Abstract
In this paper, operator based robust control for nonlinear uncertain system with unknown backlash-like hysteresis is considered. In detail, a continuous backlash-like hysteresis operator is proved to be corresponding to a one-to-one operator, that is, it is suitable to be used in operator theoretic based control theory. Moreover, an internal model control (IMC) structure with one parallel compensating operator is proposed for nonlinear uncertain system with unknown backlash-like hysteresis. Based on the proposed control scheme, the designed system is robustly stable and the desired output tracking performance can be realized simultaneously. Finally, a simulation example about nonlinear plant preceded by backlash is given to show the design procedure of the proposed method.
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G. Tao and P. V. Kokotovic, Adaptive Control of Systems with Actuator and Sensor Nonlinearities, John Wiley & Sons, Inc., 1996. [click]
G. Tao and F. L. Lewis, Adaptive Control of Nonsmooth Dynamic Systems, Springer-Verlag, New York, 2001. [click]
C.Y. Su, Y. Stepanenko, J. Svoboda, and T. P. Leung, “Robust adaptive control of a class of nonlinear systems with unknown backlash-Like hysteresis,” IEEE Transactions on Automatic Control, vol. 45, no. 12, pp. 2427–2432, 2000. [click]
R.V. Iyer, X. Tan, and P.S. Krishnaprasad, “Approximate inversion of the Preisach hysteresis operator with application to control of smart actuators,” IEEE Transactions on Automatic Control, vol. 50, pp. 798–810, 2005. [click]
C.Y. Su, Q. Wang, X. Chen, and S. Rakheja, “Adaptive variable structure control of a class of nonlinear systems with unknown Prandtl-Ishlinskii hysteresis,” IEEE Transactions on Automatic Control, vol. 50, pp. 2069–2074, 2005. [click]
X. Chen and T. Ozaki, “Adaptive control for plants in the presence of actuator and sensor uncertain hysteresis,” IEEE Transactions on Automatic Control, vol. 56, no. 1, pp. 171–177, 2005. [click]
J. W. Macki, P. Nistri, and P. Zecca, “Mathematical Models for Hysteresis,” Soc. Indust. Appl. Math., vol. 35, pp. 94–123, 1993. [click]
I. D. Mayergoyz, The Preisach Model for CityplaceHysteresis, Springer-Verlag, Berlin, Germany, 1991.
M. A. Krasnosklskii and A. V. Pokrovskii, Systems with Hysteresis, Nauka, Moscow, Russia, 1983. [click]
A. Visintin, Differential Models of Hysteresis, Springer, Berlin, 1993. [click]
M. Rakotondrabe, “Bouc-Wen modeling and inverse multiplicative structure to compensate hysteresis nonlinearity in piezoelectric actuators,” IEEE Trans. Automat. Sci. Eng., vol. 8, no. 2, pp. 428–431, 2011. [click]
E. Watai, S. Jeong, “Evaluation of basic driving charactersitics and implementation of redundant speed limiting function of a double-motor driving system,” Journal of Robotics and Mechatronics, vol. 23, no. 3, pp. 408–415, 2011.
W. H. Zhang, H. S. Zhang, and B. S. Chen, “Generalized Lyapunov equation approach to state-dependent stochastic stabilization/detectability criterion,” IEEE Transactions on Automatic Control, vol. 53, no. 7, pp. 1630–1642, 2008. [click]
Y. G. Wang, T. Y. Chai, J. Fu, and J. Sun, “Adaptive decoupling control of the forced-circulation evaporation system using neural networks and multiple models,” Proc. of the 2011 American Control Conference, San Francisco, USA, IEEE, pp. 5061–5066, 2011. [click]
S. P. Wen, Z. G. Zeng, T.W. Huang, and Y. D. Zhang, “Exponential adaptive lag synchronization of memristive neural networks via fuzzy method and applications in pseudorandom number generators,” IEEE Transactions on Fuzzy Systems, vol. 22, No. 6, pp. 1704–1713, 2014. [click]
H. Li, X. Sun, L. Wu, and H. Lam, “State and output feedback control of a class of fuzzy systems with mismatched membership functions,” IEEE Transactions on Fuzzy Systems, vol. 23, no. 6, pp. 1943–1957, 2015. [click]
R. J. P. de Figueiredo and G. Chen, Nonlinear Feedback Control Systems: An Operator Theory Approach, Academic Press, INC., New York, 1993.
G. Chen and Z. Han, “Robust right coprime factorization and robust stabilization of nonlinear feedback control systems,” IEEE Transactions on Automatic Control, vol. 43, no. 10, pp. 1505–1510, 1998. [click]
M. Deng, A. Inoue, and K. Ishikawa, “Operator based nonlinear feedback control design using robust right coprime factorization,” IEEE Transactions on Automatic Control, vol. 51, no. 4, pp. 645–648, 2006. [click]
S. Bi and M. Deng, “Operator-based robust control design for nonlinear plants with perturbation,” Int. J. Control, vol. 84, no. 4, pp. 815–821, 2011. [click]
M. Deng, A. Inoue, and Y. Baba, “Operator-based nonlinear vibration control system design of a flexible arm with Piezoelectric actuator,” International Journal of Advanced Mechatronic Systems, vol. 1, no. 1, pp. 71–76, 2008. [click]
M. Deng, C. Jiang and A. Inoue, “Operator-based robust control for nonlinear plants with uncertain non-symmetric backlash,” Asian Journal of Control, vol. 13, no. 2, pp. 317–327, 2011. [click]
S. Bi, M. Deng, L. Wang, and S. Ma, “Operator-based robust control for nonlinear uncertain systems with backlashlike hysteresis,” Proc. of the International Conference on Advanced Mechatronic Systems, pp. 710–715, 2013. [click]
N. Bu and M. Deng, “System design for nonlinear plants using operator-based robust right coprime factorization and isomorphism,” IEEE Transactions on Automatic Control, vol. 56, no. 4, pp. 952–957, 2011. [click]
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Recommended by Associate Editor Do Wan Kim under the direction of Editor PooGyeon Park. This work was supported by National Natural Science Foundation of China under grant 61203229.
Shuhui Bi received her Ph.D. degree from Okayama University, Japan, in 2010. Her research interests include nonlinear system robust control, MIMO nonlinear systems and robotics.
Lei Wang received his Master’s degree from Okayama University, Japan in 2011. His research interests are intelligent manufacturing technology and automation.
Yongguo Zhao received his Ph.D. degree from Shandong University, China, in 2008. His research interests include robotics, machine vision and intelligent manufacturing technology.
Mingcong Deng received his Ph.D. degree from Kumamoto University, Japan in 1997. His research interests include living body measurement, nonlinear system modelling, control and fault detection etc.
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Bi, S., Wang, L., Zhao, Y. et al. Operator-based robust control for nonlinear uncertain systems with unknown backlash-like hysteresis. Int. J. Control Autom. Syst. 14, 469–477 (2016). https://doi.org/10.1007/s12555-014-0449-x
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DOI: https://doi.org/10.1007/s12555-014-0449-x