Integer order approximation of fractional order systems

This paper deals with the computation of rational approximations of fractional derivatives and/or integrals and time domain analysis of fractional order systems. The objective is to compute the output signals of systems which represented by fractional order transfer functions. Therefore, all rational approximations for fractional order of 0.1, 0.2,..., 0.9 are obtained using continued fraction expansion method (CFE). Simulink block diagrams of a control system with time delayed fractional order transfer function, which controlled by a PI^λ D^μ controller, are constructed using continued fraction expansion method and unit step responses of the system are investigated for different values of λ and μ.