An Improved Active Disturbance Rejection Control for Bode's Ideal Transfer Function

This article presents an improved fractional-order active disturbance rejection control (iFO-ADRC) scheme to approximately render the open-loop transfer function of a high-order uncertain system to a weighed Bode's ideal transfer function (wBITF). The proposed feedback controller in this scheme is called iFO-ADRC-wBITF and abbreviated to iFO-BITF, which inherits the advantages of ADRC and wBITF and improves a system's robustness to open-loop gain variation and system uncertainty. As a core component of iFO-ADRC, an improved fractional-order extended state observer (iFO-ESO) can reduce the number of system states to be estimated and hence improve the performance of a closed-loop system. Frequency-domain analysis shows that iFO-ESO has better estimation performance than the typical FO-ESO in the literature. Compared with the conventional integer-order ADRC and the fractional-order controller for achieving BITF, the proposed iFO-BITF has a simpler form, better transient performance, and more robustness against parameter variation, as demonstrated in time-domain simulation. The proposed iFO-BITF is applied to a permanent magnet synchronous motor servo control system to demonstrate its capability in a real-world application.