Fractional-Order Linear Systems Modeling in Time and Frequency Domains

Non-integer order calculus is a very helpful tool, which is used in modeling and control applications. Many real processes display fractional order dynamics and their behavior is described by fractional-order differential equation. In this paper we quantify fitting the Oustaloup filter to the approximated transfer functions for given non-integer systems. The goal of this paper is to verify the accuracy of the Outsaloup filter to the fractional inertial system parameter approximation in a specified narrow frequency range and order. The pertinence of the compared models, in both time and frequency domains, is verified. Finally, the approximated model can be used to design the fractional order differentiation operator in an integer order state-space form. The presented methodology could be utilised for a general class of systems and is illustrated using numerical examples.