

EP - 1589

BT - Conference Record - IEEE Instrumentation and Measurement Technology Conference

A2 - Demidenko, S.

A2 - Ottoboni, R.

A2 - Petri, D.

A2 - Piuri, V.

A2 - Weng, D.C.T.

ER -