Skip to main content
SpringerLink
Log in

Robust Hybrid Controller Design for Batch Processes with Time Delay and Its Application in Industrial Processes

  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

A new design method of two-dimensional (2D) controller for multi-phase batch processes with time delay and disturbances is proposed to ensure the stability of the control system and realize efficient production in industry. The batch process is first converted to an equivalent but different dimensional 2D-FM switched system. Based on the 2D system framework, then sufficient conditions of a controller existence expressed by linear matrix inequalities (LMIs) that stabilizing system is given by means of the average dwell time method. Meanwhile, robust hybrid 2D controller design containing extended information is proposed and the minimum runtime lower bound of each sub-system is accurately calculated. The design advantages of the controller depend on the size of the time delay so it has a certain degree of robustness. At the same time, considering the exponential stability, the system can have a faster rate of convergence. In addition, the introduction of extended information has improved the control performance of the system to some extent. The acquisition of minimum time at different phases will promote certain production efficiency and thus reduce energy consumption. Finally, an injection process in industrial production process has been taken as an example to verify effectiveness of the proposed method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. N. Yao and L. Feng, “Fault diagnosis and fault tolerant control for non-Gaussian time-delayed singular stochastic distribution systems,” International Journal of Control, Automation, and Systems, vol. 14, no. 2, pp. 435–442, 2016.

    Google Scholar 

  2. R. Zhang and S. Wang, “Support vector machine based predictive functional control design for output temperature of coking furnace,” Journal of Process Control, vol. 18, no. 5, pp. 439–448, 2008.

    Google Scholar 

  3. Y. Wang, F. Gao, and I. F. J. Doyle, “Survey on iterative learning control, repetitive control, and run-to-run control,” Journal of Process Control, vol. 19, pp. 1589–1600, 2009.

    Google Scholar 

  4. J. Lu, Z. Cao, and F. Gao, “Batch process control-overview and outlook,” Acta Automatica Sinica, vol. 43, no. 6, pp. 933–943, 2017.

    MATH  Google Scholar 

  5. R. Zhang, R. Lu, A. Xue, and F. Gao, “Predictive functional control for linear systems under partial actuator faults and application on an injection molding batch process,” Industrial & Engineering Chemistry Research, vol. 53, no. 2, pp. 723–731, 2014.

    Google Scholar 

  6. Y. Yang and F. R. Gao, “Injection velocity control using a self-tuning adaptive controller,” International Polymer Processing, vol. 14, no. 2, pp. 196–204, 1999.

    Google Scholar 

  7. Y. Yang and F. Gao, “Adaptive control of the filling velocity of thermoplastics injection molding,” Control Engineering Practice, vol. 8, pp. 1285–1296, 2000.

    Google Scholar 

  8. E. F. Camacho and C. B. Alba, Model Predictive Control, Springer Science & Business Media, 2013.

    Google Scholar 

  9. D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. Scokaert, “Constrained model predictive control: stability and opti-mality,” Automatica, vol. 36, no. 6, pp. 789–814, 2000.

    MathSciNet  MATH  Google Scholar 

  10. R. Zhang, R. Lu, A. Xue, and F. Gao, “New minmax linear quadratic fault-tolerant tracking control for batch processes,” IEEE Transactions on Automatic Control, vol. 61, no. 10, pp. 3045–3051, 2016.

    MathSciNet  MATH  Google Scholar 

  11. R. Zhang, S. Wu, Z. Cao, J. Lu, and F. Gao, “A systematic min-max optimization design of constrained model predictive tracking control for industrial processes against uncertainty,” IEEE Transactions on Control Systems Technology, vol. 26, no. 6, pp. 2157–2164, 2018.

    Google Scholar 

  12. G. E. Rotstein and D. R. Lewin, “Control of an unstable batch chemical reactor,” Computers and Chemical Engineering, vol. 16, no. 1, pp. 27–49, 1992.

    Google Scholar 

  13. D. Bonvin, “Control and optimization of batch processes,” IEEE Control Systems, vol. 26, no. 6, pp. 34–45, 2006.

    Google Scholar 

  14. F. Gao, Y. Yang, and C. Shao, “Robust iterative learning control with applications to injection molding process,” Chemical Engineering Science, vol. 56, no. 24, pp. 7025–7034, 2001.

    Google Scholar 

  15. W. Cho, T. F. Edgar, and J. Lee, “Iterative learning dual-mode control of exothermic batch reactors,” Control Engineering Practice, vol. 16, no. 10, pp. 1244–1249, 2008.

    Google Scholar 

  16. J. Shi, F. Gao, and T. Wu, “Robust design of Integrated feedback and iterative learning control of a batch process based on a 2D Roesser system,” Journal of Process Control, vol. 15, no. 8, pp. 907–924, 2005.

    Google Scholar 

  17. J. Shi, F. Gao, and T. Wu., “Robust iterative learning control design for batch processes with uncertain perturbations and initialization,” AIChE Journal, vol. 52, no. 6, pp. 2171–2187, 2006.

    Google Scholar 

  18. J. Shi, F. Gao, and T. J. Wu, “Single-cycle and multi-cycle generalized 2d model predictive iterative learning control (2d-gpilc) schemes for batch processes,” Journal of Process Control, vol. 17, no. 9, pp. 715–727, 2007.

    Google Scholar 

  19. J. Zhang, W. B. Xie, M. Q. Shen, and L. Huang, “State augmented feedback controller design approach for T-S fuzzy system with complex actuator saturations,” International Journal of Control, Automation, and Systems, vol. 15, no. 5, 2395–2405, 2017.

    Google Scholar 

  20. S. Y. Mo, From One-time Dimensional Control to Two-time Dimensional Hybrid Control in Batch Processes, Thesis (Ph.D.), Hong Kong University of Science and Technology, 2013.

    Google Scholar 

  21. L. Wang, L. Sun, and W. Luo, “Robust constrained iterative learning predictive fault-tolerant control of uncertain batch processes,” Science China Information Science, vol. 62, pp. 1–3, 2019.

    Google Scholar 

  22. D. Li, Y. Xi, J. Lu, and F. Gao, “Synthesis of real-time-feedback-based 2D iterative learning control-model predictive control for constrained batch processes with unknown input nonlinearity,” Industrial & Engineering Chemistry Research, vol. 55, no. 51, pp. 13074–13084, 2016.

    Google Scholar 

  23. C. Han, L. Jia, and D. Peng, “Model predictive control of batch processes based on two-dimensional integration frame,” Nonlinear Analysis: Hybrid Systems, vol. 28, pp. 75–86, 2018.

    MathSciNet  MATH  Google Scholar 

  24. J. Lu, Z. Cao, and F. Gao, “Multi-point iterative learning model predictive control,” IEEE Transactions on. industrial Electronic, vol. 66, no. 8, pp. 6230–6240, 2018.

    Google Scholar 

  25. R. Zhang, S. Wu, and J. Tao, “A new design of predictive functional control strategy for batch processes in the two-dimensional framework,” IEEE Transactions on Industrial Informatics, vol. 15, no. 5, pp. 2905–2914, 2019.

    Google Scholar 

  26. Y. Q. Wang, Y. Yang, F. R. Gao, and D. H. Zhou, “Control of multi-phase batch processes: formulation and challenge,” IFAC Proceeding Volumes, vol 40, no. 5, pp. 339–344, 2007.

    Google Scholar 

  27. Y. Q. Wang, D. H. Zhou, and F. R. Gao, “Iterative learning model predictive control for multi-phase batch processes,” Journal of Process Control, vol. 18, no. 6, pp. 543–557, 2008.

    Google Scholar 

  28. W. P. Luo, L. M. Wang, R. D. Zhang, and F. R. Gao, “2D switched model-based infinite horizon LQ fault-tolerant tracking control for batch process,” Industrial & Engineering Chemistry Research, vol. 58, no. 22, pp. 9540–9551, 2019.

    Google Scholar 

  29. L. M. Wang and W. P. Luo, “Linear quadratic predictive fault-tolerant control for multi-phase batch processes,” IEEE Access, vol. 7, pp. 33598–33609, 2019.

    Google Scholar 

  30. L. M. Wang, X. He, and D. H. Zhou, “Average dwell time-based optimal iterative learning control for multi-phase batch processes,” Journal of Process Control, vol. 40, pp. 1–12, 2016.

    Google Scholar 

  31. L. Wang, Y. Shen, J. Yu, P. LI, R. Zhang, and F. Gao, “Robust iterative learning control for multi-phase batch processes: an average dwell-time method with 2D convergence indexes,” Journal International Journal of Systems Science, vol. 49, no.2, pp. 324–343, 2018.

    MathSciNet  MATH  Google Scholar 

  32. L. Wang, L. Sun, J. Yu, R. Zhang, and F. Gao, “Robust iterative learning fault-tolerant control for multi-phase batch processes with uncertainties,” Industrial & Engineering Chemistry Research, vol. 56, no. 36, pp. 10090–10109, 2017.

    Google Scholar 

  33. L. Wang, B. Liu, J. Yu, P. Li, R. Zhang, and F. Gao, “Delay-range- dependent-based hybrid iterative learning fault-tolerant guaranteed cost control for multiphase batch processes,” Industrial & Engineering Chemistry Research, vol. 57, no. 8, pp. 2932–2944, 2018.

    Google Scholar 

  34. X. Jiang and Q. L. Han, “New stability criteria for linear systems with interval time-varying delay,” Automatica, vol. 44, no. 10, pp. 2680–2685, 2008.

    MathSciNet  MATH  Google Scholar 

  35. Y. S. Lee, Y. S. Moon, W. H. Kwon, and P. Park, “Delay-dependent robust control for uncertain systems with a state-delay,” Automatica, vol. 40, no. 1, pp. 65–72, 2004.

    MathSciNet  MATH  Google Scholar 

  36. T. Liu and F. R. Gao, “Robust two-dimensional iterative learning control for batch processes with state delay and time-varying uncertainties,” Chemical Engineering Science, vol. 65, no. 23, pp. 6134–6144, 2010.

    Google Scholar 

  37. L. M. Wang, R. D. Zhang, and F. R. Gao, Iterative Learning Stabilization and Fault-tolerant Control for Batch Processes, Springer Nature Singapore Pte LtdSingapore. 2020.

    MATH  Google Scholar 

  38. J. Wang, K. Shi, Q. Huang, S. Zhong, and D. Zhang, “Stochastic switched sampled-data control for synchronization of delay chaotic neural networks with packet dropout,” Applied Mathematics and Computation, vol. 335, pp. 211–230, 2018.

    MathSciNet  Google Scholar 

  39. K. Shi, J. Wang, Y. Tang, and S. Zhong, “Reliable asynchronous sampled-data filtering of T-S fuzzy uncertain delayed neural networks with stochastic switched topologies,” Fuzzy Sets and Systems, 2018. DOI: 10.1016/j.fss.2018.11.017

    Google Scholar 

  40. J. Qiu, Y. Xia, H. Yang, and J. Zhang, “Robust stabilisation for a class of discrete-time systems with time-varying delays via delta operators,” IET Control Theory and Application, vol. 2, no. 1, pp. 87–93, 2008.

    MathSciNet  Google Scholar 

  41. J. Qiu, Y. Wei, H. R. Karimi, and H. Gao, “Reliable control of discrete-time piecewise-affine time-delay systems via output feedback,” IEEE Transactions on Reliability, vol. 67, no. 1, pp. 79–91, 2018.

    Google Scholar 

  42. K. Shi, Y. Tang, S. Zhong, C. Yin, X. Huang, and W. Wang, “Nonfragile asynchronous control for uncertain chaotic Lurie network systems with Bernoulli stochastic process,” International Journal of Robust and Nonlinear Control, vol. 28, no. 5, pp. 1693–1714, 2018.

    MathSciNet  MATH  Google Scholar 

  43. J. Qiu, K. Sun, T. Wang, and H. Gao, “observer-based fuzzy adaptive event-triggered control for pure-feedback nonlinear systems with prescribed performance,” IEEE Transactions on Fuzzy Systems, 2019. DOI: 10.1109/TFUZZ.2019.2895560

    Google Scholar 

  44. K. Shi, J, Wang, S. Zhong, X. Zhang, Y. Liu, and J. Cheng, “New reliable nonuniform sampling control for uncertain chaotic neural networks under markov switching topologies,” Applied Mathematics and Computation, vol. 347, pp. 169–193, 2019.

    MathSciNet  Google Scholar 

  45. J. Qiu, Y. Wei, and L. Wu, “A novel approach to reliable control of piecewise affine systems with actuator faults,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 64, no. 8, pp. 957–961, 2017.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Hainan Normal University, Haikou, 571158, China

    Weiyan Yu & Jiang Song

  2. School of Sciences, Liaoning Shihua University, Fushun, 113001, China

    Jingxian Yu

Authors
  1. Weiyan Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiang Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jingxian Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jingxian Yu.

Additional information

Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Ohmin Kwon under the direction of Editor Jessie (Ju H.) Park. This work is supported by Hainan Provincial Natural Science Foundation of China under Grant (619MS052, 2018CXTD338) and National Natural Science Foundation of China under Grants (11461018, 61773190).

Weiyan Yu received her Doctor degree in pure mathematics from Shaanxi Normal University, Xian, China, in 2011. She is currently a professor at college of mathematic and statistics, Hainan Normal University, Haikou, China. She is very interested in functional analysis and its applications.

Jiang Song is currently a master student with the School of Mathematics and Statistics, Hainan Normal University. His current research interests include batch process control, fault-tolerant control and fault diagnosis.

Jingxian Yu received his M.S. degree in probability and statistics from Northeastern University, Shenyang, China, in 2008. He is currently a lecturer at College of Science, Liaoning Shihua University, Funshun, China. He is good at programming with MATLAB and very interested in programming problems in control engineering.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yu, W., Song, J. & Yu, J. Robust Hybrid Controller Design for Batch Processes with Time Delay and Its Application in Industrial Processes. Int. J. Control Autom. Syst. 17, 2881–2894 (2019). https://doi.org/10.1007/s12555-019-0103-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-019-0103-8

Keywords

Search

Navigation