| Summary: | As the higher-order or generalized extended state observer (ESO), generalized proportional-integral (GPI) observer (GPIO) have been proposed to enhance the active disturbance rejection (ADR) control (ADRC) systems disturbance rejection ability. However, different ADR controllers can be deduced based on the same order GPIO, resulting in different dynamic performances. In this paper, ten different ADR controllers based on the fourth order GPIO are present. In order to reveal the relationship between these ADR controllers and the conventional ADR controllers based on the third order ESO, six different third-order-ESO-based ADR controllers are present and compared with the fourth-order-ESO-based ADR controllers. To ease the comparison between different ADRC systems, a common expression is built for different ADR controllers. A novel frequency-domain analysis method is also introduced to reveal how the observer and feedback control law affects the closed-loop control systems dynamic performance. The effectiveness of the proposed method is verified on the test bench based on dSPACE DS1103.
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