Step response invariant discretization of fractional order integrators/differentiators

Compute a discrete-time finite dimensional (z) transfer function to approximate s^r, r = real number

Description

% Step response invariant discretization of fractional order integrators
%
% srid_fod function is prepared to compute a discrete-time finite dimensional
% (z) transfer function to approximate a continuous-time fractional order
% integrator/differentiator function s^r, where "s" is the Laplace transform variable, and "r" is a
% real number in the range of (-1,1). s^r is called a fractional order
% differentiator if 0 < r < 1 and a fractional order integrator if -1 < r < 0.
%
% The proposed approximation keeps the step response "invariant"
%
% IN:
% r: the fractional order
% Ts: the sampling period
% norder: the finite order of the approximate z-transfer function
% (the orders of denominator and numerator z-polynomial are the same)
% OUT:
% sr: returns the LTI object that approximates the s^r in the sense
% of step response.
% TEST CODE
% dfod=srid_fod(-.5,.01,5);figure;pzmap(dfod)
%
% Reference: YangQuan Chen. "Impulse-invariant and step-invariant
% discretization of fractional order integrators and differentiators".
% August 2008. CSOIS AFC (Applied Fractional Calculus) Seminar.
% http://fractionalcalculus.googlepages.com/

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
Impulse response invariant discretization of fractional order integrators/differentiators

• Required Products: Control System Toolbox; Signal Processing Toolbox
• MATLAB release: MATLAB 7.4 (R2007a)