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Development of an optimized fractional-order controller featuring dead-time and disturbance compensation

  • Prashant Garg EMAIL logo and Brijendra Mishra
Published/Copyright: August 1, 2025
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Abstract

This work highlights a unique control scheme tailored for time-delayed systems under disturbances, blending a fractional filter, dead-time adjustment, and a disturbance compensator. The controller is designed using the Internal Model Control (IMC) approach and optimized through the Snake Optimization (SO) algorithm. This control scheme is applied to practical problems, such as heat exchanger systems and First Order Integrating Plus Delay Time (FOIPDT) process. Integral Absolute Error (IAE) and Integral Square Error (ISE) are key metrics for analyzing closed-loop control performance relative to existing methods. The scheme effectively enhances the closed-loop response by improving IAE values and minimizing control efforts needed to accomplish the preferred output. The Riemann surface principle is utilized for stability analysis. Disturbance rejection and robustness tests show significant improvements in closed-loop response, as illustrated in the numerical simulations.


Corresponding author: Prashant Garg, Electrical Engineering Department, Vikrant University, Gwalior, 474006, India, E-mail:

Acknowledgments

The authors gratefully acknowledges the guidance of Dr. Manish Yadav for his insightful feedback.

  1. Research ethics: Not applicable.

  2. Informed consent: Not applicable.

  3. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest The authors states no conflict of interest.

  6. Research funding: None declared.

  7. Data availability: Not applicable.

References

1. Seborg, D, Thomas, FE, Ducan, AM. Process dynamics and control. New Jersey, USA: John Wiley and Sons; 2004.Search in Google Scholar

2. Raja, GL, Ali, A. Modified series cascade control strategy for integrating processes. In: Indian Control Conference (ICC). Kanpur, India; 2018:252–7 p.10.1109/INDIANCC.2018.8307987Search in Google Scholar

3. Nagarsheth, SH, Sharma, SN. Smith predictor embedded analytical fractional- order design: a Boda’s ideal transfer function approach. IFAC-OnLine 2020;53:3749–54. https://doi.org/10.1016/j.ifacol.2020.12.2062.Search in Google Scholar

4. Raja, GL. Enhanced design of a PI-PD based smith predictor for industrial plants. IFAC-PapersOnLine 2021;54:79–84. https://doi.org/10.1016/j.ifacol.2021.12.014.Search in Google Scholar

5. Ranjan, A, Mehta, U. Fractional filter IMC-TDD controller design for integrating processes. Results in Control and Optim 2022;8:100155. https://doi.org/10.1016/j.rico.2022.100155.Search in Google Scholar

6. Smith, OJM. Closer control of loops with dead time. Chem Eng Prog 1957;53:217–19.Search in Google Scholar

7. Kumar, D, Raja, GL. Unified fractional indirect IMC-based hybrid dual-loop strategy for unstable and integrating type CSTRs. Int J Chem React Eng 2023;21:251–72. https://doi.org/10.1515/ijcre-2022-0120.Search in Google Scholar

8. Kumari, S, Aryan, P, Kumar, D, Raja, GL. Hybrid dual-loop control method for dead-time second-order unstable inverse response plants with a case study on CSTR. Int J Chem React Eng 2023;21:11–21. https://doi.org/10.1515/ijcre-2022-0035.Search in Google Scholar

9. Das, D, Chakraborty, S, Kumar, D, Raja, GL. Dual-loop PID control strategy for ramp tracking and ramp disturbance handling for unstable CSTRs. Chem Prod Process Model 2024;19:967–87. https://doi.org/10.1515/cppm-2024-0081.Search in Google Scholar

10. Kumar, D, Raja, GL, Alkhatib, M. Enhancing LFC with relocated fractional IMC for power systems under communication latency. In: Sustainable Energy and Future Electric Transportation. Hyderabad, India: Institute of Electrical and Electronics Engineers Inc; 2023:1–6 pp.Search in Google Scholar

11. Singha, P, Meenma, R, Chakraborty, S, Raja, GL. Robust pidf-pid cascade control scheme for delay-dominant stable and integrating chemical processes. J Taiwan Inst Chem Eng 2025;173:106165. https://doi.org/10.1016/j.jtice.2025.106165.Search in Google Scholar

12. Kumar, D, Raja, GL, Alkhatib, M, Deep, AK, Muduli, UR. Smith predictor based fractional LFC strategy for storage supported thermal power system amid communication dead time and cyber threats. IEEE Trans Ind Appl 2025;61:4515–29. https://doi.org/10.1109/tia.2025.3549020.Search in Google Scholar

13. Åström, KJ, Murray, RM. Feedback systems: an introduction for scientists & engineers. New Jersery: Princeton University Press; 2008.Search in Google Scholar

14. Bode, HW. Network analysis and feedback amplifier design. New York: Van Nostran; 1945.Search in Google Scholar

15. Yumuk, E, Güzelkaya, M, Eksin, İ. Analytical fractional PID controller design based on Bode’s ideal transfer function plus time delay. ISA Trans 2019;91:196–206. https://doi.org/10.1016/j.isatra.2019.01.034.Search in Google Scholar PubMed

16. Monje, CA, Chen, YQ, Vinagre, BM, Xue, D, Feliu, V. Fractional-order systems and controls: fundamentals and applications. London: Springer-Verlag; 2010.10.1007/978-1-84996-335-0Search in Google Scholar

17. Rajesh, R. Optimal tuning of FOPID controller-based PSO algorithm with a reference model for a single conical tank system. SN Appl Sci 2019;1:758. https://doi.org/10.1007/s42452-019-0754-3.Search in Google Scholar

18. Aryan, P, Raja, GL, Vilanova, R. Experimentally verified optimal bi-loop re-located IMC strategy for unstable and integrating systems with dead time. Int J Syst Sci 2023;54:1531–49. https://doi.org/10.1080/00207721.2023.2180782.Search in Google Scholar

19. Aryan, P, Raja, GL, Vilanova, R, Meneses, M. Repositioned internal model control strategy on time-delayed industrial processes with inverse behavior using equilibrium optimizer. IEEE Access 2023;11:54556–68. https://doi.org/10.1109/access.2023.3281691.Search in Google Scholar

20. Aryan, P, Raja, GL, Vilanova, R. Equilibrium optimiser tuned frequency-shifted internal model control proportional-derivative decoupled dual-loop design for industrial plants followed by experimental validation. Int J Syst Sci 2024;55:2874–96. https://doi.org/10.1080/00207721.2024.2363544.Search in Google Scholar

21. Aryan, P, Raja, GL, Vilanova, R, Meneses, M. Optimal internal model control-based decoupled dual-loop control method for boiler steam drum. In: International Conference on Emerging Technologies and Factory Automation (ETFA). IEEE: Germany; 2023:1–5 pp.10.1109/ETFA54631.2023.10275712Search in Google Scholar

22. Krishna, PS, Rao, PVK. Fractional-order PID controller for blood pressure regulation using genetic algorithm. Biomed Signal Process Control 2024;88:105564. https://doi.org/10.1016/j.bspc.2023.105564.Search in Google Scholar

23. Rezoug, A, Iqbal, J, Nemra, A. Dual FOPID-neural network controller based on fast grey wolf optimizer: application to two-inputs two-outputs helicopter, Syst Sci Control Eng 2025;13, 2449156, https://doi.org/10.1080/21642583.2024.2449156.Search in Google Scholar

24. Hashim, A, F, Hussein, AG. Snake optimizer: a novel meta-heuristic optimization algorithm. Knowl Base Syst 2022;22:108320.10.1016/j.knosys.2022.108320Search in Google Scholar

25. Ni, P, Su, X, Fu, J, Bai, Y. A hybrid snake optimizer with crisscross learning strategy for constrained structural optimization. Eng Optim 2025:1–36. https://doi.org/10.1080/0305215x.2025.2469664.Search in Google Scholar

26. Raja, GL, Ali, A. New PI-PD controller design strategy for industrial unstable and integrating processes with dead-time and inverse response. J Control Automation and Electr Syst 2021;32:266–80.10.1007/s40313-020-00679-5Search in Google Scholar

27. Das, D, Chakraborty, S, Naskar, AK. Controller design on a new 2DOF PID structure for different processes having an integrating nature for both the step and ramp type of signals. Int J Syst Sci 2023;54:1423–50. https://doi.org/10.1080/00207721.2023.2177903.Search in Google Scholar

Received: 2025-04-29
Accepted: 2025-06-29
Published Online: 2025-08-01

© 2025 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 17.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/cppm-2025-0109/pdf
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