Abstract and Applied Analysis

Robust Backstepping Control for Cold Rolling Main Drive System with Nonlinear Uncertainties

Xu Yang, Kai-xiang Peng, and Chao-nan Tong

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The nonlinear model of main drive system in cold rolling process, which considers the influence with parameter uncertainties such as clearance and variable friction coefficient, as well as external disturbance by roll eccentricity and variation of strip material quality, is built. By transformation, the lower triangular structure form of main drive system is obtained. The backstepping algorithm based on signal compensation is proposed to design a linear time-invariant (LTI) robust controller, including a nominal controller and a robust compensator. A comparison with PI controller shows that the controller has better disturbance attenuation performance and tracking behaviors. Meanwhile, according to its LTI characteristic, the robust controller can be realized easily; therefore it is also appropriated to high speed dynamic rolling process.

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Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 387890, 7 pages.

First available in Project Euclid: 26 February 2014

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Yang, Xu; Peng, Kai-xiang; Tong, Chao-nan. Robust Backstepping Control for Cold Rolling Main Drive System with Nonlinear Uncertainties. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 387890, 7 pages. doi:10.1155/2013/387890. https://projecteuclid.org/euclid.aaa/1393450221

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  • J. X. Zou and L. J. Xu, Vibration in Rolling Mills, pp. 88–107, Metallurgical Industry Press, Beijing, China, 1998, (Chinese).
  • X. Yang and C. N. Tong, “Coupling dynamic model and control of chatter in cold rolling,” Journal of Dynamic Systems, Measurement and Control-Transactions of the ASME, vol. 134, no. 4, Article ID 041001, 8 pages, 2012.
  • M. N. Skripalenko, M. M. Skripalenko, D. A. Ashikhmin et al., “Wavelet analysis of fluctuations in the thickness of cold-rolled strip,” Metallurgist, vol. 57, no. 7-8, pp. 606–611, 2013.
  • P. V. Krot, “Transient torsional vibrations control in the geared drive trains of the hot rolling mills,” in Proceedings of the IEEE Conference on Control Application, Part of 2009 IEEE Multi-Conference on System and Control, pp. 1368–1373, July 2009.
  • V. Panjković, R. Gloss, J. Steward, S. Dilks, R. Steward, and G. Fraser, “Causes of chatter in a hot strip mill: observations, qualitative analyses and mathematical modelling,” Journal of Materials Processing Technology, vol. 212, no. 4, pp. 954–961, 2012.
  • Y. Kimura, Y. Sodani, N. Nishiura, N. Ikeuchi, and Y. Mihara, “Analysis of chatter in tandem cold rolling mills,” ISIJ International, vol. 43, no. 1, pp. 77–84, 2003.
  • I. Prihod'ko, P. Krot, K. Solov'yov et al., “Vibration monitoring system and the new methods of chatter early diagnostics for tandem mill control,” in Proceedings of the International Conference on Vibration in Rolling Mills, pp. 87–106, London, UK, 2006.
  • Z. J. Huang, L. X. Gao, and Y. F. Liao, Machinery Vibration Monitoring and Fault Diagnosis, pp. 45–80, Chemical industry Press, Beijing, China, 2010, (Chinese).
  • W. Liang, J. He, S. Yu, W. Long, and X. Cai, “Electromechanical coupling analysis of cold strip steel temper mill,” Journal of Central South University of Technology, vol. 31, no. 1, pp. 78–80, 2000.
  • S. Yin, S. X. Ding, A. Haghani et al., “A comparison study of basic data-driven fault diagnosis and process monitoring methods on the benchmark Tennessee Eastman process,” Journal of Process Control, vol. 22, no. 9, pp. 1567–1581, 2012.
  • H. Dong, Z. Wang, J. Lam, and H. Gao, “Fuzzy-model-based robust fault detection with stochastic mixed time delays and successive packet dropouts,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 42, no. 2, pp. 365–376, 2012.
  • S. X. Ding, “Integrated design of feedback controllers and fault detectors,” Annual Reviews in Control, vol. 33, no. 2, pp. 124–135, 2009.
  • H. Dong, Z. Wang, and H. Gao, “Fault detection for Markovian jump systems with sensor saturations and randomly varying nonlinearities,” IEEE Transactions on Circuits and Systems I, vol. 59, no. 10, pp. 2354–2362, 2012.
  • S. Yin, H. Luo, and S. X. Ding, “Real-time implementation of fault-tolerant control systems with performance optimization,” IEEE Transactions on Industrial Electronics, vol. 61, no. 5, pp. 2402–2411, 2014.
  • R. Zhang and C. Tong, “Torsional vibration control of the main drive system of a rolling mill based on an extended state observer and linear quadratic control,” Journal of Vibration and Control, vol. 12, no. 3, pp. 313–327, 2006.
  • E. J. M. Geddes and I. Postlethwaite, “Improvements in product quality in tandem cold rolling using robust multivariable control,” IEEE Transactions on Control Systems Technology, vol. 6, no. 2, pp. 257–269, 1998.
  • R. Freeman and P. Kokotovic, “Backstepping design of robust controller for a class of nonlinear systems,” Proceedings of the IFAC Nonlinear Control System Design Symposium, pp. 307–312, June 1992.
  • Z. Jiang and D. J. Hill, “A robust adaptive backstepping scheme for nonlinear systems with unmodeled dynamics,” IEEE Transactions on Automatic Control, vol. 44, no. 9, pp. 1705–1711, 1999.
  • N. Yagiz and Y. Hacioglu, “Backstepping control of a vehicle with active suspensions,” Control Engineering Practice, vol. 16, no. 12, pp. 1457–1467, 2008.
  • Y. Yu and Y. Zhong, “Robust backstepping output tracking control for SISO uncertain nonlinear systems with unknown virtual control coefficients,” International Journal of Control, vol. 83, no. 6, pp. 1182–1192, 2010.
  • M. Krstic and M. Bernent, “Non-overshooting control of strict-feedback nonlinear systems,” in Proceedings of the American Control Conference (ACC '07), pp. 4494–4499, July 2007.
  • H. Li, G. Meng, Z. Meng, and B. Wen, “Effects of boundary conditions on a self-excited vibration system with clearance,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 4, pp. 571–580, 2007.
  • P. Hu, H. Zhao, and K. F. Ehmann, “Third-octave-mode chatter in rolling. Part 1: chatter model,” Proceedings of the Institution of Mechanical Engineers B, vol. 22, no. 8, pp. 1267–1277, 2006.
  • X. Yang, C. Tong, G. Yue, and J. Meng, “Coupling dynamic model of chatter for cold rolling,” Journal of Iron and Steel Research International, vol. 17, no. 12, pp. 30–34, 2010.
  • R. C. Zhang, Vibration characteristics analysis and control research of the rolling mill electromechanical coupling system [Ph.D. dissertation], University of Science and Technology, Beijing, China, 2006.
  • S. Mtakula, “An approach of the nonlinear control of rolling mills,” in Proceedings of the Advanced Process Control Application for Industry, Workshop of the IEEE Industry Application Society, pp. 1–8, Vancouver, Canada, 2005. \endinput