Characteristic analysis and optimal control of the thickness and tension system on tandem cold rolling

  • Yun-Jian Hu
  • Jie SunEmail author
  • Qing-Long Wang
  • Fang-Chen Yin
  • Dian-Hua Zhang


The tandem cold-rolling process is a multivariable, nonlinear, and strongly coupled complex control procedure, in which the key technologies of automatic gauge control (AGC) and automatic tension control (ATC) are extremely comprehensive, and high precision is required. This paper analyzes the rolling characteristics of tandem cold-rolling process and proposes an innovative multivariable optimization strategy based on inverse linear quadratic (ILQ) optimal control theory for thickness and tension control. First, a new state space model of the tandem cold-rolling process was introduced and verified based on the basic equations of rolling technology and field data. Then, meaningful influence rules on the complex rolling process were obtained by analyzing rolling characteristics. For the complex rolling process, a novel ILQ control strategy was introduced into the thickness and tension control system. As a result, by a series of experiments, the effect of disturbance on the thickness and tension was attenuated to an arbitrary degree of accuracy through the proposed control strategy. Simulation results showed the excellent control performance of the proposed ILQ control strategy compared with the conventional proportion and integration (PI) control strategy.


State space model Tandem cold-rolling Thickness control Tension control ILQ 


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Funding information

This work was supported by the National Key R&D Program of China (2017YFB0304100), the National Natural Science Foundation of China (51774084, 51634002), and the Fundamental Research Funds for the Central Universities (N160704004, N170708020).


  1. 1.
    Kimura Y, Sodani Y, Nishiura N, Ikeuchi N, Mihara Y (2003) Analysis of chatter in tandem cold rolling mills. ISIJ Int 43(1):77–84. CrossRefGoogle Scholar
  2. 2.
    Takami KM, Mahmoudi J, Dahlquist E (2010) Adaptive control of cold rolling system in electrical strips production system with online-offline predictors. Int J Adv Manuf Technol 50(9-12):917–930. CrossRefGoogle Scholar
  3. 3.
    Zhang X, Chen SZ, ZHANG HY, Zhang XW, Zhang DH, Sun J (2014) Modeling and analysis of interstand tension control in 6-high tandem cold rolling mill. J Iron Steel Res Int 21(9):830–836. CrossRefGoogle Scholar
  4. 4.
    Bu HN, Yan ZW, Zhang DH (2017) A novel approach to improve the computing accuracy of rolling force and forward slip. Ironmak Steelmak, 1–8.
  5. 5.
    Guo RM (1991) Evaluation of dynamic characteristics of HAGC system. Iron Steel Eng 68(7):52–61Google Scholar
  6. 6.
    Pires CTA, Ferreira HC, Sales RM, Silva MA (2006) Set-up optimization for tandem cold mills: a case study. J Mater Process Technol 173(3):368–375. CrossRefGoogle Scholar
  7. 7.
    Asano K, Morari M (1998) Interaction measure of tension-thickness control in tandem cold rolling. Control Eng Pract 6(8):1021-1027
  8. 8.
    Reddy NV, Suryanarayana G (2001) A set-up model for tandem cold rolling mills. J Mater Process Technol 116(2):269–277. CrossRefGoogle Scholar
  9. 9.
    Geddes EJM (1994) Multivariable control of a high performance tandem cold rolling mill. In: Proceedings of the 1994 International Conference on Control-Control '94, UK,Coventry, pp 202-207.
  10. 10.
    Geddes EJM, Postlethwaite I (1998) Improvements in product quality in tandem cold rolling using robust multivariable control. IEEE Trans Control Syst Technol 6(2):257–269. CrossRefGoogle Scholar
  11. 11.
    Pittner J, Simaan MA, Samaras NS (2007) A novel approach for optimal control of continuous tandem cold metal rolling. In: Proceedings of the 42nd Industry Applications Annual Meeting, USA, New Orleans, LA, pp 374–381.
  12. 12.
    Pittner J, Simaan MA (2008) Optimal control of tandem cold rolling using a pointwise linear quadratic technique with trims. J Dyn Sys, Meas, Control 130(2):021006–1–021006–11. CrossRefGoogle Scholar
  13. 13.
    Takami KM, Mahmoudi J, Dahlquist E, Lindenmo M (2011) Multivariable data analysis of a cold rolling control system to minimise defects. Int J Adv Manuf Technol 54(5–8):553–565. CrossRefGoogle Scholar
  14. 14.
    Ozaki K, Ohtsuka T, Fujimoto K, Kitamura A, Nakayama M (2009) Nonlinear receding horizon control of a tandem cold mill in acceleration and deceleration conditions. In: Proceedings of the 2009 ICCAS-SICE. IEEE, Fukuoka, pp 2158–2163Google Scholar
  15. 15.
    Fujita N, Kimura Y (2012) Influence of plate-out oil film on lubrication characteristics in cold rolling. ISIJ Int 52(5):850–857.
  16. 16.
    Fujita N, Kimura Y, Kobayashi K, Itoh K, Amanuma Y, Sodani Y (2016) Dynamic control of lubrication characteristics in high speed tandem cold rolling. J Mater Process Technol 229:407–416. CrossRefGoogle Scholar
  17. 17.
    Rigler GW, Aberl HR, Staufer W, Aistleitner K (1996) Improved rolling mill automation by means of advanced control techniques and dynamic simulation. IEEE Trans Ind Appl 32(3):599–607. CrossRefGoogle Scholar
  18. 18.
    Ratnoo A, Ghose D (2015) State-dependent Riccati-equation-based guidance law for impact-angle-constrained trajectories. J Guid Control Dyn 32(1):320–326. CrossRefGoogle Scholar
  19. 19.
    Aboukandil H, Freiling G, Ionescu V, Jank G (2003) Matrix Riccati equations in control and systems theory. IEEE Trans Automat Contr 49 (10):2094–2095.
  20. 20.
    Zhang X, Zhang Q, Sun C (2009) Gauge and tension control in unsteady state of cold rolling using mixed H 2 /H control. In: Proceedings of the 2009 IEEE International Conference on Control and Automation, New Zealand, Christchurch, pp 2072–2076.
  21. 21.
    Poursina M, Rahmatipour M, Mirmohamadi H (2015) A new method for prediction of forward slip in the tandem cold rolling mill. Int J Adv Manuf Technol 78(9–12):1827–1835. CrossRefGoogle Scholar
  22. 22.
    Kadoya Y, Ooi T, Washikita Y, Seki Y (1999) Strip gage and tension control at cold tandem mill based on ILQ design theory. In: Proceedings of the 1999 IEEE International Conference on Control Applications, USA, Kohala Coast, Hi, pp 23–28.
  23. 23.
    Gokcek C, Kabamba PT, Meerkov SM (2001) An LQR/LQG theory for systems with saturating actuators. IEEE Trans Autom Control 46(10):1529–1542. MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Fujii T (1987) A new approach to the LQ design from the viewpoint of the inverse regulator problem. IEEE Trans Autom Control 32(11):995–1004. MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  • Yun-Jian Hu
    • 1
  • Jie Sun
    • 1
    Email author
  • Qing-Long Wang
    • 1
  • Fang-Chen Yin
    • 1
  • Dian-Hua Zhang
    • 1
  1. 1.The State Key Laboratory of Rolling and AutomationNortheastern UniversityShenyangPeople’s Republic of China

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