Optimization of zero–pole interlacing for indirect discrete approximations of noninteger order operators

To realize the basic units of fractional order controllers, it is necessary to approximate irrational differintegrators. Many methods deal with analog approximation. But not many results exist for discrete approximation. In this case, approximations are most times poor in some frequency range, or the quality of the approximation is good in a narrow frequency interval. This paper proposes an indirect discretization method that takes advantage from the particle swarm optimization (PSO) to approximate fractional order operators. The method employs an heuristic procedure to optimize the interlacing of zero–pole pairs on the real axis. Then, a discretization rule is applied to obtain the discrete approximation. Simulation results show that the frequency response obtained by PSO improves the approximation offered by other efficient and recent indirect discretization techniques.