Abstract
This paper proposes new numerical algorithms for calculating the time domain responses of fractional order transfer functions (FOTFs). FOTFs are divided into two categories, explicit fractional order transfer functions (EFOTFs) and implicit fractional order transfer functions (IFOTFs). Transforming an EFOTF into an equivalent fractional order differential equation, its time domain response can be obtained by solving the equation by the difference method. IFOTF cannot be transformed into an equivalent equation, so its time domain response cannot be calculated by existing difference methods. A new numerical algorithm is designed for calculating a convolution and its inverse operation, the time domain response of IFOTF can be calculated based on the algorithm. Error analysis shows that the proposed numerical algorithms are of first-order accuracy. Four calculation examples are presented, and the results are consistent with the theoretical analysis.
Highlights
Fractional calculus is a theory about the integration and differentiation of non-integer order
If a fractional order transfer functions (FOTFs) can be transformed into an equivalent fractional order differential equation, its time domain response can be calculated by solving the equation with a numerical algorithm; such a FOTF is called explicit fractional order transfer function (EFOTF) in this paper
If a FOTF cannot be transformed into an equivalent fractional order differential equation, its time domain response cannot be calculated by the difference algorithm; such a FOTF is called implicit fractional order transfer function (IFOTF) in this paper
Summary
Fractional calculus is a theory about the integration and differentiation of non-integer order. If a FOTF can be transformed into an equivalent fractional order differential equation, its time domain response can be calculated by solving the equation with a numerical algorithm; such a FOTF is called explicit fractional order transfer function (EFOTF) in this paper. If a FOTF cannot be transformed into an equivalent fractional order differential equation, its time domain response cannot be calculated by the difference algorithm; such a FOTF is called implicit fractional order transfer function (IFOTF) in this paper. The time domain response can be calculated by the proposed algorithm without considering the specific form of the IFOTF. For the IFOTFs which can only be analyzed by frequency methods before, the proposed algorithm can give their time domain characteristics directly.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
