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

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Abstract

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.

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References

  • 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.

    Article  Google Scholar 

  • Moore, K. L. (1999). Iterative learning control—an expository overview. Applied Computational Controls, Signals Processing Circuits, 1, 151–241.

    Article  Google Scholar 

  • Gopinath, S., & Kar, I. N. (2004). Iterative learning control scheme for manipulators including actuator dynamics. Mechanism and Machine Theory, 39, 1367–1384.

    Article  MATH  MathSciNet  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

  • 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.

    Article  Google Scholar 

  • 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 

  • Gao, F. R., Yang, Y., & Shao, C. (2001). Robust iterative learning control with applications to injection molding process. Chemical Engineering Science, 56, 7025–7034.

    Article  Google Scholar 

  • Yang, Y., Yao, K., & Gao, F. R. (2012). Overall control system for injection molding process. Interational Polymer Processing, 27, 40–59.

    Article  Google Scholar 

  • 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).

  • 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.

    Article  Google Scholar 

  • Shaw, W. T. (1982). Computer control of batch processes. Cockeysville, MD: EMC Controls Inc.

    Google Scholar 

  • Lee, J. H., & Lee, K. S. (2007). Iterative learning control applied to batch processes: An overview. Control Engineering Practice, 15, 1306–1318.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Amann, N., Owens, D. H., & Rogers, E. (1996). Iterative learning control using optimal feedback and feedforward actions. International Journal of Control, 65, 277–293.

    Article  MATH  MathSciNet  Google Scholar 

  • Moon, J., Doh, T., & Chung, M. J. (1998). A robust approach to iterative learning control design for uncertain systems. Automatica, 34, 1001–1004.

    Article  MATH  MathSciNet  Google Scholar 

  • Kaczorek, T. (1985). Two-dimensional linear systems. Berlin: Springer.

    MATH  Google Scholar 

  • 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.

    Article  MATH  MathSciNet  Google Scholar 

  • Rogers, E., & Owens, D. H. (1994). 2D systems theory and applications—a maturing area. In Proceedings of international conference control (pp. 63–69).

  • 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).

  • 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.

    Article  MATH  MathSciNet  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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).

  • 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).

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

  • 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.

  • 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.

    Article  Google Scholar 

  • Wang, Y., Yang, Y., & Zhao, Z. (2013). Robust stability analysis for an enhanced ILC-based PI controller. Journal of Process Control, 23, 201–214.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MATH  MathSciNet  Google Scholar 

  • 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).

  • Xu, J. X., & Xu, J. (2002). Iterative learning control for non-uniform trajectory tracking problems. In Proceedings of IFAC 15th world congress.

  • The Society of the Plastics Industry Website “About SPI”. (2012). http://www.plasticsindustry.org.

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Acknowledgments

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)

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Authors and Affiliations

  1. Department of Chemical and Biochemical Engineering, School of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian, People’s Republic of China

    Jia Shi, Zhikai Cao & Hua Zhou

  2. Department of Control Science and Engineering, Zhejiang University, Hangzhou, Zhejiang, People’s Republic of China

    Bo Yang & Yi Yang

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  1. Jia Shi
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  2. Bo Yang
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  3. Zhikai Cao
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  4. Hua Zhou
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  5. Yi Yang
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Correspondence to Yi Yang.

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Shi, J., Yang, B., Cao, Z. et al. Two-dimensional generalized predictive control (2D-GPC) scheme for the batch processes with two-dimensional (2D) dynamics. Multidim Syst Sign Process 26, 941–966 (2015). https://doi.org/10.1007/s11045-015-0336-5

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