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Analytically designed dual-loop fractional-order IMC for integrating plants with inverse behavior

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Abstract

A novel double-loop control architecture with a fractional-order IMC (internal model control) in the outer loop is suggested for integrating plants with dead time and inverse response behavior. The inner loop controller is tuned using the maximum sensitivity concept to stabilize the plant, and it also enhances the disturbance response. The IMC controller is analytically designed to achieve improved closed-loop performance and robustness. The proposed tuning rules involve three design parameters \(\beta ,\alpha \) and \(\lambda \), whose method of selection is explained through extensive simulations and stability analysis. The suitability of the proposed control is verified for a wide class of processes, including higher-order and double-integrating processes with non-minimum phase characteristics. The suggested control has the capability of producing a fast and smooth set-point tracking response and rejecting the load disturbance effectively even in the presence of measurement noise. Random perturbations are also introduced in the process parameters to further investigate the system’s robustness.

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References

  1. Luyben WL (2003) Identification and tuning of integrating processes with deadtime and inverse response. Ind Eng Chem Res 42(13):3030–3035

    Article  Google Scholar 

  2. Seborg DE, Edgar TF, Mellichamp DA, Doyle FJ III (2016) Process dynamics and control. Wiley, Hoboken

    Google Scholar 

  3. Begum KG, Rao AS, Radhakrishnan T (2017) Enhanced IMC based PID controller design for non-minimum phase (NMP) integrating processes with time delays. ISA Trans 68:223–234

    Article  Google Scholar 

  4. Chidambaram M, Sree RP (2003) A simple method of tuning PID controllers for integrator/dead-time processes. Comput Chem Eng 27(2):211–215

    Article  Google Scholar 

  5. Kaya I, Tan N, Atherton DP (2006) A refinement procedure for PID controllers. Electr Eng 88:215–221

    Article  Google Scholar 

  6. Skogestad S (2003) Simple analytic rules for model reduction and PID controller tuning. J Process Control 13(4):291–309. https://doi.org/10.1016/S0959-1524(02)00062-8

    Article  MathSciNet  Google Scholar 

  7. Chanti Babu D, Santosh Kumar DB, Padma Sree R (2016) Tuning of PID controllers for unstable systems using direct synthesis method. Indian Chem Eng 59(3):215–241. https://doi.org/10.1080/00194506.2016.1255570

    Article  Google Scholar 

  8. Kumar S, Ajmeri M (2023) Enhanced design of PI controller with lead-lag filter for unstable and integrating plus time delay processes. Chem Prod Process Model 18(5):793–809. https://doi.org/10.1515/cppm-2023-0008

    Article  Google Scholar 

  9. Rao AS, Rao V, Chidambaram M (2009) Direct synthesis-based controller design for integrating processes with time delay. J Frank Inst 346(1):38–56

    Article  MathSciNet  Google Scholar 

  10. Vanavil B, Krishna Chaitanya K, Seshagiri Rao A (2013) Improved PID controller design for unstable time delay processes based on direct synthesis method and maximum sensitivity. Int J Syst Sci 46(8):1349–1366. https://doi.org/10.1080/00207721.2013.822124

    Article  MathSciNet  Google Scholar 

  11. Panda RC (2009) Synthesis of PID controller for unstable and integrating processes. Chem Eng Sci 64(12):2807–2816

    Article  Google Scholar 

  12. Gu D, Ou L, Wang P, Zhang W (2006) Relay feedback autotuning method for integrating processes with inverse response and time delay. Ind Eng Chem Res 45(9):3119–3132

    Article  Google Scholar 

  13. Pai N-S, Chang S-C, Huang C-T (2010) Tuning PI/PID controllers for integrating processes with deadtime and inverse response by simple calculations. J Process Control 20(6):726–733

    Article  Google Scholar 

  14. Ajmeri M, Ali A (2015) Two degree of freedom control scheme for unstable processes with small time delay. ISA Trans 56:308–326

    Article  Google Scholar 

  15. Chandran K et al (2020) Modified cascade controller design for unstable processes with large dead time. IEEE Access 8:157022–157036

    Article  Google Scholar 

  16. Jeng J-C, Lin S-W (2012) Robust proportional-integral-derivative controller design for stable/integrating processes with inverse response and time delay. Ind Eng Chem Res 51(6):2652–2665

    Article  Google Scholar 

  17. Uma S, Chidambaram M, Rao AS (2010) Set point weighted modified Smith predictor with PID filter controllers for non-minimum-phase (NMP) integrating processes. Chem Eng Res Des 88(5–6):592–601

    Article  Google Scholar 

  18. Nema S, Padhy PK (2015) Identification and cuckoo PI-PD controller design for stable and unstable processes. Trans Inst Meas Control 37(6):708–720. https://doi.org/10.1177/0142331214546351

    Article  Google Scholar 

  19. Park JH, Sung SW, Lee I-B (1998) An enhanced PID control strategy for unstable processes. Automatica 34(6):751–756

    Article  Google Scholar 

  20. Vijayan V, Panda RC (2012) Design of PID controllers in double feedback loops for SISO systems with set-point filters. ISA Trans 51(4):514–521

    Article  Google Scholar 

  21. Kaya I (2020) Integral-proportional derivative tuning for optimal closed loop responses to control integrating processes with inverse response. Trans Inst Meas Control 42(16):3123–3134

    Article  Google Scholar 

  22. Lloyds Raja G, Ali A (2021) New PI-PD controller design strategy for industrial unstable and integrating processes with dead time and inverse response. J Control Autom Electr Syst 32(2):266–280. https://doi.org/10.1007/s40313-020-00679-5

    Article  Google Scholar 

  23. Kumari S, Aryan P, Raja GL (2021) Design and simulation of a novel FOIMC-PD/P double-loop control structure for CSTRs and bioreactors. Int J Chem React Eng 19(12):1287–1303

    Article  Google Scholar 

  24. Mondal R, Dey J (2022) A novel design methodology on cascaded fractional order (FO) PI-PD control and its real time implementation to Cart-Inverted Pendulum System. ISA Trans 130:565–581

    Article  Google Scholar 

  25. Gnaneshwar K, Trivedi R, Padhy PK (2022) Robust design of fractional order IMC controller for fractional order processes with time delay. Int J Numer Model Electron Netw Devices Fields 35(5):e3009

    Article  Google Scholar 

  26. Ajmeri M, Ali A (2017) Analytical design of modified Smith predictor for unstable second-order processes with time delay. Int J Syst Sci 48(8):1671–1681

    Article  MathSciNet  Google Scholar 

  27. Begum KG, Rao AS, Radhakrishnan T (2016) Maximum sensitivity based analytical tuning rules for PID controllers for unstable dead time processes. Chem Eng Res Des 109:593–606

    Article  Google Scholar 

  28. Skogestad S, Postlethwaite I (2005) Multivariable feedback control: analysis and design. Wiley, Hoboken

    Google Scholar 

  29. Ajmeri M (2024) Novel twofold control for delayed industrial processes with integrating and inverse response characteristics. IFAC J Syst Control 27:100242

    Article  MathSciNet  Google Scholar 

  30. Chen Y, Hu C, Moore KL (2003) Relay feedback tuning of robust PID controllers with iso-damping property. In: 42nd IEEE international conference on decision and control (IEEE Cat. No. 03CH37475) IEEE, Vol 3, pp 2180–2185

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Acknowledgements

Authors would like to thank NIT Patna and Darbhanga College of Engineering, Darbhanga, for providing opportunity to do research work.

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Authors and Affiliations

  1. Electrical Engineering Department, NIT Patna, Patna, India

    Sanjay Kumar & Moina Ajmeri

  2. Electrical and Electronics Engineering, Darbhanga College of Engineering, Darbhanga, India

    Sanjay Kumar

Authors
  1. Sanjay Kumar
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  2. Moina Ajmeri
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Contributions

SK involved in contributions, conceptualization, simulations, theoretical development, result analysis and manuscript writing. MA involved in contributions, conceptualization, result analysis, manuscript writing and supervision.

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Correspondence to Sanjay Kumar.

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Kumar, S., Ajmeri, M. Analytically designed dual-loop fractional-order IMC for integrating plants with inverse behavior. Int. J. Dynam. Control (2024). https://doi.org/10.1007/s40435-024-01421-8

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  • DOI: https://doi.org/10.1007/s40435-024-01421-8

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