Review Reports - Embedding System Knowledge in Nonlinear Active Disturbance Rejection Control: Insights from a Magnetic Levitation System

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Two new active disturbance rejection control (ADRC) structures for nonlinear systems are introduced: a locally linearized gain-scheduled variant and a fully nonlinear formulation. Both approaches incorporate model knowledge to enhance performance but differ in how nonlinear dynamics are integrated into the control and observer design. The first proposed structure employs a state-dependent local approximation of the nonlinear model to generate dynamic controller and observer gains, aiming to balance robustness and accuracy. In contrast, the second one directly embeds the full nonlinear dynamics into both the control law and extended state observer, tightly coupling performance to model fidelity. The proposed methods were experimentally validated on a magnetic levitation system, known for its strong nonlinearity, and compared with a classical linear ADRC. Furthermore, stability analysis of the methods was conducted using Lyapunov theory. Results show that the linearized structure consistently improves regulation performance over linear LADRC and, in most cases, achieves similar results to nonlinear ADRC with lower computational effort. However, the performance of the nonlinear approach may degrade under modeling inaccuracies and limited observer bandwidth. The study highlights that the way model information is integrated–rather than its level of detail–has a decisive impact on control quality. Finally, practical design guidelines are provided to assist in selecting an appropriate ADRC structure for nonlinear applications where robustness, computational efficiency, and limited model knowledge must be balanced.

1、The contribution of paper should be enhanced, nLGADRC is proposed in literater "P. Lin, Y. Shi and X. -M. Sun, "A Class of Nonlinear Active Disturbance Rejection Loop Filters for Phase-Locked Loop," in IEEE Transactions on Industrial Electronics, vol. 69, no. 2, pp. 1920-1928, Feb. 2022, doi: 10.1109/TIE.2021.3060663." The LGADRC is also proposed in "B. Guo, S. Bacha, M. Alamir, A. Hably and C. Boudinet, "Generalized Integrator-Extended State Observer With Applications to Grid-Connected Converters in the Presence of Disturbances," in IEEE Transactions on Control Systems Technology, vol. 29, no. 2, pp. 744-755, March 2021, doi: 10.1109/TCST.2020.2981571".

2、The legends of Figures 3 and 4 should be consistent with the original text.

3、The more comparsion experiments should be given in paper.

4、The English of the paper should be polished.

5、The conclusion should be enhanced.

Comments on the Quality of English Language

The English should be polished.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Accepted in the present form

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The authors addresses an gap in the field of Active Disturbance Rejection Control (ADRC) by introducing two new structures for nonlinear systems: a fully nonlinear variant (nLGADRC) and a locally linearized formulation (LGADRCc). The paper is well-motivated, theoretically rigorous and supported by experimental validation on a magnetic levitation system (MLS). This is a challenging benchmark due to its strong nonlinearities.

There are several points which needs to be improved:

Section 2 is mathematically dense. Including a block diagram or schematic for each ADRC variant would significantly improve comprehension.
There are some notations, i.e,, which appear late in the text; a summary table of symbols would help.
Evaluation of computational cost are missing will improve the experimental section.
The claim that nLGADRC requires higher computational effort is reasonable but not supported by data/experiments. A brief complexity comparison (e.g., number of operations or execution time) would be valuable.
Table 3 should be placed closer to the experimental results for better flow.
Figures 2 and 3 could include numerical performance indicators, i.e., the algorithm for performance avaluation, etc

There are several points which needs to be improved:

Section 2 is mathematically dense. Including a block diagram or schematic for each ADRC variant would significantly improve comprehension.
There are some notations, i.e,, which appear late in the text; a summary table of symbols would help.
Evaluation of computational cost are missing will improve the experimental section.
The claim that nLGADRC requires higher computational effort is reasonable but not supported by data/experiments. A brief complexity comparison (e.g., number of operations or execution time) would be valuable.
Table 3 should be placed closer to the experimental results for better flow.
Figures 2 and 3 could include numerical performance indicators, i.e., the algorithm for performance avaluation, etc