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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
Article

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.

Keywords

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

Notes

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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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

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