Full‐order and reduced‐order LESO analysis based on complementary filtering and its impact on LADRC performance

Abstract The linear extended state observer (LESO) is a key component of linear active disturbance rejection control (LADRC). Existing tuning approaches predominantly rely on the bandwidth method and lack a unified filter‐based interpretation and criteria for structural selection. This paper analyzes, from the viewpoint of complementary filtering, the influence of full‐order and reduced‐order LESOs on the performance of LADRC. Based on extended‐state modeling, the dynamics of the observation error are derived, and it is proven that the state estimation and disturbance estimation form a pair of complementary filters in the frequency domain. A correspondence between the LESO parameters and low‐pass filter prototypes is further established. Under a common bandwidth, the frequency response and phase characteristics of full‐order and reduced‐order LESOs are compared, showing that the reduced‐order structure provides better robustness and a more favorable noise‐attenuation trade‐off. Simulation studies and magnetic‐levitation experiments verify that the Bessel‐type reduced‐order LESO can effectively improve the tracking and disturbance‐rejection performance of LADRC, providing an interpretable design guideline for LESO structure selection and parameter tuning.