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A digital control approach for unstable-first-order- plus-dead-time systems with P and PI controllers

  • Key Laboratory of High-efficiency and Clean Mechanical Manufacture, Ministry of Education, School of Mechanical Engineering, Shandong University, Jinan 250061, China

Funds:  Supported by China Fundamental Research Funds for the Center Universities (10062013YWF13-ZY-68).
Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2014.10.002
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  • Author Bio:

    LENG Tongtong, female, born in 1986, Master candidate. Research field: Robust control for precision electromechanical systems. E-mail: tongtong0116@126.com

  • Corresponding author: YAN Peng
  • Received Date: 08 August 2013
  • Accepted Date: 27 February 2014
  • Rev Recd Date: 27 February 2014
  • Publish Date: 30 October 2014
    Abstract

  • Abstract

    Many dynamical systems can be modeled by unstable-first-order-plus-dead-time (UFOPDT) transfer functions. However, analysis and synthesis of UFOPDT systems are much more challenging due to the general difficulties of infinite dimensionality and the instability of the plant. Considering the control of such systems, explicit tuning formulae were derived for proportional (P) and proportional-integral (PI) controllers, based on the digitized open loop systems. Stability range was also discussed for the feedback systems with delays. Compared with existing results, the presented method significantly improved the accuracy and sufficiency, and simplified the tuning process. Numerical example about an isothermal chemical reactor control problem was given to illustrate this algorithm, and several relevant methods were also compared.

    Abstract

    Many dynamical systems can be modeled by unstable-first-order-plus-dead-time (UFOPDT) transfer functions. However, analysis and synthesis of UFOPDT systems are much more challenging due to the general difficulties of infinite dimensionality and the instability of the plant. Considering the control of such systems, explicit tuning formulae were derived for proportional (P) and proportional-integral (PI) controllers, based on the digitized open loop systems. Stability range was also discussed for the feedback systems with delays. Compared with existing results, the presented method significantly improved the accuracy and sufficiency, and simplified the tuning process. Numerical example about an isothermal chemical reactor control problem was given to illustrate this algorithm, and several relevant methods were also compared.
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    • References(12)
  • [1]
    Kheirizad I, Jalali A A, Khandani K. Stabilization of fractionalorder unstable delay systems by fractional-order controllers[J]. Journal of Systems and Control Engineering, 2012, 226(9):1 166-1 173.
    [2]
    Luo Y, Chen Y Q. Stabilizing and robust fractional order PI controller synthesis for first order plus time delay systems[J]. Automatica, 2012, 48(9): 2 159-2 167.
    [3]
    Hohenbichler N. All stabilizing PID controllers for time delay systems[J]. Automatica, 2009; 45(11): 2 678-2 684.
    [4]
    YU Tao, LIU Xiang, SUN Youxian. Frequency-domain design of PI Controllers for first-order systems with time delay[J]. Journal of University of Science and Technology of China, 2005, 35(S): 167-173.
    余涛, 刘翔, 孙优贤. 一阶时滞系统PI控制器的频率设计法[J]. 中国科学技术大学学报, 2005, 35(S): 167-173.
    [5]
    Bellman R, Cooke K L. Differential-Difference Equations[M]. New York: Academic Press, 1963.
    [6]
    De Paor A M, OMalley M. Controllers of Ziegler-Nichols type for unstable process with time delay[J]. International Journal of Control, 1989, 49(4): 1 273-1 284.
    [7]
    Bahavarnia M, Tavazoei M. A new view to Ziegler-Nichols step response tuning method: Analytic non-fragility justification[J]. Journal of Process Control, 2013, 23(1): 23-33.
    [8]
    Venkatashankar V, Chidambaram M. Design of P and PI controllers for unstable first-order plus time delay systems[J]. International Journal of Control, 1994, 60(1): 137-144.
    [9]
    Ho W K, Xu W. PID tuning for unstable processes based on gain and phase-margin specifications[J]. IEE Proceedings of Control Theory and Applications, 1998, 145(5): 392-396.
    [10]
    孙明玮,焦纲领,杨瑞光,等. PI控制下开环不稳定对象可行稳定裕度范围的研究[J].自动化学报,2011,37(3):385-388.
    [11]
    Paraskevopoulos P N, Pasgianos G D, Arvanitis K G. PID-type controller tuning for unstable first order plus dead time processes based on gain and phase margin specifications[J]. IEEE Transactions on Control Systems Technology, 2006, 14(5): 926-936.
    [12]
    Normey-Rico J E, Camacho E F. Simple robust dead-time compensator for first-order plus dead-time unstable processes[J]. Industrial & Engineering Chemistry Research, 2008, 47(14): 4 784-4 790.
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    [1]
    Kheirizad I, Jalali A A, Khandani K. Stabilization of fractionalorder unstable delay systems by fractional-order controllers[J]. Journal of Systems and Control Engineering, 2012, 226(9):1 166-1 173.
    [2]
    Luo Y, Chen Y Q. Stabilizing and robust fractional order PI controller synthesis for first order plus time delay systems[J]. Automatica, 2012, 48(9): 2 159-2 167.
    [3]
    Hohenbichler N. All stabilizing PID controllers for time delay systems[J]. Automatica, 2009; 45(11): 2 678-2 684.
    [4]
    YU Tao, LIU Xiang, SUN Youxian. Frequency-domain design of PI Controllers for first-order systems with time delay[J]. Journal of University of Science and Technology of China, 2005, 35(S): 167-173.
    余涛, 刘翔, 孙优贤. 一阶时滞系统PI控制器的频率设计法[J]. 中国科学技术大学学报, 2005, 35(S): 167-173.
    [5]
    Bellman R, Cooke K L. Differential-Difference Equations[M]. New York: Academic Press, 1963.
    [6]
    De Paor A M, OMalley M. Controllers of Ziegler-Nichols type for unstable process with time delay[J]. International Journal of Control, 1989, 49(4): 1 273-1 284.
    [7]
    Bahavarnia M, Tavazoei M. A new view to Ziegler-Nichols step response tuning method: Analytic non-fragility justification[J]. Journal of Process Control, 2013, 23(1): 23-33.
    [8]
    Venkatashankar V, Chidambaram M. Design of P and PI controllers for unstable first-order plus time delay systems[J]. International Journal of Control, 1994, 60(1): 137-144.
    [9]
    Ho W K, Xu W. PID tuning for unstable processes based on gain and phase-margin specifications[J]. IEE Proceedings of Control Theory and Applications, 1998, 145(5): 392-396.
    [10]
    孙明玮,焦纲领,杨瑞光,等. PI控制下开环不稳定对象可行稳定裕度范围的研究[J].自动化学报,2011,37(3):385-388.
    [11]
    Paraskevopoulos P N, Pasgianos G D, Arvanitis K G. PID-type controller tuning for unstable first order plus dead time processes based on gain and phase margin specifications[J]. IEEE Transactions on Control Systems Technology, 2006, 14(5): 926-936.
    [12]
    Normey-Rico J E, Camacho E F. Simple robust dead-time compensator for first-order plus dead-time unstable processes[J]. Industrial & Engineering Chemistry Research, 2008, 47(14): 4 784-4 790.
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