Identifying digital and fractional transfer functions from a frequency response

• Published in: International journal of control Vol. 84; no. 3; pp. 445 - 457
• Main Authors: VALERIO, Duarte, SA DA COSTA, Jose
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 01.03.2011; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Applied sciences; Computer science; control theory; systems; Control theory. Systems; digital transfer function; Exact sciences and technology; fractional calculus; frequency response; Modelling and identification; system identification; fractional calculus; digital transfer function; Frequency response; System identification; Transfer function; Pole zero method; Poles and zeros; Fractional derivative
• ISSN: 0020-7179; 1366-5820
• DOI: 10.1080/00207179.2011.560397

In this article, an existing exact algorithm for identifying a continuous transfer function from frequency data, giving major importance to phase data, is further developed. The new version allows identifying a digital transfer function, or a continuous fractional order transfer function with a fixed order of commensurability (i.e. a ratio of two polynomials in s α , α ∉ ℤ). This is straightforward if the desired transfer function is to have only zeros or only poles; if a transfer function with both zeros and poles is sought, however, a numerical method must be resorted to.