Padé Approximation Method for Fractional-Order Systems

The first stage of designing a control system is identification, which involves creating a model of the system. For some systems, a description using a fractional-order model may be more beneficial. However, classical control theory methods are most often adapted to integer order models. Therefore, there is a need to approximate fractional order systems. Various methods used for this purpose are as follows: Oustaloup's method, CFE (Continued Fraction Expansion) method, Matsuda's method, M-SBL method, and many others. The article considers the use of the Padé approximation in this case (most often used to approximate time delays in system identification and modelling). According to the principle of operation of the Padé approximation, it has wider approximation possibilities compared to the mentioned methods. It allows the designer to approximate the full form of the transfer function, which includes fractional order components. The approximation does not have to take place only for the mentioned components, as is the case with methods from the known literature. On the basis on the selected criteria, various approximation methods were compared in simulations with the Padé method.