This work was supported by National Natural Science Foundation of China (No. 61473012).
Recommended by Guest Editor Rong-Hu Chi
The repetitive control (RC) or repetitive controller problem for nonminimum phase nonlinear systems is both challenging and practical. In this paper, we consider an RC problem for the translational oscillator with a rotational actuator (TORA), which is a nonminimum phase nonlinear system. The major difficulty is to handle both a nonminimum phase RC problem and a nonlinear problem simultaneously. For such purpose, a new RC design, namely the additive-state-decomposition-based approach, is proposed, by which the nonminimum phase RC problem and the nonlinear problem are separated. This makes RC for the TORA benchmark tractable. To demonstrate the effectiveness of the proposed approach, a numerical simulation is given.
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R. W. Longman. On the theory and design of linear repetitive control system.
European Journal of Control, vol. 16, no. 5, pp. 447–496, 2010.
J. V. Flores, J. M. Gomes Da Silva Jr., L. F. A. Pereira, D. Sbarbaro. Repetitive control design for mimo systems with saturating actuators.
IEEE Transactions on Automatic Control, vol. 57, no. 1, pp. 192–198, 2012.
L. Zhou, J. H. She, M. Wu. Design of a discrete-time output-feedback based repetitive-control system.
International Journal of Automation and Computing, vol. 10, no. 4, pp. 343–349, 2013.
Y. F. Shan, K. K. Leang. Accounting for hysteresis in repetitive control design: Nanopositioning example.
Automatica, vol. 48, no. 8, pp. 1751–1758, 2012.
W. Z. Lu, K. L. Zhou, D. W. Wang. General parallel structure digital repetitive control.
International Journal of Control, vol. 86, no. 1, pp. 70–83, 2013.
Q. Quan, K. Y. Cai. A survey of repetitive control for nonlinear systems.
Science Foundation in China, vol. 18, no. 2, pp. 45–53, 2010.
Z. Yang, S. C. P. Yam, L. K. Li, Y. W. Wang. Universal repetitive learning control for nonparametric uncertainty and unknown state-dependent control direction matrix.
IEEE Transactions on Automatic Control, vol. 55, no. 7, pp. 1710–1715, 2010.
Q. Quan, K. Y. Cai. A filtered repetitive controller for a class of nonlinear systems.
IEEE Transactions on Automatic Control, vol. 56, no. 2, pp. 399–405, 2011.
C. X. Hu, B. Yao, Z. Chen, Q. F. Wang. Adaptive robust repetitive control of an industrial biaxial precision gantry for contouring tasks.
IEEE Transactions on Control Systems Technology, vol. 19, no. 6, pp. 1559–1568, 2011.
M. X. Sun. Partial-period adaptive repetitive control by symmetry.
Automatica, vol. 48, no. 9, pp. 2137–2144, 2012.
C. J. Wan, D. S. Bernstein, V. T. Coppola. Global stabilization of the oscillating eccentric rotor.
Nonlinear Dynamics, vol. 10, no. 1, pp. 49–62, 1996.
J. X. Zhao, I. Kanellakopoulos. Flexible backstepping design for tracking and disturbance attenuation.
International Journal of Robust and Nonlinear Control, vol. 8, no. 4–5, pp. 331–348, 1998.
Q. Quan, K. Y. Cai, H. Lin. Additive-state-decomposition-based tracking control framework for a class of nonminimum phase systems with measurable nonlinearities and unknown disturbances.
International Journal of Robust and Nonlinear Control, vol. 25, no. 2, pp. 163–178, 2015.
Q. Quan, K. Y. Cai. Additive-state-decomposition-based tracking control for TORA benchmark.
Journal of Sound and Vibration, vol. 332, no. 20, pp. 4829–4841, 2013.
J. Huang, G. Q. Hu. Control design for the nonlinear benchmark problem via the output regulation method.
Journal of Control Theory and Applications, vol. 2, no. 1, pp. 11–19, 2013.
A. Pavlov, B. Janssen, N. van de Wouw, H. Nijmeijer. Experimental output regulation for a nonlinear benchmark system.
IEEE Transactions on Control Systems Technology, vol. 15, no. 4, pp. 786–793, 2007.
C. Fabio. Output regulation for the TORA benchmark via rotational position feedback.
Automatica, vol. 47, no. 3, pp. 584–590, 2011.
W. Y. Lan, B. M. Chen, Z. T. Ding. Adaptive estimation and rejection of unknown sinusoidal disturbances through measurement feedback for a class of non-minimum phase nonlinear MIMO systems.
International Journal of Adaptive Control and Signal Processing, vol. 20, no. 2, pp. 77–97, 2006.
Y. Jiang, J. Huang. Output regulation for a class of weakly minimum phase systems and its application to a nonlinear benchmark system. In
Proceedings of the American Control Conference, IEEE, Saint. Louis, USA, pp. 5321–5326, 2009.
H. K. Khalil.
Nonlinear Systems, New York, USA: Prentice-Hall, 2002.
H. J. Sussmann, E. D. Sontag, Y. Yang. A general result on the stabilization of linear systems using bounded controls.
IEEE Transactions on Automatic Control, vol. 39, no. 12, pp. 2411–2425, 1994.
Über diesen Artikel
Repetitive control for TORA benchmark: An additive-state-decomposition-based approach
Quan Quan Kai-Yuan Cai
Institute of Automation, Chinese Academy of Sciences