Approximation techniques

This chapter will focus on practical realization or equivalent circuit implementation of the fractional-order systems and controllers in a finite-dimensional integer-order system. Hence, for achieving the approximated integer-order transfer function of the fractional-order system or controller, a novel curve fitting based approximation techniques for fractional-order differentiator or integrator are developed. The advantage of the techniques is that they are simple, easy to implement and can fit around the desired frequency range. The chapter also provides the MATLAB commands for implementing the developed algorithms. The simulation results in the frequency domain show that the proposed approach produced better parameter approximation for the desired frequency range as compared to Oustaloup, refined Oustaloup, and Matsuda techniques. Furthermore, time domain and stability analysis also validate the frequency domain results. © Springer Nature Switzerland AG 2020.