Multidimensional Systems and Signal Processing

, Volume 26, Issue 4, pp 941–966 | Cite as

Two-dimensional generalized predictive control (2D-GPC) scheme for the batch processes with two-dimensional (2D) dynamics

  • Jia Shi
  • Bo Yang
  • Zhikai Cao
  • Hua Zhou
  • Yi Yang


Iterative learning control (ILC) system is essentially a special feedback control system with two-dimensional (2D) dynamics that can be designed and optimized under the framework of 2D system theories. Motivated by this viewpoint, it is proposed in this paper to describe a batch process with 2D dynamics directly using a 2D controlled auto-regressive moving average model, and then, design a 2D feedback controller, referred to as two-dimensional generalized predictive control, in the framework of model predictive control. The proposed design method naturally results in an ILC algorithm when the process is assumed as a one dimensional process performing a given task repetitively and guarantees the better control performance along cycle by utilizing the cycle-wise dynamics of the process. The proposed control scheme is the further generalization and extension of the two-dimensional generalized predictive iterative learning control scheme which has been developed in the previous works. It solves the problem in some degree that conventional ILC cannot guarantee the convergence when there are non-repeatable dynamics in the processes and/or in desired trajectories. The effectiveness and the applicability are illustrated by the comparisons of the simulation results and the experimental results on packing pressure control of the injection molding process.


Two-dimensional (2D) systems Iterative learning control (ILC) Generalized predictive control (GPC) Batch processes Injection molding 



The authors gratefully acknowledge the financial support of National Natural Science Foundation of China (Nos. 61174093, 61273145), Guangdong Innovative and Entrepreneurial Research Team Program (No. 2013G076), and Shenzhen Technology Research Program (No. JSGG 20130624101448362)


  1. Ahn, H., Chen, Y., & Moore, K. L. (2007). Iterative learning control—brief survey and categorization. IEEE Transactions on Systems, Man, and Cybernetics-Part C: Applications and Reviews, 37, 1090–1121.CrossRefGoogle Scholar
  2. Moore, K. L. (1999). Iterative learning control—an expository overview. Applied Computational Controls, Signals Processing Circuits, 1, 151–241.CrossRefGoogle Scholar
  3. Gopinath, S., & Kar, I. N. (2004). Iterative learning control scheme for manipulators including actuator dynamics. Mechanism and Machine Theory, 39, 1367–1384.MATHMathSciNetCrossRefGoogle Scholar
  4. Mezghani, M., Roux, G., Cabassud, M., et al. (2002). Application of iterative learning control to an exothermic semibatch chemical reactor. IEEE Transactions on Control Systems Technology, 10, 822–834.CrossRefGoogle Scholar
  5. Youssef, C. B., Waissman, J., & Vazquez, G. (2003). An Iterative learning control strategy for a fedbatch phenol degradation reactor. In Proceedings of IASTED international conference on circuits, signals, systems.Google Scholar
  6. Xiong, Z., & Zhang, J. (2003). Product quality trajectory tracking in batch processes using iterative learning control based on time-varying perturbation models. Industrial and Engineering Chemistry Research, 42, 6802–6814.CrossRefGoogle Scholar
  7. Youssef, B. C., & Zepeda, A. (2012). Iterative learning estimation of a parameterized input trajectory to control fedbatch fermentation processes: A case study. Revista Mexicana de Ingenieria Quimica, 11, 351–362.Google Scholar
  8. Gao, F. R., Yang, Y., & Shao, C. (2001). Robust iterative learning control with applications to injection molding process. Chemical Engineering Science, 56, 7025–7034.CrossRefGoogle Scholar
  9. Yang, Y., Yao, K., & Gao, F. R. (2012). Overall control system for injection molding process. Interational Polymer Processing, 27, 40–59.CrossRefGoogle Scholar
  10. Solomon, P. R., Rosenthal, P., Spartz, M., et al. (2001). Advanced process control in semiconductor manufacturing. In Proceedings of annual quality congress proceedings (pp. 185–187).Google Scholar
  11. Su, A., Jeng, J., Huang, H., et al. (2007). Control relevant issues in semiconductor manufacturing—overview with some new results. Control Engineering Practice, 15, 1268–1279.CrossRefGoogle Scholar
  12. Shaw, W. T. (1982). Computer control of batch processes. Cockeysville, MD: EMC Controls Inc.Google Scholar
  13. Lee, J. H., & Lee, K. S. (2007). Iterative learning control applied to batch processes: An overview. Control Engineering Practice, 15, 1306–1318.CrossRefGoogle Scholar
  14. Shi, J., Gao, F. R., & Wu, T. J. (2005). Robust design of integrated feedback and iterative learning control of a batch process based on a 2D Roesser system. Journal of Process Control, 15, 907–924.CrossRefGoogle Scholar
  15. Amann, N., Owens, D. H., & Rogers, E. (1996). Iterative learning control using optimal feedback and feedforward actions. International Journal of Control, 65, 277–293.MATHMathSciNetCrossRefGoogle Scholar
  16. Moon, J., Doh, T., & Chung, M. J. (1998). A robust approach to iterative learning control design for uncertain systems. Automatica, 34, 1001–1004.MATHMathSciNetCrossRefGoogle Scholar
  17. Kaczorek, T. (1985). Two-dimensional linear systems. Berlin: Springer.MATHGoogle Scholar
  18. Kurek, J. E., & Zaremba, M. B. (1993). Iterative learning control synthesis based on 2-D system theory. Ieee Transactions on Automatic Control, 38, 121–125.MATHMathSciNetCrossRefGoogle Scholar
  19. Rogers, E., & Owens, D. H. (1994). 2D systems theory and applications—a maturing area. In Proceedings of international conference control (pp. 63–69).Google Scholar
  20. Amann, N., Owens, D. H., & Rogers, E. (1994). 2D systems theory applied to learning control systems. In Proceedings of conference on decision and control (pp. 985–986).Google Scholar
  21. Owens, D. H., Amann, E. R. N., & French, M. (2000). Analysis of linear iterative learning control schemes—a 2D systems/repetitive processes approach. Multidimensional Systems and Signal Processing, 11, 125–177.MATHMathSciNetCrossRefGoogle Scholar
  22. Fang, Y., & Chow, T. W. S. (2003). 2-D analysis for iterative learning controller for discrete-time systems with variable initial conditions. IEEE Transactions on Circuits and Systems I-Fundamental Theory and Applications, 50, 722–727.CrossRefGoogle Scholar
  23. French, M., Rogers, E., Wibowo, H., et al. (2001). A 2D systems approach to iterative learning control based on nonlinear adaptive control techniques. In Proceedings of 2001 IEEE international symposium circuits system (pp. 429–432).Google Scholar
  24. Shi, J., Gao, F. R., & Wu, T. J. (2006). 2D model predictive iterative learning control schemes for batch processes. In Proceedings of IFAC international symposium on advanced control of chemical processes 2006 (pp. 215–220).Google Scholar
  25. Shi, J., Gao, F. R., & Wu, T. J. (2006). From two-dimensional linear quadratic optimal control to iterative learning control. Paper 1. Two-dimensional linear quadratic optimal controls and system analysis. Industrial and Engineering Chemistry Research, 45, 4603–4616.CrossRefGoogle Scholar
  26. Shi, J., Gao, F. R., & Wu, T. J. (2006). From two-dimensional linear quadratic optimal control to iterative learning control. Paper 2. Iterative learning controls for batch processes. Industrial and Engineering Chemistry Research, 45, 4617–4628.CrossRefGoogle Scholar
  27. Shi, J., Gao, F. R., & Wu, T. J. (2007). Single-cycle and multi-cycle generalized 2D model predictive iterative learning control (2D-GPILC) schemes for batch processes. Journal of Process Control, 17, 715–727.CrossRefGoogle Scholar
  28. Shi, J., Gao, F. R., & Wu, T. J. (2007). Higher-order generalized 2D predictive iterative learning control schemes. In Proceedings of 8th international symposium on dynamics and control of process systems, DYCOPS2007.Google Scholar
  29. Yang Y., Shi J., & Gao, F. R. (2012). Injection velocity control using 2D model predictive iterative learning algorithm. In Proceedings of the SPE ANTEC@NPE2012 conference.Google Scholar
  30. Wang, Y., Liu, T., & Zhao, Z. (2012). Advanced PI control with simple learning set-point design: Application on batch processes and robust stability analysis. Chemical Engineering Science, 71, 153–165.CrossRefGoogle Scholar
  31. Wang, Y., Yang, Y., & Zhao, Z. (2013). Robust stability analysis for an enhanced ILC-based PI controller. Journal of Process Control, 23, 201–214.CrossRefGoogle Scholar
  32. Wang, L., Mo, S., Zhou, D., et al. (2013). Delay-range-dependent robust 2D iterative learning control for batch processes with state delay and uncertainties. Journal of Process Control, 23, 715–730.CrossRefGoogle Scholar
  33. Wang, L., Mo, S., Qu, H., & Gao, F. R. (2013). \(H_\infty \) Design of 2D controller for batch processes with uncertainties and interval time-varying delays. Control Engineering Practice, 21, 1321–1333.CrossRefGoogle Scholar
  34. Liu, T., Wang, X. Z., & Chen, J. (2014). Robust PID based indirect-type iterative learning control for batch processes with time-varying uncertainties. Journal of Process Control, 12, 95–106.CrossRefGoogle Scholar
  35. Hladowski, L., Galkowski, K., Cai, Z., et al. (2010). Experimentally supported 2D systems based iterative learning control law design for error convergence and performance. Control Engineering Practice, 18(4), 339–348.CrossRefGoogle Scholar
  36. Cichy, B., Gałkowski, K., & Rogers, E. (2014). 2D systems based robust iterative learning control using noncausal finite-time interval data. Systems and Control Letters, 64, 36–42.MATHMathSciNetCrossRefGoogle Scholar
  37. Shi, J., Gao, F. R., Jiang, Q., et al. (2009). A design framework for iterative learning control (ILC) based on 2-dimensional model predictive control (2D-MPC). In Proceedings of the 21st Chinese control and decision conference (2009 CCDC) (pp. 1746–1751).Google Scholar
  38. Xu, J. X., & Xu, J. (2002). Iterative learning control for non-uniform trajectory tracking problems. In Proceedings of IFAC 15th world congress.Google Scholar
  39. The Society of the Plastics Industry Website “About SPI”. (2012).

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Jia Shi
    • 1
  • Bo Yang
    • 2
  • Zhikai Cao
    • 1
  • Hua Zhou
    • 1
  • Yi Yang
    • 2
  1. 1.Department of Chemical and Biochemical Engineering, School of Chemistry and Chemical EngineeringXiamen UniversityXiamenPeople’s Republic of China
  2. 2.Department of Control Science and EngineeringZhejiang UniversityHangzhouPeople’s Republic of China

Personalised recommendations