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Direct synthesis based sliding mode controller design for unstable second order with dead-time processes with its application on continuous stirred tank reactor

  • Mohammed Hasmat Ali EMAIL logo and Md Nishat Anwar
Published/Copyright: November 15, 2023
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Abstract

Unstable processes are challenging to control because they have one or more positive poles that produce unrestrained dynamic activity. Controlling such unstable plants becomes more challenging with the occurrence of the delay. This article presents a novel direct synthesis based sliding mode controller design for unstable second order plus dead-time processes. A sliding surface with three parameters has been considered. The continuous control law, which is responsible for maintaining the system mode to the desired sliding surface mode, has been obtained using the direct synthesis approach. The discontinuous control law parameters have been obtained using the differential evolution optimization technique. A desired reference model is considered for the direct synthesis method, and an objective function is constituted in terms of performance measure (integral absolute error) and control effort measure (total variation of controller output) for the optimization approach. Illustrative examples show the superiority of the proposed controller design method over recently reported literature, especially in terms of load rejection. The proposed controller approach is further extended to control the temperature of a nonlinear chemical reactor. Furthermore, the robustness of the proposed controller is also investigated for plant parametric uncertainty.


Corresponding author: Mohammed Hasmat Ali, Department of Electrical Engineering, National Institute of Technology Patna, Patna, India, E-mail:

  1. Research ethics: Not applicable.

  2. Author contribution: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Competing interests: We have no conflict of competing interests.

  4. Research funding: None declared.

  5. Data availability: Not applicable.

References

1. Ravikishore, C, Kumar, DTVP, Sree, RP. Enhanced performance of PID controllers for unstable time delay systems using direct synthesis method. Indian Chem Eng 2021;63:1–17. https://doi.org/10.1080/00194506.2020.1736650.Search in Google Scholar

2. Raza, A, Anwar, MN. A unified approach of PID controller design for unstable processes with time delay. J Cent South Univ 2020;27:2643–61. https://doi.org/10.1007/s11771-020-4488-6.Search in Google Scholar

3. Shamsuzzoha, M. Closed-loop PI/PID controller tuning for stable and integrating process with time delay. Ind Eng Chem Res 2013;52:12973–92. https://doi.org/10.1021/ie401808m.Search in Google Scholar

4. Atif Siddiqui, M, Anwar, MN, Laskar, SH. Enhanced control of unstable cascade systems using direct synthesis approach. Chem Eng Sci 2021;232:116322. https://doi.org/10.1016/j.ces.2020.116322.Search in Google Scholar

5. 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

6. Ajmeri, M. Analytical design of enhanced PID controller with set-point filter for unstable processes with time delay. Int J Dyn Control 2023;11:564–73. https://doi.org/10.1007/s40435-022-00987-5.Search in Google Scholar

7. Ajmeri, M, Ali, A. Analytical design of modified Smith predictor for unstable second-order processes with time delay. Int J Syst Sci 2017;48:1671–81. https://doi.org/10.1080/00207721.2017.1280554.Search in Google Scholar

8. Herrera, M, Camacho, O, Leiva, H, Smith, C. An approach of dynamic sliding mode control for chemical processes. J Process Control 2020;85:112–20. https://doi.org/10.1016/j.jprocont.2019.11.008.Search in Google Scholar

9. Camacho, O. A predictive approach based-Sliding Mode Control. In: IFAC proceedings volumes (IFAC-PapersOnline). Spain: IFAC; 2002:381–5 pp.10.3182/20020721-6-ES-1901.00632Search in Google Scholar

10. Camacho, O, Smith, CA. Sliding mode control: an approach to regulate nonlinear chemical processes. ISA Trans 2000;39:205–18. https://doi.org/10.1016/s0019-0578(99)00043-9.Search in Google Scholar PubMed

11. Camacho, O, Rojas, R, García, W. Variable structure control applied to chemical processes with inverse response. ISA Trans 1999;38:55–72. https://doi.org/10.1016/s0019-0578(99)00005-1.Search in Google Scholar

12. Sun, Z, Xie, H, Zheng, J, Man, Z, He, D. Path-following control of Mecanum-wheels omnidirectional mobile robots using nonsingular terminal sliding mode. Mech Syst Signal Process 2021;147:107128. https://doi.org/10.1016/j.ymssp.2020.107128.Search in Google Scholar

13. Chen, L, Van, M. Sliding mode control of a class of underactuated system with non-integrable momentum. J Franklin Inst 2020;357:9484–504. https://doi.org/10.1016/j.jfranklin.2020.07.022.Search in Google Scholar

14. Mehta, U, Rojas, R. Smith predictor based sliding mode control for a class of unstable processes. Trans Inst Meas Control 2015;39:1–9. https://doi.org/10.1177/0142331215619973.Search in Google Scholar

15. Kaya, I. Sliding-mode control of stable processes. Ind Eng Chem Res 2007;46:571–8. https://doi.org/10.1021/ie0607806.Search in Google Scholar

16. Siddiqui, MA, Anwar, MN, Laskar, SH. Sliding mode controller design for second-order unstable processes with dead-time. J Electr Eng 2020;71:237–45. https://doi.org/10.2478/jee-2020-0032.Search in Google Scholar

17. Li, X, Sun, G, Shao, X. Discrete-time pure-tension sliding mode predictive control for the deployment of space tethered satellite with input saturation. Acta Astronaut 2020;170:521–9. https://doi.org/10.1016/j.actaastro.2020.02.009.Search in Google Scholar

18. Xie, Z, Sun, T, Kwan, T, Wu, X. Motion control of a space manipulator using fuzzy sliding mode control with reinforcement learning. Acta Astronaut 2020;176:156–72. https://doi.org/10.1016/j.actaastro.2020.06.028.Search in Google Scholar

19. Lü, L, Zhang, F, Zou, C. Finite-time synchronization in the laser network based on sliding mode control technology. Optik (Stuttg) 2021;225:165605. https://doi.org/10.1016/j.ijleo.2020.165605.Search in Google Scholar

20. Menaga, D, Sankaranarayanan, V. Performance comparison for grid connected photovoltaic system using sliding mode control. J King Saud Univ – Eng Sci 2021;33:1–7. https://doi.org/10.1016/j.jksues.2020.04.012.Search in Google Scholar

21. Ebrahim, MA, Ahmed, MN, Ramadan, HS, Becherif, M, Zhao, J. Optimal metaheuristic-based sliding mode control of VSC-HVDC transmission systems. Math Comput Simul 2021;179:178–93. https://doi.org/10.1016/j.matcom.2020.08.009.Search in Google Scholar

22. Mani, P, Joo, YH. Fuzzy logic-based integral sliding mode control of multi-area power systems integrated with wind farms. Inf Sci (Ny) 2021;545:153–69. https://doi.org/10.1016/j.ins.2020.07.076.Search in Google Scholar

23. Hao, LY, Zhang, H, Li, H, Li, TS. Sliding mode fault-tolerant control for unmanned marine vehicles with signal quantization and time-delay. Ocean Eng 2020;215:107882. https://doi.org/10.1016/j.oceaneng.2020.107882.Search in Google Scholar

24. Liu, X, Zhang, M, Chen, J, Yin, B. Trajectory tracking with quaternion-based attitude representation for autonomous underwater vehicle based on terminal sliding mode control. Appl Ocean Res 2020;104:102342. https://doi.org/10.1016/j.apor.2020.102342.Search in Google Scholar

25. Wang, W, Xia, Y, Chen, Y, Xu, G, Chen, Z, Xu, K. Motion control methods for X-rudder underwater vehicles: model based sliding Mode and non-model based iterative sliding mode. Ocean Eng 2020;216:108054. https://doi.org/10.1016/j.oceaneng.2020.108054.Search in Google Scholar

26. Islam, Y, Ahmad, I, Zubair, M, Shahzad, K. Double integral sliding mode control of Leukemia Therapy. Biomed Signal Process Control 2020;61:102046. https://doi.org/10.1016/j.bspc.2020.102046.Search in Google Scholar

27. Rezvani-Ardakani, S, Mohammad-Ali-Nezhad, S, Ghasemi, R. Epilepsy control using a fixed time integral super twisting sliding mode control for Pinsky–Rinzel pyramidal model through ion channels with optogenetic method. Comput Methods Programs Biomed 2020;195:105665. https://doi.org/10.1016/j.cmpb.2020.105665.Search in Google Scholar PubMed

28. Camacho, O, Rojas, R. A general sliding mode controller for nonlinear chemical processes. J Dyn Syst Meas Control 2000;122:650–5. https://doi.org/10.1115/1.1318351.Search in Google Scholar

29. Mehta, U, Kaya, I. Smith predictor with sliding mode control for processes with large dead times. J Electr Eng 2017;68:463–9. https://doi.org/10.1515/jee-2017-0081.Search in Google Scholar

30. Camacho, O, Smith, C, Moreno, W. Development of an internal model sliding mode controller. Ind Eng Chem Res 2003;42:568–73. https://doi.org/10.1021/ie010481a.Search in Google Scholar

31. Rojas, R, Camacho, O, González, L. A sliding mode control proposal for open-loop unstable processes. ISA Trans 2004;43:243–55. https://doi.org/10.1016/s0019-0578(07)60034-2.Search in Google Scholar PubMed

32. Sivaramakrishnan, S, Tangirala, AK, Chidambaram, M. Sliding mode controller for unstable systems. Chem Biochem Eng Q 2008;22:41–7.Search in Google Scholar

33. Camacho, O, De la Cruz, F. Smith predictor based-sliding mode controller for integrating processes with elevated deadtime. ISA Trans 2004;43:257–70. https://doi.org/10.1016/s0019-0578(07)60035-4.Search in Google Scholar PubMed

34. Ebrahimi, N, Ozgoli, S, Ramezani, A. Model-free sliding mode control, theory and application. Proc Inst Mech Eng Part I J Syst Control Eng 2018;232:1292–301. https://doi.org/10.1177/0959651818780597.Search in Google Scholar

35. Zhu, Q. Complete model-free siding mode control (CMFSMC). Sci Rep 2021;11:1–15. https://doi.org/10.1038/s41598-021-01871-6.Search in Google Scholar PubMed PubMed Central

36. De La Parte, MMP, Camacho, O, Camacho, EF. A GPC-based sliding mode controller for nonlinear chemical processes. In: Proceedings of the European control conference 2001; 2001:3777–82 pp.10.23919/ECC.2001.7076522Search in Google Scholar

37. Shamsuzzoha, M, Lee, M. Analytical design of enhanced PID filter controller for integrating and first order unstable processes with time delay. Chem Eng Sci 2008;63:2717–31. https://doi.org/10.1016/j.ces.2008.02.028.Search in Google Scholar

38. Eltaeib, T, Mahmood, A. Differential evolution: a survey and analysis. Appl Sci 2018;8:1–25. https://doi.org/10.3390/app8101945.Search in Google Scholar

39. Barik, AK, Das, DC. Expeditious frequency control of solar photovoltaic/biogas/biodiesel generator based isolated renewable microgrid using grasshopper optimisation algorithm. IET Renew Power Gener 2018;12:1659–67. https://doi.org/10.1049/iet-rpg.2018.5196.Search in Google Scholar

40. Seer, QH, Nandong, J. Stabilization and PID tuning algorithms for second-order unstable processes with time-delays. ISA Trans 2017;67:233–45. https://doi.org/10.1016/j.isatra.2017.01.017.Search in Google Scholar PubMed

41. Atic, S, Kaya, I. PID controller design based on generalized stability boundary locus to control unstable processes with dead time. In: 2018 26th Mediterr conf control autom; 2018:1–6 pp.10.1109/MED.2018.8442568Search in Google Scholar

42. Anwar, N, Pan, S. A frequency response model matching method for PID controller design for processes with dead-time. ISA Trans 2014;55:175–87. https://doi.org/10.1016/j.isatra.2014.08.020.Search in Google Scholar PubMed

43. Shamsuzzoha, M. A unified approach for proportional-integral-derivative controller design for time delay processes. Kor J Chem Eng 2015;32:583–96. https://doi.org/10.1007/s11814-014-0237-6.Search in Google Scholar

44. Yang, XP, Wang, QG, Hang, CC, Lin, C. IMC-based control system design for unstable processes. Ind Eng Chem Res 2002;41:4288–94. https://doi.org/10.1021/ie010812j.Search in Google Scholar

45. Cho, W, Lee, J, Edgar, TF. Simple analytic proportional-integral-derivative (PID) controller tuning rules for unstable processes. Ind Eng Chem Res 2014;53:5048–54. https://doi.org/10.1021/ie401018g.Search in Google Scholar

46. Shamsuzzoha, M, Lee, M. Enhanced disturbance rejection for open-loop unstable process with time delay. ISA Trans 2009;48:237–44. https://doi.org/10.1016/j.isatra.2008.10.010.Search in Google Scholar PubMed

47. Siddiqui, MA, Anwar, MN, Laskar, SH. Control of nonlinear jacketed continuous stirred tank reactor using different control structures. J Process Control 2021;108:112–24. https://doi.org/10.1016/j.jprocont.2021.11.005.Search in Google Scholar

48. Jeng, JC. Simultaneous closed-loop tuning of cascade controllers based directly on set-point step-response data. J Process Control 2014;24:652–62. https://doi.org/10.1016/j.jprocont.2014.03.007.Search in Google Scholar

Received: 2023-06-30
Accepted: 2023-10-06
Published Online: 2023-11-15

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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