Approximating the Fractional-Order Element for the Robust Control Framework

Fractional order calculus in modelling and control applications has been increasingly popular in every scientific field due to its versatility and superiority in various instances. However, the main issue of fractional order elements is related to their implementation. Usually, integer order elements are used through different approximation methods to implement such elements. None of the existing methods discuss the introduction of a fractional element in a fixed-structure robust synthesis method. MATLAB realp objects do not allow the use of other than classical arithmetic operations, while existing approximations use exponential terms. To overcome this shortcoming, this work proposes and offers an algorithm for a method of approximation useful in robust controller synthesis.