论文信息 - Two direct Tustin discretization methods for fractional-order differentiator/integrator

Two direct Tustin discretization methods for fractional-order differentiator/integrator

This paper deals with fractional calculus and its approximate discretization. Two direct discretization methods useful in control and digital filtering are presented for discretizing the fractional-order differentiator or integrator. Detailed mathematical formulae and tables are given. An illustrative example is presented to show the practically usefulness of the two proposed discretization schemes. Comparative remarks between the two methods are also given.

[1] Dennis S. Bernstein,et al. Naive control of the double integrator , 2001 .

[2] D. Matignon. Stability results for fractional differential equations with applications to control processing , 1996 .

[3] I. Podlubny. Fractional differential equations , 1998 .

[4] Kuldip S. Rattan,et al. Adaptive control of a single-link flexible manipulator , 1990 .

[5] K. Moore,et al. Discretization schemes for fractional-order differentiators and integrators , 2002 .

[6] William H. Press,et al. Numerical recipes in C , 2002 .

[7] A. Oustaloup. La dérivation non entière , 1995 .

[8] I. Petras,et al. The fractional - order controllers: Methods for their synthesis and application , 2000, math/0004064.

[9] S. Manabe. The non-integer integral and its application to control systems. , 1961 .

[10] R. Hilfer. Applications Of Fractional Calculus In Physics , 2000 .

[11] L. Debnath,et al. Integral Transforms and Their Applications, Second Edition , 2006 .

[12] Mukarram Ahmad,et al. Continued fractions , 2019, Quadratic Number Theory.

[13] C. Lubich. Discretized fractional calculus , 1986 .

[14] M. E. Bise,et al. Fractional calculus application in control systems , 1990, IEEE Conference on Aerospace and Electronics.

[15] Jon F. Claerbout,et al. Fundamentals of Geophysical Data Processing: With Applications to Petroleum Prospecting , 1985 .