A numerical approximation method for fractional order systems with new distributions of zeros and poles.

A multiple-zero-pole (MZP) method is proposed for general SISO fractional order dynamic systems in this paper. Based on amplitude–frequency curve, a new rational approach to fractional differentiator is designed. There are three advantages of MZP method. 1) A more generalized form of approximation system is proposed by design the distribution of zeros and poles in a new way. 2) The same fractional differentiator can be approximated in many different forms. 3) The robustness of the approximation system is enhanced by using integer order integrators to construct fractional differentiator. The feasibility of the method is assessed in the illustrative examples, and the simulations prove the effectiveness.