TY - GEN
T1 - Closed-Form Discretization of Fractional-Order Differential and Integral Operators
AU - El-Khazali, Reyad
AU - Machado, J. A.Tenreiro
N1 - Publisher Copyright:
© 2019, Springer Nature Singapore Pte Ltd.
PY - 2019
Y1 - 2019
N2 - This paper introduces a closed-form discretization of fractional-order differential or integral Laplace operators. The proposed method depends on extracting the necessary phase requirements from the phase diagram. The magnitude frequency response follows directly due to the symmetry of the poles and zeros of the finite z-transfer function. Unlike the continued fraction expansion technique, or the infinite impulse response of second-order IIR-type filters, the proposed technique generalizes the Tustin operator to derive a first-, second-, third-, and fourth-order discrete-time operators (DTO) that are stable and of minimum phase. The proposed method depends only on the order of the Laplace operator. The resulted discrete-time operators enjoy flat-phase response over a wide range of discrete-time frequency spectrum. The closed-form DTO enables one to identify the stability regions of fractional-order discrete-time systems or even to design discrete-time fractional-order controllers. The effectiveness of this work is demonstrated via several numerical simulations.
AB - This paper introduces a closed-form discretization of fractional-order differential or integral Laplace operators. The proposed method depends on extracting the necessary phase requirements from the phase diagram. The magnitude frequency response follows directly due to the symmetry of the poles and zeros of the finite z-transfer function. Unlike the continued fraction expansion technique, or the infinite impulse response of second-order IIR-type filters, the proposed technique generalizes the Tustin operator to derive a first-, second-, third-, and fourth-order discrete-time operators (DTO) that are stable and of minimum phase. The proposed method depends only on the order of the Laplace operator. The resulted discrete-time operators enjoy flat-phase response over a wide range of discrete-time frequency spectrum. The closed-form DTO enables one to identify the stability regions of fractional-order discrete-time systems or even to design discrete-time fractional-order controllers. The effectiveness of this work is demonstrated via several numerical simulations.
KW - Discrete-time integro-differential operators
KW - Discrete-time operator
KW - Fractional calculus
KW - Frequency response
KW - Transfer function
UR - http://www.scopus.com/inward/record.url?scp=85076741283&partnerID=8YFLogxK
U2 - 10.1007/978-981-15-0430-3_1
DO - 10.1007/978-981-15-0430-3_1
M3 - Conference contribution
AN - SCOPUS:85076741283
SN - 9789811504297
T3 - Springer Proceedings in Mathematics and Statistics
SP - 1
EP - 17
BT - Fractional Calculus - ICFDA 2018
A2 - Agarwal, Praveen
A2 - Agarwal, Praveen
A2 - Agarwal, Praveen
A2 - Baleanu, Dumitru
A2 - Chen, YangQuan
A2 - Momani, Shaher
A2 - Machado, José António Tenreiro
PB - Springer
T2 - International Conference on Fractional Differentiation and its Applications, ICFDA 2018
Y2 - 16 July 2018 through 18 July 2018
ER -