Discretization Schemes for Fractional-Order Differentiators and Integrators
نویسندگان
چکیده
For fractional-order differentiator where is a real number, its discretization is a key step in digital implementation. Two discretization methods are presented. The first scheme is a direct recursive discretization of the Tustin operator. The second one is a direct discretization method using the Al-Alaoui operator via continued fraction expansion (CFE). The approximate discretization is minimum phase and stable. Detailed discretization procedures and short MATLAB scripts are given. Examples are included for illustration.
منابع مشابه
Pole-zero Approximations of Digital Fractional-order Integrators and Differentiators Using Signal Modeling Techniques
A novel strategy to the development of digital pole-zero approximations to fractional-order integrators and differentiators is presented here. The scheme is based in the signal modeling techniques applied to deterministic signals, namely the Padé, the Prony and the Shanks methods. It is shown that the illustrated algorithms yield good results both in the time and the frequency domains. Moreover...
متن کاملThe new implicit finite difference scheme for two-sided space-time fractional partial differential equation
Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...
متن کاملLinear Phase Second Order Recursive Digital Integrators and Differentiators
In this paper, design of linear phase second order recursive digital integrators and differentiators is discussed. New second order digital integrators have been designed by using Genetic Algorithm (GA) optimization method. Thereafter, by modifying the transfer function of these integrators appropriately, new digital differentiators have been obtained. The proposed digital integrators and diffe...
متن کاملClass of Recursive Wideband Digital Differentiators and Integrators
New designs of recursive digital differentiators are obtained by optimizing a general fourth-order recursive digital filter over different Nyquist bands. In addition, another design of recursive digital differentiators is also obtained by optimizing the specified pole-zero locations of existing recursive digital differentiator of second-order system. Further, new designs of recursive digital in...
متن کاملDesign of Improved Fractional Order Integrators using Indirect Discretization Method
This paper has adopted rational approximation based on Regular Newton method, for frequency domain fitting of transfer functions of fractional order integrators (FOIs). Further, different discretized mathematical models of one-half, one-third and one-fourth order integrators based on Al-Alaoui operator and New optimized four segment operator have been also developed using these rational approxi...
متن کامل