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Tuning and implementation variants of discrete-time ADRC

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Abstract

Practical implementations of active disturbance rejection control (ADRC) will almost always take place in discretized form. Since applications may have quite different needs regarding their discrete-time controllers, this article summarizes and extends the available set of ADRC implementations to provide a suitable variant for as many as possible use cases. In doing so, the gap between quasi-continuous and discrete-time controller tuning is closed for applications with low sampling frequencies. The main contribution of this article is the derivation of three different discrete-time implementations of error-based ADRC. It is shown that these are almost one-to-one counterparts of existing output-based implementations, to the point where transfer functions and coefficients can be reused in unaltered form. In this way, error-based implementations become firmly rooted in the established landscape of discrete-time ADRC. Furthermore, it becomes possible to equip error-based variants with windup protection abilities known from output-based ADRC.

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Notes

  1. For output-based ADRC, this is a replication of the example in [18].

References

  1. Han, J. (2009). From PID to active disturbance rejection control. IEEE Transactions on Industrial Electronics, 56(3), 900–906. https://doi.org/10.1109/TIE.2008.2011621

    Article  Google Scholar 

  2. Zheng, Q., & Gao, Z. (2010). On practical applications of active disturbance rejection control. Proceedings of the 29th Chinese Control Conference (pp. 6095–6100).

  3. Zheng, Q., & Gao, Z. (2018). Active disturbance rejection control: Some recent experimental and industrial case studies. Control Theory and Technology, 16(4), 301–313. https://doi.org/10.1007/s11768-018-8142-x

    Article  MathSciNet  MATH  Google Scholar 

  4. Talole, S. E. (2018). Active disturbance rejection control: Applications in aerospace. Control Theory and Technology, 16, 314–323. https://doi.org/10.1007/s11768-018-8114-1

    Article  MathSciNet  MATH  Google Scholar 

  5. Fareh, R., Khadraoui, S., Abdallah, M. Y., Baziyad, M., & Bettayeb, M. (2021). Active disturbance rejection control for robotic systems: A review. Mechatronics, 80, 102671. https://doi.org/10.1016/j.mechatronics.2021.102671

    Article  Google Scholar 

  6. Gao, Z. (2006). Active disturbance rejection control: A paradigm shift in feedback control system design. Proceedings of the 2006 American Control Conference (pp. 2399–2405). https://doi.org/10.1109/ACC.2006.1656579

  7. Gao, Z. (2003). Scaling and bandwidth-parameterization based controller tuning. Proceedings of the 2003 American Control Conference (pp. 4989–4996). https://doi.org/10.1109/ACC.2003.1242516

  8. Miklosovic, R., Radke, A., & Gao, Z. (2006). Discrete implementation and generalization of the extended state observer. Proceedings of the 2006 American Control Conference (pp. 2209–2214). https://doi.org/10.1109/ACC.2006.1656547

  9. Madonski, R., Gao, Z., & Łakomy, K. (2015). Towards a turnkey solution of industrial control under the active disturbance rejection paradigm. 54th Annual Conference of the Society of Instrument and Control Engineers of Japan (SICE) (pp. 616–621). https://doi.org/10.1109/SICE.2015.7285478

  10. Herbst, G. (2016). Practical active disturbance rejection control: Bumpless transfer, rate limitation, and incremental algorithm. IEEE Transactions on Industrial Electronics, 63(3), 1754–1762. https://doi.org/10.1109/TIE.2015.2499168

    Article  Google Scholar 

  11. Madonski, R., & Herman, P. (2015). Survey on methods of increasing the efficiency of extended state disturbance observers. ISA Transactions, 56, 18–27. https://doi.org/10.1016/j.isatra.2014.11.008

    Article  Google Scholar 

  12. Fu, C., & Tan, W. (2016). Tuning of linear ADRC with known plant information. ISA Transactions, 65, 384–393. https://doi.org/10.1016/j.isatra.2016.06.016

    Article  Google Scholar 

  13. Zhou, R., & Tan, W. (2019). Analysis and tuning of general linear active disturbance rejection controllers. IEEE Transactions on Industrial Electronics, 66(7), 5497–5507. https://doi.org/10.1109/TIE.2018.2869349

    Article  Google Scholar 

  14. Tian, G., & Gao, Z. (2007). Frequency response analysis of active disturbance rejection based control system. IEEE International Conference on Control Applications (pp.1595–1599). https://doi.org/10.1109/CCA.2007.4389465

  15. Huang, C., & Gao, Z. (2013). On transfer function representation and frequency response of linear active disturbance rejection control. Proceedings of the 32th Chinese Control Conference (pp. 72–77)

  16. Zheng, Q., & Gao, Z. (2016). Active disturbance rejection control: Between the formulation in time and the understanding in frequency. Control Theory and Technology, 14(3), 250–259. https://doi.org/10.1007/s11768-016-6059-9

    Article  MathSciNet  MATH  Google Scholar 

  17. Herbst, G. (2021). Transfer function analysis and implementation of active disturbance rejection control. Control Theory and Technology, 19, 19–34. https://doi.org/10.1007/s11768-021-00031-5

    Article  MathSciNet  MATH  Google Scholar 

  18. Herbst, G. (2021). A minimum-footprint implementation of discrete-time ADRC. 2021 European Control Conference (ECC) (pp. 107–112). https://doi.org/10.23919/ECC54610.2021.9655120

  19. Michałek, M.M. (2016). Robust trajectory following without availability of the reference time-derivatives in the control scheme with active disturbance rejection. Proceedings of the 2016 American Control Conference (pp. 1536–1541). https://doi.org/10.1109/ACC.2016.7525134

  20. Mandali, A., Dong, L., & Morinec, A. (2020). Robust controller design for automatic voltage regulation. Proceedings of the 2020 American Control Conference (pp. 2617–2622). https://doi.org/10.23919/ACC45564.2020.9147208

  21. Lechekhab, T. E., Manojlović, S. M., Stanković, M. R., Madonski, R., & Simić, S. M. (2021). Robust error-based active disturbance rejection control of a quadrotor. Aircraft Engineering and Aerospace Technology, 93(1), 89–104. https://doi.org/10.1108/AEAT-12-2019-0266

    Article  Google Scholar 

  22. Madonski, R., Łakomy, K., & Yang, J. (2021). Simplifying ADRC design with error-based framework: Case study of a DC-DC buck power converter. Control Theory and Technology, 19, 94–112. https://doi.org/10.1007/s11768-021-00035-1

    Article  MathSciNet  MATH  Google Scholar 

  23. Huang, T., Hu, G., Yan, Y., Zeng, D., & Meng, Z. (2022). Combined feedforward and error-based active disturbance rejection control for diesel particulate filter thermal regeneration. ISA Transactions. https://doi.org/10.1016/j.isatra.2022.09.013

    Article  Google Scholar 

  24. Madonski, R., Herbst, G., & Stankovic, M. (2023). ADRC in output and error form: Connection, equivalence, performance. Control Theory and Technology. https://doi.org/10.1007/s11768-023-00129-y

    Article  Google Scholar 

  25. Madonski, R., Shao, S., Zhang, H., Gao, Z., Yang, J., & Li, S. (2019). General error-based active disturbance rejection control for swift industrial implementations. Control Engineering Practice, 84, 218–229. https://doi.org/10.1016/j.conengprac.2018.11.021

    Article  Google Scholar 

  26. Åström, K. J., & Murray, R. M. (2021). Feedback Systems: An Introduction for Scientists and Engineers. Princeton, NJ, USA: Princeton University Press.

    MATH  Google Scholar 

  27. Herbst, G. (2013). A simulative study on active disturbance rejection control (ADRC) as a control tool for practitioners. Electronics, 2(3), 246–279. https://doi.org/10.3390/electronics2030246

    Article  Google Scholar 

  28. Franklin, G. F., Workman, M. L., & Powell, D. (1997). Digital Control of Dynamic Systems. Boston, MA, USA: Addison-Wesley Longman Publishing.

    MATH  Google Scholar 

  29. Miklosovic, R., & Radke, A. (2007). High performance tracking control for the practitioner. Proceedings of the 2007 American Control Conference, pp. 3009–3014. https://doi.org/10.1109/ACC.2007.4283051

  30. Zhang, Y., Zhang, Y., Wang, J., & Ma, R. (2013). An active disturbance rejection control of induction motor using DSP+FPGA. 25th Chinese Control and Decision Conference (CCDC) (pp. 4047–4052). https://doi.org/10.1109/CCDC.2013.6561659

  31. Stanković, M. R., Manojlović, S. M., Simić, S. M., Mitrović, S. T., & Naumović, M. B. (2016). FPGA system-level based design of multi-axis ADRC controller. Mechatronics, 40, 146–155. https://doi.org/10.1016/j.mechatronics.2016.10.005

    Article  Google Scholar 

  32. Ahi, B., & Nobakhti, A. (2018). Hardware implementation of an ADRC controller on a gimbal mechanism. IEEE Transactions on Control Systems Technology, 26(6), 2268–2275. https://doi.org/10.1109/TCST.2017.2746059

    Article  Google Scholar 

  33. Desai, R., Patre, B.M., & Pawar, S.N. (2018). Active disturbance rejection control with adaptive rate limitation for process control application. 2018 Indian Control Conference (ICC) (pp. 131–136). https://doi.org/10.1109/INDIANCC.2018.8307966

  34. Ramírez-Neria, M., Luviano-Juárez, A., Lozada-Castillo, N., Ochoa-Ortega, G., & Madonski, R. (2020). Discrete-time active disturbance rejection control: A delta operator approach. In A. Bartoszewicz, J. Kabziński, J. Kacprzyk (Eds.), Advanced, Contemporary Control (pp. 1383–1395). Cham, Switzerland: Springer International Publishing. https://doi.org/10.1007/978-3-030-50936-1_115

  35. Peng, Y., Vrančič, D., & Hanus, R. (1996). Anti-windup, bumpless, and conditioned transfer techniques for PID controllers. IEEE Control Systems Magazine, 16(4), 48–57. https://doi.org/10.1109/37.526915

    Article  Google Scholar 

  36. Åström, K.J., & Hägglund, T. (2006). Advanced PID Control. Durham, NC, USA: ISA—The Instrumentation, Systems, and Automation Society.

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Authors and Affiliations

  1. University of Applied Sciences Zwickau, Zwickau, Germany

    Gernot Herbst

  2. Energy and Electricity Research Center, Jinan University, Guangzhou, China

    Rafal Madonski

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  1. Gernot Herbst
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Correspondence to Gernot Herbst.

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The authors have no competing interests to declare that are relevant to the content of this article.

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The work of R. Madonski was supported by the Fundamental Research Funds for the Central Universities (Project no. 21620335).

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Herbst, G., Madonski, R. Tuning and implementation variants of discrete-time ADRC. Control Theory Technol. 21, 72–88 (2023). https://doi.org/10.1007/s11768-023-00127-0

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