Compensation for Input Nonlinearities in Repetitive Control Systems Based on Improved Equivalent-Input-Disturbance Approach
Wenjing Cai*, Min Wu*, †, Jinhua She*,**, and Luefeng Chen*
*School of Automation, China University of Geosciences
Wuhan, Hubei 430074, China
**School of Engneering, Tokyo University of Technology
Hachioji, Tokyo 192-0982, Japan
The equivalent-input-disturbance (EID) approach is used to deal with the problem of tracking period signals for a plant with input actuator nonlinearities in a repetitive control system. First, an EID estimator is constructed by taking the full advantage of an extended state observer (ESO), the design of the ESO is explained. Next, an EID estimate, which represents the synthetic effect of the nonlinearities, is incorporated into a repetitive control law to compensate for the effect caused by the nonlinearities. This method does not require any prior information about the nonlinearities. It guarantees perfect tracking for periodic reference input and satisfactory compensation for input nonlinearities at the same time. Finally, simulation and experimental results show the effectiveness of the method.
-  T. Inoue, S. Iwai, and M. Nakano, “High accuracy control of a proton synchrotron magnet power supply,” Proc. of 8th IFAC World Congress, pp. 3137-3142, 1981.
-  T. Tezuka, T. Yamashita, T. Sato, Y. Abiko, T. Kanai, and M. Sawada, “Application of a new automatic gauge control system for the tandem cold mill,” IEEE Trans. on Industrial Electronics, Vol.38, No.2, pp. 553-558, 2002.
-  J. D. Alvarez, L. J. Yebra, and M. Berenguel, “Repetitive control of tabular heat exchangers,” J. of Process Control, Vol.17, No.9, pp. 689-791, 2007.
-  G. A. Ramos and R. Costa-Castello, “Power factor correction and harmonic compensation using second-order odd-harmonic repetitive control,” IET Control and Applications, Vol.6, No.11, pp. 1633-1644, 2012.
-  K. L. Zhou, D. W. Wang, B. Zhang, and Y. G. Wang, “Plug-in dual-mode-structure repetitive controller for CVCF PMW inverters,” IEEE Trans. on Industrial Electronics, Vol.56, No.3, pp. 784-791, 2008.
-  L. Zhou, J. H. She, M. Wu, Y. He, and S. W. Zhou, “Estimation and rejection of aperiodic disturbance in a modified repetitive-control system,” IET Control Theory and Applications, Vol.8, No.10, pp. 882-889, 2014.
-  M. Wu, L. Zhou, and J. H. She, “Design of observer-based Η robust repetitive-control system.” IEEE Trans. on Automatic Control, Vol.56, No.6, pp. 1452-1457, 2011.
-  M. Wu, Y. H. Lan, J. H. She, and Y. He, “Design of non-fragile guaranteed-cost repetitive-control system based on two-dimensional model,” Asian J. of Contrrol, Vol.14, No.1, pp. 109-124, 2012.
-  D. Recker, P. Kokotovic, D. Rhode, and J. Winkelman, “Adaptive nonlinear control of systems containing a deadzone,” Proc. of the 30th IEEE Conf. on Decision and Control, pp. 2111-2115, 1991.
-  X. S. Wang, C. Y. Su, and H. Hong, “Robust adaptive control of a class of nonlinear systems with unknown dead-zone,” Automatica, Vol.40, No.3, pp. 407-413, 2004.
-  M. Wu, Z. Y. Feng, Y. He, and J. H She, “Improved delay-dependent absolute stability and robust stability for a class of nonlinear systems with a time-varying delay,” Int. J. of Robust and Nonlinear Control, Vol.20, No.6, pp. 694-702, 2010.
-  C. Y. Ning, Y. He, M. Wu, and J. H. She, “Improved razumikhin-type theorem for input-to-state stability of nonlinear time-delay systems,” IEEE Trans. on Automatica Control, Vol.59, No.7, pp. 1983-1988, 2014.
-  W. J. Chen, J. D. Wu, and J. H. She, “Design of compensator for input dead zone of actuator nonlinearities,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.17, No.6, pp. 805-812, 2013.
-  R. R. Selmic and F. L. Lewis, “Deadzone compensation in motion control systems using neural networks,” IEEE Trans. on Automatic Control, Vol.45, No.4, pp. 602-613, 2000.
-  S. Nishikawa and J. Yoneyama, “Guaranteed cost output feedback control of fuzzy systems via LMI approach,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.14, No.6, pp. 567-573, 2010.
-  H. G. Han, “Adaptive controller for T-S fuzzy model with modeling error,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.15, No.7, pp. 759-766, 2011.
-  S. Hara, T. Omata, and M. Nakano, “Synthesis of repetitive control systems and its applications,” Proc. of the 24th IEEE Conf. on Decision and Control, New York, USA, pp. 1387-1392, 1985.
-  H. Hikita, M. Yamashita, and Y. Kubota, “Repetitive control for a class of nonlinear systems,” JSME Int. J., Vol.36, No.4, pp. 430-434, 1993.
-  J. Ghosh and S. Barbara, “Application of repetitive controllers to nonlinear plants,” Proc. of the American Control Conf., Vol.5, pp. 2692-2697, 1998.
-  J. H. She, M. X. Fang, Y. Ohyama, H. Hashimoto, and M. Wu, “Improving disturbance- rejection performance based on an equivalent-input-disturbance approach,” IEEE Trans. on Industrial Electronics. Vol.55, No.1, pp. 380-389, 2008.
-  R. J. Liu, M. Wu, G. P. Liu, and J. H. She, “Active disturbance-rejection control based on an improved equivalent-input-disturbance approach,” IEEE/ ASME Trans. on Mechatronics, Vol.18, No.4, pp. 1410-1413, 2013.
-  J. Q. Liu, W. J. Chen, M. Wu, J. H. She, and Y. He, “Compensation in repetitive control system for aperiodic disturbances and input dead zone,” Preprints of the 19th Int. Federation of Automatica Control, pp. 2752-2757, 2014.
-  J. Q. Han, “A class of uncertain extended state observer,” Control and Decision, Vol.10, No.1, pp. 85-88, 1995.
-  S. H. Li, J. Yang, W. H. Chen, and X. S. Chen, “Generalized extended state observer based control for systems with mismatched uncertainties,” IEEE Trans. on Industrial Electronics, Vol.59, No.12, pp. 4792-4802, 2012.
-  J. H. She, A. Zhang, X. Lai, and M. Wu, “Global stabilization of 2-DOF underactuated mechanical systems – an equivalent-input-disturbance approach,” Nonlinear Dynamics, Vol.69, pp. 495-509, 2012.
-  M. Wu, B. G. Xu, W. H. Cao, and J. H. She, “Aperiodic disturbance rejection in repetitive-control systems,” IEEE Trans. on Control Systems Technology, Vol.22, No.3, pp. 1044-1051, 2014.
-  R. J. Liu, G. P. Liu, M. Wu, F. C. Xiao, and J. H. She, “Robust disturbance rejection based on equivalent-input-disturbance approach,” IET Control Theory and Applications, Vol.7, No.9, pp. 1261-1268, 2013.
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 International License.