Normalized Robust FOPID Controller Regulation Based on Small Gain Theorem

Abstract

In this paper, a normalized robust FOPID controller regulation algorithm is proposed. Only one parameter $k$ is necessary to be tuned in the controller regulation process, so the proposed control algorithm is convenient to be applied on both fractional-order systems and integer-order systems. A robustness evaluation function is constructed based on the small gain theorem. Larger robustness evaluation function value will help the system achieve better robustness performance. Another parameter, $\beta$, is also available to serve as a tuning knob when larger robust evaluation function value is needed. Therefore, the controlled systems can be stabilized and can achieve quite satisfactory robust control performance using the proposed algorithm. The corresponding robust analysis results are obtained according to different conditions in the discussion. For a special case of widely used fractional-order systems, the FOPI and FOID controllers are presented based on the same tuning scheme together with their robustness discussion. Some examples are shown to verify the robustness of systems controlled by the proposed algorithm.