Modeling and identification of a non integer order system

A fractional integrator operator is defined in this paper : its originality is that its non integer order action is limited to a frequential band. This operator is approximated by a conventional integrator associated to a fractional phase lead filter. The state-space representation of this operator allows modeling of more complex non integer order differential equations. The fractional order has been converted in a few design parameters that can be easily estimated with the help of an OE identification technique associated to a special formulation of sensitivity functions. The applicability of this new modeling and identification methodology is illustrated by a numerical simulation.