On dealing with harmonic uncertainties in the class of active disturbance rejection controllers

In this work, the problem of governing systems subjected to harmonic uncertainties is addressed. An active disturbance rejection control (ADRC) framework is proposed here with a key component being a novel resonant extended state observer (RESO). In contrary to the conventional ADRC-based solutions, the introduced one gives the ability to directly estimate and mitigate the influence of harmonic uncertainties. By structuring the whole observer-centred control topology into one degree-of-freedom, compact, feedback error-form (similar to industry-proven PID), the proposed approach can be straightforwardly implemented and commissioned across popular industrial control platforms. Its effectiveness is systematically analysed in terms of tracking accuracy, disturbance rejection and noise sensitivity. The new technique is generalised for the class of nonlinear control-affine systems and expressed with three special forms, each one providing certain advantages to control design. Additionally, an experimental case study is conducted, showing superior performance of the proposed solution against a conventional one. Finally, the stability of the developed approach is rigorously proved using singular perturbation theory.