Fractional-order controllers are based on fractional differentiators and integrators, which extend classical integral or derivative actions to improve performance and robustness of feedback loops. The fractional (irrational) operators are usually realized by continued fractions leading to rational approximations. Stable and minimum-phase transfer functions, with interlaced distribution of real zeros and poles, are also requested as suitable approximations. This paper proves that two classes of continued-fractions-based approximations have negative zeros and poles enjoying the interlacing property, for any fractional order v, with |v| < 1, and for any degree, m, of the approximating transfer function.
Conditions for a Class of Rational Approximants of Fractional Differentiators/Integrators to Enjoy the Interlacing Property / Maione, Guido. - ELETTRONICO. - 44:1(2011), pp. 13984-13989. (Intervento presentato al convegno 18th IFAC World Congress 2011, IFAC WC 2011 tenutosi a Milano, Italy nel August 28 - September 2, 2011) [10.3182/20110828-6-IT-1002.01035].
Conditions for a Class of Rational Approximants of Fractional Differentiators/Integrators to Enjoy the Interlacing Property
Guido Maione
2011-01-01
Abstract
Fractional-order controllers are based on fractional differentiators and integrators, which extend classical integral or derivative actions to improve performance and robustness of feedback loops. The fractional (irrational) operators are usually realized by continued fractions leading to rational approximations. Stable and minimum-phase transfer functions, with interlaced distribution of real zeros and poles, are also requested as suitable approximations. This paper proves that two classes of continued-fractions-based approximations have negative zeros and poles enjoying the interlacing property, for any fractional order v, with |v| < 1, and for any degree, m, of the approximating transfer function.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.