Fig. 6. Gang-of-six comparison (frequency domain) with or without half-gain tuning for controller and/or observer within ADRC. As predicted in Section 5.1, the half-gain observer (“L/2”) case provides enhanced high-frequency damping in $G_{un}(j\omega)$ almost without any side-effects on other performance criteria. The “K/2” cases, on the other hand, will—while still yielding some additional high-frequency damping in $G_{un}$—involve slower reaction to reference signal changes and more overshoot induced by disturbances at the plant input.
Fig. 7. To ease and support the interpretability of Figure 6, a time-domain perspective is given in this figure with the step responses of the gang-of-six transfer functions with or without half-gain tuning.