Geometric Interpretation of Discrete Fractional Order Controllers Based on Sampling Time Scaling Property and Experimental Verification of Fractional 1/S^α Systems’ Robustness

This article proposes a geometric interpretation of discrete fractional order controllers based on sampling time scaling property. Due to its clear interpretation, satisfactory accuracy and easy programming, the property could be used as a reliable simulation and realization method for fractional order control systems. The experiments of one-inertia speed control with fractional order integral controllers realized by the proposed sampling time property are also carried out to verify the theoretical robustness of fractional 1/s^α systems. The experimental results show the superior robustness performances of fractional 1/s^α systems against saturation non-linearity and inertia variation, which highlights the promising aspects of fractional order control.