On the equivalence between Generalized Proportional Integral Observer and Disturbance Observer

This paper presents the equivalence between generalized proportional integral observer (GPIO) and disturbance observer (DOB), which is applicable to reduced-order GPIO (ROGPIO), full-order GPIO (FOGPIO), and extended state observer (ESO). From this equivalence, established in frequency-domain, comprehensive analyses are performed regarding the influence of the system order, the number of extended states, the uncertain control gain, and the tuning method on the robustness and performance of GPIO. In addition, the equivalence allows a detailed comparison between ROGPIO and FOGPIO in the active disturbance rejection control (ADRC) framework. Finally, experimental validation of the main results is presented for the study case of a synchronous buck converter.