Abstract
In this paper, a robust control approach for a class of nonlinear systems preceded by unknown hysteresis nonlinearities is addressed. Due to the complexity of the hysteresis characteristics, the hysteresis can not be linearized directly, and the effects caused by the hysteresis will degrade the system performance. Therefore, it is necessary to design an effective controller mitigating the negative effects. In this paper, the unknown hysteresis is represented by a differential equation-based hysteresis model - Duhem model. By exploring the characteristics of the Duhem model, the developed robust controller ensures the global stability of the system without constructing the hysteresis inverse. The effectiveness of the proposed control approach is demonstrated through a simulation example.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bessa, W.M.: Some remarks on the boundedness and convergence properties of smooth sliding mode controllers. International Journal of Automation and Computing 6(2), 154–158 (2009)
Brokate, M., Sprekels, J.: Hysteresis and Phase Transitions. Springer, Berlin (1996)
Chen, X., Hisayama, T., Su, C.-Y.: Adaptive control for continuous-time systems preceded by hysteresis. IEEE Trans. Automat. Contr. 53(4), 1019–1025 (2008)
Chua, L.O., Stromsmoe, K.A.: Mathematical model for dynamic hysteresis loops. Int. J. Engng. Sci. 9, 435–450 (1971)
Coleman, B.D., Hodgdon, M.L.: On a class of constitutive relations for ferromagnetic hysteresis. Arch. Rational Mech. Anal., 375–396 (1987)
Duhem, P.: Die dauernden Aenderungen und die Thermodynamik. I, Z. Phys. Chem. 22, 543–589 (1897)
Feng, Y., Hu, Y.-M., Rabbath, C.A., Su, C.-Y.: Robust adaptive control for a class of perturbed strict-feedback nonlinear systems with unknown Prandtl-Ishlinskii hysteresis. International Journal of Control 81(11), 1699–1708 (2008)
Krasnosel’skii, M.A., Pokrovskii, A.V.: Systems with Hysteresis. Springer, New York (1989)
Klein, O., Krejci, P.: Outwards pointing hysteresis operators and asymptotic behaviour of evolution equations. Nonlinear Analysis: Real World Applications 4(5), 755–785 (2003)
Krejci, P., Kuhnen, K.: Inverse control of systems with hysteresis and creep. IEE Proc.-Control Theory and Applications 148(3), 185–192 (2001)
Liu, S., Huang, T., Yen, J.: Tracking control of shape-memory-alloy actuators based on self-sensing feedback and inverse hysteresis compensation. Sensor 10, 112–127 (2010)
Macki, J.W., Nistri, P., Zecca, P.: Mathematical models for hysteresis. SIAM Review 35(1), 94–123 (1993)
Mayergoyz, I.D.: Mathematical Models of Hysteresis. Springer, New York (1991)
Oh, J., Bernstein, D.S.: Semilinear Duhem model for rate-independent and rate-dependent hysteresis. IEEE Trans, Automat. Contr. 50(5), 631–645 (2005)
Oh, J., Bernstein, D.S.: Piecewise linear identification for the rate-independent and rate-dependent Duhem hysteresis models. IEEE Trans. Automat. Contr. 52(3), 576–582 (2007)
Slotine, J.J.E., Li, W.: Applied Nonlinear Control. China Machine Press (2004)
Shyu, K.K., Liu, W.J., Hsu, K.C.: Decentralised variable structure control of uncertain large-scale systems containing a dead-zone. IEE Proc. Control Theory Appl. 150(5), 467–475 (2003)
Su, C.-Y., Stepanenko, Y., Svoboda, J., Leung, T.P.: Robust adaptive control of a class of nonlinear systems with unknown backlash-like hysteresis. IEEE Trans. Automat. Contr. 45(12), 2427–2432 (2000)
Feng, Y., Hu, Y.-M., Rabbath, C.A., Su, C.-Y.: Robust adaptive control for a class of perturbed strict-feedback nonlinear systems with unknown Prandtl-Ishlinskii hysteresis. International Journal of Control 81(11), 1699–1708 (2008)
Tan, X., Baras, J.S.: Modeling and Control of Hysteresis in Magnetostrictive Actuators. Automatica 40(9), 1469–1480 (2004)
Tan, X., Baras, J.S.: Adaptive identification and control of hysteresis in smart materials. IEEE Trans, Automat. Contr. 50(16), 827–839 (2005)
Tao, G., Kokotović, P.V.: Adaptive control of plants with unknown hysteresis. IEEE Trans. Automat. Contr. 40, 200–212 (1995)
Visintin, A.: Differential Models of Hysteresis. Springer, New York (1994)
Wang, Q., Su, C.-Y.: Robust adaptive control of a class of nonlinear systems including actuator hysteresis with Prandtl-Ishlinskii presentations. Automatica 42(5), 859–867 (2006)
Zhou, J., Wen, C.-Y., Zhang, Y.: Adaptive backstepping control of a class of uncertain nonlinear systems with unknown backlash-like hysteresis. IEEE Trans. Automat. Contr. 49(10), 1751–1757 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Feng, Y., Du, J., Su, CY. (2010). On the Robust Control of Systems Preceded by Differential Equation-Based Hysteresis Nonlinearities. In: Liu, H., Ding, H., Xiong, Z., Zhu, X. (eds) Intelligent Robotics and Applications. ICIRA 2010. Lecture Notes in Computer Science(), vol 6424. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16584-9_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-16584-9_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16583-2
Online ISBN: 978-3-642-16584-9
eBook Packages: Computer ScienceComputer Science (R0)