# Fractional-Order Linear System Transformation to the System Described by a Classical Equation

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1196)

## Abstract

In the paper, a method of “intigeration" of a linear time-invariant continuous or discrete-time system described by fractional-order differential/difference equations is proposed. The word intigeration means a procedure of connecting in series to the fractional plant a fractional element called further an “intigerator" such that the resulting two block system is described by the classical integer order differential/difference equation. The intigerator synthesis method is given. The stability conditions of the integer system are given. The proposed procedure enables to use classical methods of PID control tuning. It may also be used to tune the variable-, fractional – order PID controller.

## Keywords

Fractional calculus Fractional-order transfer function Linear fractional-order continuous system Linear fractional-order discrete system PID control

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