Research Article
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PID Controller Design Based on CCSR for Integrating Systems with Time Delay

Year 2025, Volume: 11 Issue: 3, 321 - 330, 31.12.2025
https://izlik.org/JA43UK76CB

Abstract

Time-delayed integral processes are frequently encountered and difficult to control, especially in the chemical industry. There are several basic reasons why integral systems are difficult to control. The most critical of these are memory effect, delays and complex tuning requirements. In this study, a PID (Proportional - Integral - Derivative) control design procedure is presented for time-delayed integral processes. The procedure is based on the calculation of the convex stability region center. In the first stage of the proposed PID design procedure, the kd (derivative gain) value that maximizes the area of the stabilizing kp - ki (proportional and integral gains) parameters region without disturbing the convexity with respect to the kp axis is selected. Then, the coordinates of the convex stability region center obtained for this value and the parameters kp and ki are determined. The proposed design procedure is a computational method with graphical evaluation. It does not use any iterative method. Another feature that distinguishes the proposed design procedure from its counterparts is that it does not require any filters, weight functions or extra parameters. In this respect, the procedure does not overshadow the simplicity feature, which is the biggest advantage of PID controllers in practice. Comparative simulation studies show that the PID controller designed with the proposed method have been provided good settling time performance.

References

  • [1] L. Yiming, J. Bi, W. Han and W. Tan, “Tuning of PID/PIDD2 controllers for integrating processes with robustness specification” ISA Transactions vol. 140, pp. 224-236, September 2023. doi: 10.1016/j.isatra.2023.05.015
  • [2] S. Yu and X. Li, “Proportional–Integral–Derivative Controller Performance Assessment and Retuning Based on General Process Response Data,” ACS Omega , vol. 6, no.15, pp. 10207-10223, 2021. doi: 10.1021/acsomega.1c00523
  • [3] C. Anil and R. P. Sree, “Tuning of PID controllers for integrating systems using direct synthesis method,” ISA Transactions, vol. 57, pp. 211–219, 2015. doi: 10.1016/j.isatra.2015.03.002
  • [4] B. W. Bequette, Process control modeling, design and simulation, NewDelhi: Prentice-Hall, 2003.
  • [5] S. Kumar and M. Ajmeri, “Analytically designed dual-loop fractional-order IMC for integrating plants with inverse behavior,” International Journal of Dynamics and Control, vol. 42, 2024. doi: 10.1007/s40435-024-01421-8
  • [6] L. Wang and W. R. Cluett, “Tuning PID.Controllers for integrating processes,” IEE Proceedings - Control Theory and Applications, vol. 144, no, 1997. doi: 10.1049/ip-cta:1997143
  • [7] L. Bodizs, M. Titica, N. Faria, B. Srinivasan, D. Dochain and D. Bonvin, “Oxygen control for an industrial pilot scale fed batch filamentous fungal fermentation,” Journal of Process Control, vol. 17, pp. 595–606, 2007. doi: 10.1016/j.jprocont.2007.01.019
  • [8] M. A. Gomez and A. Egorov, “A Lyapunov-Krasovskii based approach to observability and detectability of linear time-delay systems,” IFAC-PapersOnLine, vol. 58, no. 27, pp. 213–218, 2024. doi: 10.1016/j.ifacol.2024.10.326
  • [9] C. Onat, I. B. Kucukdemiral, S. Sivrioglu and I. Yuksek, “LPV model based gain-scheduling controller for a full vehicle active suspension system,” Journal of Vibration and Control, vol. 13, no.11, pp. 1629-1666, 2007. doi: 10.1177/1077546307078784
  • [10] C. Onat, I. B. Kucukdemiral, S. Sivrioglu, I. Yuksek and G. Cansever, “LPV gain scheduling controller design for a non-linear quarter vehicle active suspension system,” Transactions of the Institute of Measurement and Control, vol. 31, no. 1, pp.71-95, 2009. doi: 10.1177/0142331208090630
  • [11] J. Zhang, D. Efimov, (2020), A Lyapunov-Razumikhin condition of ISS for switched time-delaye systems under average dwell time commutation, IFAC PapersOnLine, vol. 53, no. 2, pp.1986–1991. doi: 10.1016/j.ifacol.2020.12.2568
  • [12] B. Şenol, U. Demiroǧlu, and R. Matušů, “Analytical approach on the design of fractional order proportional-integral controller for second order plus time delay models,” Journal of the Faculty of Engineering and Architecture of Gazi University, vol. 37, no. 1, pp. 121–136, 2022. doi: 10.17341/gazimmfd.879929
  • [13] Y. Wei, Y. Hu, Y. Dai, and Y. Wang, “A generalized padé approximation of time delay operator,” International Journal of Control, Automation and Systems., vol. 14, no. 1, pp. 181–187, 2016. doi: 10.1007/s12555-013-0240-4
  • [14] M. M Özyetkin and D. Astekin, “Zaman gecikmeli sistemler için Padé yaklaşımı ve kesirli dereceli PI kontrolör için yeni bir tasarım metodu,” Journal of the Faculty of Engineering and Architecture of Gazi University, vol. 38, no. 2, pp. 639-651, 2023. doi:10.17341/gazimmfd.948709
  • [15] M. M. Ozyetkin, C. Onat and Tan, N. “PI-PD controller design for time delay systems via the weighted geometrical center method,” Asian Journal of Control, vol. 22, no. 5, pp. 1811-1826, 2020. doi: 10.1002/asjc.2088
  • [16] C. Onat, “WGC based robust and gain scheduling PI controller design for condensing boilers,” Advances in Mechanical Engineering, vol. 2014, 659051, 2014. doi:10.1155/2014/659051
  • [17] C. Onat, “Bir Motorda Yakıt Hava Oranının Denetimini Kararlı Kılan PI Denetçilerinin Çözümlemesi,” Mühendis ve Makina, vol. 53. no. 626, pp. 42-45, 2012.
  • [18] C. Onat, “A new concept on PI design for time delay systems: Weighted geometrical center,” International Journal of Innovative Computing, Information and Control, vol. 9, no. 4, pp. 1539-1556, 2013.
  • [19] C. Onat, M. Daskin, A. Turan and Ö. Özgüven, “Manyetik Levitasyon Sistemleri İçin Ağırlıklı Geometrik Merkez Yöntemi ile PI-PD Kontrolcü Tasarımı,” Mühendis ve Makina, vol. 62, no. 704, pp. 556-579, 2021. doi: 10.46399/muhendismakina.910501
  • [20] Y. Guler and I. Kaya, “Load Frequency Control of Single-Area Power System with PI–PD Controller Design for Performance Improvement,” Journal of Electrical Engineering and Technology, vol. 18, pp. 2633–2648, 2023. doi: 10.1007/s42835-022-01371-1
  • [21] M. Zheng , T. Huang and G. Zhang, “A New Design Method for PI-PD Control of UnstableFractional-Order System with Time Delay,” Complexity, vol. 2019, pp. 1-12, 2019. doi: 10.1155/2019/3253497
  • [22] A. Vasickaninova, M. Bakosova, L. Cirka, M. Kaluz and J. Oravac, “Robust controller design for a laboratory heat exchanger,” Applied Thermal Engineering, vol. 128, pp. 1297-1309. 2018. doi: 10.1016/j.applthermaleng.2017.09.086
  • [23] M. Ghooi, S. Jain, and Y. V. Hote, “Proportional integral derivative controller tuning via Kronecker summation and modified particle swarm optimization with experimental validation,” Engineering Optimisation., vol. 53, no. 2, pp. 237–257, 2021. doi: 10.1080/0305215X.2020.1716745
  • [24] Q. B. Jin and Q. Liu, “Analytical IMC-PID design in terms of performance/robustness tradeoff for integrating processes: from 2-Dof to 1-Dof,” Journal of Process Control, vol. 24, pp.22–32, 2014. doi: 10.1016/j.jprocont.2013.12.011
  • [25] C. V. N. Rao and R. P. Sree, “IMC based controller design for integrating systems with time delay,” Indian Chemical Engineer, vol. 52, no. 3, pp. 194–218, 2010. doi: 10.1080/00194506.2010.547972
  • [26] A. S. Rao, V. S. R. Rao and M. Chidambaram, “Direct synthesis-based contr oller design for integrating processes with time delay,” Journal Franklin Institute, vol. 346, pp. 38–56, 2009. doi: 10.1016/j.jfranklin.2008.06.004
  • [27] R. P. Sree and M. Chidambaram, “Simple and robust method of tuning PID controller for integrator/dead time processes,” Journal of Chemical Engineering of Japan, vol. 38, pp. 113–9, 2005.
  • [28] P. Srivastava, A. Gupta and N. Kaistha, “Sustainable Glycerol Carbonate Manufacturing: Process, Synthesis, Design, and Control,” Industrial & Engineering Chemistry Research, vol. 63, no. 4, pp. 1926-1940, 2024. doi: 10.1021/acs.iecr.3c02513
  • [29] M. Shamsuzzoha and M. Lee, “Enhanced disturbance rejection for open-loop unstable process with time delay,” ISA Transactions, vol. 48, pp. 237–44, 2009. doi: 10.1016/j.isatra.2008.10.010
  • [30] N. S. Pai, S. C. Chang and C. T. Huang, “Tuning PI/PID controllers for integrating processes with deadtime and inverse response by simple calculations,” Journal of Process Control, vol. 20, pp. 726–733, 2010. doi: 10.1016/j.jprocont.2010.04.003
  • [31] A. Ali and S. Majhi, “Integral criteria for optimal tuning of PI/PID controllers for integrating processes,” Asian Journal of Control, vol. 13, no. 2, pp. 328–37, 2011. doi: 10.1002/asjc.278
  • [32] G. Syrcos and I. K. Kookos, “PID controller tuning using mathematical programming,” Chemical Engineering and Process,ing: Process Intensification, vol. 44, pp. 41–9, 2005. doi: 10.1016/j.cep.2004.04.001
  • [33] I. Kaya, “PI-PD controllers for controlling stable processes with inverse response and dead time,” Electrical Engineering, vol. 98, pp. 55–65, 2016. doi: 10.1007/s00202-015-0352-3
  • [34] I. Kaya, “PI-PD controller design for control of unstable and integrating processes,” ISA Transactions, vol. 42, pp. 1–21, 2003. doi: 10.1016/S0019-0578(07)60118-9
  • [35] N. Tan, “Computation of stabilizing PI-PD controllers,” International Journal of Control, Automation and Systems, vol. 7, no. 2, pp. 175–84, 2009. doi: 10.1007/s12555-009-0203-y
  • [36] C. Onat, “A new design method for PI–PD control of unstable processes with dead time.” ISA Transactions., vol. 84, pp.69–81, 2019. doi: 10.1016/j.isatra.2018.08.029
  • [37] H. İrgan, R. Menak and N. Tan, “A comparative study on PI-PD controller design using stability region centroid methods for unstable, integrating and resonant systems with time delay,” Measurement and Control, vol. 2024, pp.1-21, 2024. doi: 10.1177/00202940241253114
  • [38] M. M. Ozyetkin, C. Onat and N. Tan, “PID tuning method for integrating processes having time delay and inverse response,” IFAC-PapersOnLine vol. 51, no.4, pp. 274–279, 2018. doi: 10.1016/j.ifacol.2018.06.077
  • [39] K. Sharma, A. K. Yadav and B. B. Sharma, “Kharitonov theorem-based robust control approach for sustainable microgrid against DoS cyber-attack,” Digital Chemical Engineering, vol. 7, pp.1-8, 100099, 2023. doi: 10.1016/j.dche.2023.100099
  • [40] N. S. Pai, S. C. Chang and C. T. Huang, “Tuning PI/PID controllers for integrating processes with dead time and inverse response by simple calculations,” Journal of Process Control, vol. 20, no. 6, pp. 726–33, 2010. doi: 10.1016/j.jprocont.2010.04.003

Year 2025, Volume: 11 Issue: 3, 321 - 330, 31.12.2025
https://izlik.org/JA43UK76CB

Abstract

References

  • [1] L. Yiming, J. Bi, W. Han and W. Tan, “Tuning of PID/PIDD2 controllers for integrating processes with robustness specification” ISA Transactions vol. 140, pp. 224-236, September 2023. doi: 10.1016/j.isatra.2023.05.015
  • [2] S. Yu and X. Li, “Proportional–Integral–Derivative Controller Performance Assessment and Retuning Based on General Process Response Data,” ACS Omega , vol. 6, no.15, pp. 10207-10223, 2021. doi: 10.1021/acsomega.1c00523
  • [3] C. Anil and R. P. Sree, “Tuning of PID controllers for integrating systems using direct synthesis method,” ISA Transactions, vol. 57, pp. 211–219, 2015. doi: 10.1016/j.isatra.2015.03.002
  • [4] B. W. Bequette, Process control modeling, design and simulation, NewDelhi: Prentice-Hall, 2003.
  • [5] S. Kumar and M. Ajmeri, “Analytically designed dual-loop fractional-order IMC for integrating plants with inverse behavior,” International Journal of Dynamics and Control, vol. 42, 2024. doi: 10.1007/s40435-024-01421-8
  • [6] L. Wang and W. R. Cluett, “Tuning PID.Controllers for integrating processes,” IEE Proceedings - Control Theory and Applications, vol. 144, no, 1997. doi: 10.1049/ip-cta:1997143
  • [7] L. Bodizs, M. Titica, N. Faria, B. Srinivasan, D. Dochain and D. Bonvin, “Oxygen control for an industrial pilot scale fed batch filamentous fungal fermentation,” Journal of Process Control, vol. 17, pp. 595–606, 2007. doi: 10.1016/j.jprocont.2007.01.019
  • [8] M. A. Gomez and A. Egorov, “A Lyapunov-Krasovskii based approach to observability and detectability of linear time-delay systems,” IFAC-PapersOnLine, vol. 58, no. 27, pp. 213–218, 2024. doi: 10.1016/j.ifacol.2024.10.326
  • [9] C. Onat, I. B. Kucukdemiral, S. Sivrioglu and I. Yuksek, “LPV model based gain-scheduling controller for a full vehicle active suspension system,” Journal of Vibration and Control, vol. 13, no.11, pp. 1629-1666, 2007. doi: 10.1177/1077546307078784
  • [10] C. Onat, I. B. Kucukdemiral, S. Sivrioglu, I. Yuksek and G. Cansever, “LPV gain scheduling controller design for a non-linear quarter vehicle active suspension system,” Transactions of the Institute of Measurement and Control, vol. 31, no. 1, pp.71-95, 2009. doi: 10.1177/0142331208090630
  • [11] J. Zhang, D. Efimov, (2020), A Lyapunov-Razumikhin condition of ISS for switched time-delaye systems under average dwell time commutation, IFAC PapersOnLine, vol. 53, no. 2, pp.1986–1991. doi: 10.1016/j.ifacol.2020.12.2568
  • [12] B. Şenol, U. Demiroǧlu, and R. Matušů, “Analytical approach on the design of fractional order proportional-integral controller for second order plus time delay models,” Journal of the Faculty of Engineering and Architecture of Gazi University, vol. 37, no. 1, pp. 121–136, 2022. doi: 10.17341/gazimmfd.879929
  • [13] Y. Wei, Y. Hu, Y. Dai, and Y. Wang, “A generalized padé approximation of time delay operator,” International Journal of Control, Automation and Systems., vol. 14, no. 1, pp. 181–187, 2016. doi: 10.1007/s12555-013-0240-4
  • [14] M. M Özyetkin and D. Astekin, “Zaman gecikmeli sistemler için Padé yaklaşımı ve kesirli dereceli PI kontrolör için yeni bir tasarım metodu,” Journal of the Faculty of Engineering and Architecture of Gazi University, vol. 38, no. 2, pp. 639-651, 2023. doi:10.17341/gazimmfd.948709
  • [15] M. M. Ozyetkin, C. Onat and Tan, N. “PI-PD controller design for time delay systems via the weighted geometrical center method,” Asian Journal of Control, vol. 22, no. 5, pp. 1811-1826, 2020. doi: 10.1002/asjc.2088
  • [16] C. Onat, “WGC based robust and gain scheduling PI controller design for condensing boilers,” Advances in Mechanical Engineering, vol. 2014, 659051, 2014. doi:10.1155/2014/659051
  • [17] C. Onat, “Bir Motorda Yakıt Hava Oranının Denetimini Kararlı Kılan PI Denetçilerinin Çözümlemesi,” Mühendis ve Makina, vol. 53. no. 626, pp. 42-45, 2012.
  • [18] C. Onat, “A new concept on PI design for time delay systems: Weighted geometrical center,” International Journal of Innovative Computing, Information and Control, vol. 9, no. 4, pp. 1539-1556, 2013.
  • [19] C. Onat, M. Daskin, A. Turan and Ö. Özgüven, “Manyetik Levitasyon Sistemleri İçin Ağırlıklı Geometrik Merkez Yöntemi ile PI-PD Kontrolcü Tasarımı,” Mühendis ve Makina, vol. 62, no. 704, pp. 556-579, 2021. doi: 10.46399/muhendismakina.910501
  • [20] Y. Guler and I. Kaya, “Load Frequency Control of Single-Area Power System with PI–PD Controller Design for Performance Improvement,” Journal of Electrical Engineering and Technology, vol. 18, pp. 2633–2648, 2023. doi: 10.1007/s42835-022-01371-1
  • [21] M. Zheng , T. Huang and G. Zhang, “A New Design Method for PI-PD Control of UnstableFractional-Order System with Time Delay,” Complexity, vol. 2019, pp. 1-12, 2019. doi: 10.1155/2019/3253497
  • [22] A. Vasickaninova, M. Bakosova, L. Cirka, M. Kaluz and J. Oravac, “Robust controller design for a laboratory heat exchanger,” Applied Thermal Engineering, vol. 128, pp. 1297-1309. 2018. doi: 10.1016/j.applthermaleng.2017.09.086
  • [23] M. Ghooi, S. Jain, and Y. V. Hote, “Proportional integral derivative controller tuning via Kronecker summation and modified particle swarm optimization with experimental validation,” Engineering Optimisation., vol. 53, no. 2, pp. 237–257, 2021. doi: 10.1080/0305215X.2020.1716745
  • [24] Q. B. Jin and Q. Liu, “Analytical IMC-PID design in terms of performance/robustness tradeoff for integrating processes: from 2-Dof to 1-Dof,” Journal of Process Control, vol. 24, pp.22–32, 2014. doi: 10.1016/j.jprocont.2013.12.011
  • [25] C. V. N. Rao and R. P. Sree, “IMC based controller design for integrating systems with time delay,” Indian Chemical Engineer, vol. 52, no. 3, pp. 194–218, 2010. doi: 10.1080/00194506.2010.547972
  • [26] A. S. Rao, V. S. R. Rao and M. Chidambaram, “Direct synthesis-based contr oller design for integrating processes with time delay,” Journal Franklin Institute, vol. 346, pp. 38–56, 2009. doi: 10.1016/j.jfranklin.2008.06.004
  • [27] R. P. Sree and M. Chidambaram, “Simple and robust method of tuning PID controller for integrator/dead time processes,” Journal of Chemical Engineering of Japan, vol. 38, pp. 113–9, 2005.
  • [28] P. Srivastava, A. Gupta and N. Kaistha, “Sustainable Glycerol Carbonate Manufacturing: Process, Synthesis, Design, and Control,” Industrial & Engineering Chemistry Research, vol. 63, no. 4, pp. 1926-1940, 2024. doi: 10.1021/acs.iecr.3c02513
  • [29] M. Shamsuzzoha and M. Lee, “Enhanced disturbance rejection for open-loop unstable process with time delay,” ISA Transactions, vol. 48, pp. 237–44, 2009. doi: 10.1016/j.isatra.2008.10.010
  • [30] N. S. Pai, S. C. Chang and C. T. Huang, “Tuning PI/PID controllers for integrating processes with deadtime and inverse response by simple calculations,” Journal of Process Control, vol. 20, pp. 726–733, 2010. doi: 10.1016/j.jprocont.2010.04.003
  • [31] A. Ali and S. Majhi, “Integral criteria for optimal tuning of PI/PID controllers for integrating processes,” Asian Journal of Control, vol. 13, no. 2, pp. 328–37, 2011. doi: 10.1002/asjc.278
  • [32] G. Syrcos and I. K. Kookos, “PID controller tuning using mathematical programming,” Chemical Engineering and Process,ing: Process Intensification, vol. 44, pp. 41–9, 2005. doi: 10.1016/j.cep.2004.04.001
  • [33] I. Kaya, “PI-PD controllers for controlling stable processes with inverse response and dead time,” Electrical Engineering, vol. 98, pp. 55–65, 2016. doi: 10.1007/s00202-015-0352-3
  • [34] I. Kaya, “PI-PD controller design for control of unstable and integrating processes,” ISA Transactions, vol. 42, pp. 1–21, 2003. doi: 10.1016/S0019-0578(07)60118-9
  • [35] N. Tan, “Computation of stabilizing PI-PD controllers,” International Journal of Control, Automation and Systems, vol. 7, no. 2, pp. 175–84, 2009. doi: 10.1007/s12555-009-0203-y
  • [36] C. Onat, “A new design method for PI–PD control of unstable processes with dead time.” ISA Transactions., vol. 84, pp.69–81, 2019. doi: 10.1016/j.isatra.2018.08.029
  • [37] H. İrgan, R. Menak and N. Tan, “A comparative study on PI-PD controller design using stability region centroid methods for unstable, integrating and resonant systems with time delay,” Measurement and Control, vol. 2024, pp.1-21, 2024. doi: 10.1177/00202940241253114
  • [38] M. M. Ozyetkin, C. Onat and N. Tan, “PID tuning method for integrating processes having time delay and inverse response,” IFAC-PapersOnLine vol. 51, no.4, pp. 274–279, 2018. doi: 10.1016/j.ifacol.2018.06.077
  • [39] K. Sharma, A. K. Yadav and B. B. Sharma, “Kharitonov theorem-based robust control approach for sustainable microgrid against DoS cyber-attack,” Digital Chemical Engineering, vol. 7, pp.1-8, 100099, 2023. doi: 10.1016/j.dche.2023.100099
  • [40] N. S. Pai, S. C. Chang and C. T. Huang, “Tuning PI/PID controllers for integrating processes with dead time and inverse response by simple calculations,” Journal of Process Control, vol. 20, no. 6, pp. 726–33, 2010. doi: 10.1016/j.jprocont.2010.04.003
There are 40 citations in total.

Details

Primary Language English
Subjects Machine Theory and Dynamics
Journal Section Research Article
Authors

Cem Onat 0000-0002-4295-4860

Submission Date October 22, 2024
Acceptance Date September 4, 2025
Publication Date December 31, 2025
IZ https://izlik.org/JA43UK76CB
Published in Issue Year 2025 Volume: 11 Issue: 3

Cite

IEEE [1]C. Onat, “PID Controller Design Based on CCSR for Integrating Systems with Time Delay”, GJES, vol. 11, no. 3, pp. 321–330, Dec. 2025, [Online]. Available: https://izlik.org/JA43UK76CB

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