Design of analog variable fractional order differentiator and integrator

• Published in: Nonlinear dynamics Vol. 69; no. 4; pp. 1577 - 1588
• Main Authors: Charef, Abdelfatah, Idiou, Daoud
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.09.2012; Springer Nature B.V
• Subjects: Approximation; Automotive Engineering; Classical Mechanics; Control; Differentiators; Digital; Dynamical Systems; Engineering; Frequencies; Frequency bands; Integrators; Interpolation; Mathematical analysis; Mechanical Engineering; Original Paper; Poles; Polynomials; Rational functions; Vibration; Fractional order differentiator; Interpolation; Fractional order integrator; Farrow structure; Rational function approximation
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-012-0370-x

This paper deals with the design of analog variable fractional order differentiator s m and integrator s − m , for 0< m <1, for a given frequency band, a subject that has not been yet investigated. The main feature of this analog variable fractional order integrator or differentiator is that its frequency characteristics can be changed without redesigning a new one. First, analog rational function approximation of the fractional order differentiator s m and integrator s − m are derived with the new idea to keep all its poles to be independent of the fractional orders  m . Next, we have used the polynomial interpolation method to design the variable fractional order analog integrator and differentiator that can be implemented by an analog structure like the digital Farrow structure. Finally, some examples are presented to illustrate the efficiency and the effectiveness of the proposed design method.