Predictive Extended State Observer-Based Active Disturbance Rejection Control for Systems with Time Delay
Open accessAbstract
The latest research on disturbance rejection mechanisms has shown active disturbance rejection control (ADRC) to be an effective controller for uncertainties and nonlinear dynamics embedded in systems to be controlled. The significance of the ADRC controller is its model-free nature, as it requires minimal knowledge of the system model. In addition, it can actively estimate and compensate for the impact of internal and external disturbances present, with the aid of its crucial subsystem called the extended state observer (ESO). However, ADRC controller design becomes more challenging owing to different system disturbances, such as output disturbances, measurement noise, and varying time-delays persistent in the system’s communication channels. Most disturbance rejection techniques aim to reduce internal perturbations and external disturbances (input and output disturbance). However, output disturbance rejection with measurement noise under time-delay control is still a challenging problem. This paper presents a novel predictive ESO-based ADRC controller for time-delay systems by employing predictive methods to compensate for the disturbances originating from time delay. The prediction mechanism of the novel (proposed) controller design is greatly attributed to the extended state predictor observer (ESPO) integrated with the delay-based ADRC inside the proposed controller method. Thus, the proposed controller can predict the unknown system dynamics generated during the delay and compensate for these dynamics via disturbance rejection under time-delay control. This approach uses the optimization mechanism to determine controller parameters, where the genetic algorithm (GA) is employed with the integral of time-weighted absolute error (ITAE) as the fitness function. The proposed controller is validated by controlling second-order systems with time delay. Type 0, Type 1, and Type 2 systems are considered as the controlled plants, with disturbances (unknown dynamics due to delay and external disturbance), along with measurement noise present. The proposed controller method is compared with state-of-the-art methods, such as the modified time-delay-based ADRC method and the ESPO-based controller method. The findings indicate that the method proposed in this paper outperforms its existing competitors by compensating for the dynamics during the time delay and shows robust behaviour, improved disturbance rejection, and a fair extent of resilience to noise.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The selection of the ESPO observer bandwidth ωe is regulated by the Hurwitz stability criterion.
“The Hurwitz stability criterion regulates the selection of 𝜔 𝑒 ; thus, the complete details of the ESPO used in this study are outlined in [30,31].”
From A comparative study on time-delay estimation for time-delay nonlinear system control (2025) · cites this paper as [30]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
From PID to Active Disturbance Rejection Control
Han, J. (2009) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2008.2011621 · Cited by 6,803 · see citing works
Time-delay systems: an overview of some recent advances and open problems
Richard, J.-P. (2003) · Automatica · doi:10.1016/s0005-1098(03)00167-5 · Cited by 3,353 · see citing works
Scaling and bandwidth-parameterization based controller tuning
Gao, Z. (2005) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.1109/acc.2003.1242516 · Cited by 2,453 · see citing works
Bilateral teleoperation: An historical survey
Hokayem, P. F., & Spong, M. W. (2006) · Automatica · doi:10.1016/j.automatica.2006.06.027 · Cited by 1,678 · see citing works
On the centrality of disturbance rejection in automatic control
Gao, Z. (2013) · ISA Transactions · doi:10.1016/j.isatra.2013.09.012 · Cited by 485 · see citing works
Auto Disturbance Rejection Controller and It's Applications
Han, J. Q. (1998) · Kongzhi yu juece · Cited by 341 · see citing works
On Validation of Extended State Observer Through Analysis and Experimentation
Zheng, Q. C., Gao, L. Q., & Gao, Z. (2012) · Journal of Dynamic Systems Measurement and Control · doi:10.1115/1.4005364 · Cited by 254 · see citing works
Modified active disturbance rejection control for time-delay systems
Zhao, S., & Gao, Z. (2013) · ISA Transactions · doi:10.1016/j.isatra.2013.09.013 · Cited by 244 · see citing works
Active disturbance rejection control for uncertain multivariable systems with time-delay
Xia, Y., Shi, P., Liu, G. P., Rees, D., & Han, J. (2006) · IET Control Theory and Applications · doi:10.1049/iet-cta:20050138 · Cited by 200 · see citing works
Active disturbance rejection control for robotic systems: A review
Fareh, R., Khadraoui, S., Abdallah, M. Y., Baziyad, M., & Bettayeb, M. (2021) · Mechatronics · doi:10.1016/j.mechatronics.2021.102671 · Cited by 192 · see citing works
Optimal fast tracking observer bandwidth of the linear extended state observer
Yoo, D., Yau, S. S. ‐., & Gao, Z. (2006) · International Journal of Control · doi:10.1080/00207170600936555 · Cited by 185 · see citing works
Active disturbance rejection control: Old and new results
Feng, H., & Guo, B. (2017) · Annual Reviews in Control · doi:10.1016/j.arcontrol.2017.05.003 · Cited by 178 · see citing works
Predictive active disturbance rejection control for processes with time delay
Zheng, Q., & Gao, Z. (2013) · ISA Transactions · doi:10.1016/j.isatra.2013.09.021 · Cited by 175 · see citing works
Predictor-Based Extended-State-Observer Design for Consensus of MASs With Delays and Disturbances
Wang, C., Zuo, Z., Qi, Z., & Ding, Z. (2018) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2018.2799798 · Cited by 166 · see citing works
Active disturbance rejection control for uncertain time-delay nonlinear systems
Ran, M., Wang, Q., Dong, C., & Xie, L. (2020) · Automatica · doi:10.1016/j.automatica.2019.108692 · Cited by 136 · see citing works
A Systematic Review of Multilateral Teleoperation Systems
Shahbazi, M., Atashzar, S. F., & Patel, R. V. (2018) · IEEE Transactions on Haptics · doi:10.1109/toh.2018.2818134 · Cited by 122 · see citing works
On comparison of modified ADRCs for nonlinear uncertain systems with time delay
Chen, S., Xue, W., Zhong, S., & Huang, Y. (2018) · Science China Information Sciences · doi:10.1007/s11432-017-9403-x · Cited by 122 · see citing works
A Tuning Method of Active Disturbance Rejection Control for a Class of High-Order Processes
He, T., Wu, Z., Li, D., et al. (2019) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2019.2908592 · Cited by 105 · see citing works
On transitioning from PID to ADRC in thermal power plants
Wu, Z., Gao, Z., Li, D., et al. (2021) · Control Theory and Technology · doi:10.1007/s11768-021-00032-4 · Cited by 105 · see citing works
Tuning of Smith predictor based generalized ADRC for time-delayed processes via IMC
Zhang, B., Tan, W., & Li, J. (2019) · ISA Transactions · doi:10.1016/j.isatra.2019.11.002 · Cited by 61 · see citing works
A Review on Haptic Bilateral Teleoperation Systems
Nahri, S. N. F., Du, S., & van Wyk, B. J. (2021) · Journal of Intelligent & Robotic Systems · doi:10.1007/s10846-021-01523-x · Cited by 54 · see citing works
Self-citationActive disturbance rejection control design for high-order integral systems
Wu, Z., Shi, G., Li, D., et al. (2021) · ISA Transactions · doi:10.1016/j.isatra.2021.06.038 · Cited by 50 · see citing works
Application of model free active disturbance rejection controller in nuclear reactor power control
Sun, A., Pu, S., He, Z., et al. (2021) · Progress in Nuclear Energy · doi:10.1016/j.pnucene.2021.103907 · Cited by 43 · see citing works
Zhang, X., Zhang, X., Xue, W., & Xin, B. (2021) · Advanced Control for Applications · doi:10.1002/adc2.89 · Cited by 42 · see citing works
Xue, W., Liu, P., Chen, S., & Huang, Y. (2016) · 2016 16th International Conference on Control, Automation and Systems (ICCAS) · doi:10.1109/iccas.2016.7832475 · Cited by 35 · see citing works
Analysis of active disturbance rejection control for processes with time delay
Tan, W., & Fu, C. (2015) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.1109/acc.2015.7171948 · Cited by 32 · see citing works
Active Disturbance Rejection Control Applied to High-order Systems with Parametric Uncertainties
Chu, Z., Wu, C. Q., & Sepehri, N. (2019) · International Journal of Control Automation and Systems · doi:10.1007/s12555-018-0509-8 · Cited by 32 · see citing works
Linear Active Disturbance Rejection Control for Processes With Time Delays: IMC Interpretation
Fu, C., & Tan, W. (2020) · IEEE Access · doi:10.1109/access.2020.2967806 · Cited by 29 · see citing works
Li, P., Wang, L., Zhu, G., & Zhang, M. (2020) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2020.3039203 · Cited by 25 · see citing works
Cheng, Y., Chen, Z., Sun, M., et al. (2019) · The Canadian Journal of Chemical Engineering · doi:10.1002/cjce.23513 · Cited by 16 · see citing works
Genetic Algorithm for optimization using MATLAB
Saraswat, M., & Sharma, A. K. (2013) · International Journal of Advanced Research in Computer Science · doi:10.26483/ijarcs.v4i3.1561 · Cited by 15 · see citing works
Wang, X., Zhou, Y., Zhao, Z., et al. (2019) · IEEE Access · doi:10.1109/access.2019.2939905 · Cited by 15 · see citing works
Predictive ESO-based control with guaranteed stability for uncertain MIMO constrained systems
Castillo, A., Santos, T. L. M., García, P., et al. (2020) · ISA Transactions · doi:10.1016/j.isatra.2020.12.014 · Cited by 14 · see citing works
Modeling and simulation of Active-Disturbance-Rejection Controller with Simulink
Jiang, P., Hao, J.-Y., Zong, X.-P., et al. (2010) · International Conference on Machine Learning and Cybernetics · doi:10.1109/icmlc.2010.5580604 · Cited by 10 · see citing works
Chen, S., Xue, W., Huang, Y., & Liu, P. (2017) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc.2017.7963743 · Cited by 10 · see citing works
Chen, G., Liu, D., Mu, Y., et al. (2021) · Mathematical Problems in Engineering · doi:10.1155/2021/5560123 · Cited by 10 · see citing works
Rasolomampionona, D., Kłos, M., Cirit, C., et al. (2022) · IEEE International Conference on Environment and Electrical Engineering and IEEE Industrial and Commercial Power Systems Europe (EEEIC / I&CPS Europe) · doi:10.1109/eeeic/icpseurope54979.2022.9854535 · Cited by 9 · see citing works
Haptic System Interface Design and Modelling for Bilateral Teleoperation Systems
Nahri, S. N. F., Du, S., & van Wyk, B. J. (2020) · 2020 International SAUPEC/RobMech/PRASA Conference · doi:10.1109/saupec/robmech/prasa48453.2020.9041010 · Cited by 8 · see citing works
Self-citationPawar, S. N., Chile, R. H., & Patre, B. M. (2021) · Transactions of the Institute of Measurement and Control · doi:10.1177/01423312211002599 · Cited by 8 · see citing works
Active Disturbance Rejection Control Design for a Haptic Machine Interface Platform
Nahri, S. N. F., Du, S., & van Wyk, B. J. (2021) · Advances in Science Technology and Engineering Systems Journal · doi:10.25046/aj060199 · Cited by 4 · see citing works
Self-citationKumar, V. A., Cao, Z., Man, Z., et al. (2021) · Automatika · doi:10.1080/00051144.2021.2011686 · Cited by 4 · see citing works
Wang, F., Liu, P., Xie, M., et al. (2022) · Machines · doi:10.3390/machines10070592 · Cited by 3 · see citing works
Flagged first, then by citations
Research works printed but not linked: 7
- Han, J. A class of extended state observers for uncertain systems. Control Decis. 1995, 10, 85-88.
- Niculescu, S.-I. Delay Effects on Stability: A Robust Control Approach; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2001; Volume 269.
- Wang, L.; Li, Q.; Tong, C.; Yin, Y. Overview of active disturbance rejection control for systems with time-delay. Control Theory Appl. 2013, 30, 1521-1533. [CrossRef] · DOI
- Wang, S.; Sun, G.; Liu, S. Active disturbance rejection sliding mode control for time-delay systems. J. Syst. Simul. 2019, 31, 102.
- YV Wen-bin, Y.D. Modeling and Simulation of an Active Disturbance Rejection Controller Based on Matlab/Simulink. Int. J. Res. Eng. Sci. 2015, 3, 62-69.
- Han, J.-q. Auto disturbances rejection control technique. Front. Sci. 2007, 1, 24-31.
- Martins, F.G. Tuning PID controllers using the ITAE criterion. Int. J. Eng. Educ. 2005, 21, 867.
Cited by
Sorted by citations
Time-Delay Estimation Improves Active Disturbance Rejection Control for Time-Delay Nonlinear Systems
Nahri, S. N. F., Du, S., van Wyk, B. J., & Nyasulu, T. D. (2024) · Machines · doi:10.3390/machines12080552 · Cited by 7 · see citing works
Self-citationA comparative study on time-delay estimation for time-delay nonlinear system control
Nahri, S. N. F., Department of Electrical Engineering, F. O. E. A. T. B. E., Du, S., van Wyk, B. J., & Ajayi, O. K. (2025) · AIMS Electronics and Electrical Engineering · doi:10.3934/electreng.2025015 · Cited by 3 · see citing works
Self-citationFatima Nahri, S. N., Du, S., van Wyk, B. J., Kayode Ajayi, O., Nyasulu, T. D., & Yu, H. (2025) · 2025 33rd Southern African Universities Power Engineering Conference (SAUPEC) · doi:10.1109/saupec65723.2025.10944363 · Cited by 3 · see citing works
Self-citation
- Authors
- Nahri, S. N. F., Du, S., & van Wyk, B. J.
- Affiliations
- Tshwane University of Technology (ZA)
- Department of Electrical Engineering, Faculty of Engineering and the Built Environment, Tshwane University of Technology, Pretoria 0183, South Africa
- Corresponding author
- Du, Shengzhi
- Venue
- Machines
- Publisher
- MDPI AG
- Published
- 2023-01-20
- Volume
- 11
- Issue
- 2
- Pages
- 144
- ISSN
- 2075-1702 (ISSN-L)
- OpenAlex
- W4317617598
- Cited by
- 23
- References
- 42
- Citations by year
- 2026: 5 · 2025: 8 · 2024: 7 · 2023: 3
- FWCI
- 2.47
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Machines (publishedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Funders
- National Research Foundation of South Africa (98398, 138783)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Adaptive Control of Nonlinear Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Advanced Control Systems Design
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Keywords
- active disturbance rejection control, extended state observer, time-delay systems, measurement noise, genetic algorithm tuning, second-order systems, robust control
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
