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Adaptive control of a class of non-linear systems preceded by backlash-like hysteresis

Published online by Cambridge University Press:  04 September 2014

JIANPING CAI ,
LUJUAN SHEN  and
FUZHEN WU
JIANPING CAI
Affiliation:
Zhejiang University of Water Resource and Electric Power Hangzhou, 310018, P.R.China
LUJUAN SHEN
Affiliation:
Zhejiang University of Water Resource and Electric Power Hangzhou, 310018, P.R.China
FUZHEN WU
Affiliation:
Zhejiang University of Water Resource and Electric Power Hangzhou, 310018, P.R.China
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Abstract

We consider a class of uncertain non-linear systems preceded by unknown backlash-like hysteresis, which is modelled by a differential equation. We propose a new state feedback robust adaptive control scheme using a backstepping technique and properties of the differential equation. In this control scheme, we construct a new continuous function to design an estimator to estimate the unknown constant parameters and the unknown bound of a ‘disturbance-like’ term. The transient performance of the output tracking error can be guaranteed by the introduction of pre-estimates of the unknown parameters in our controller together with update laws. We do not require bounds on the ‘disturbance-like’ term or unknown system parameters in this scheme. The global stability of the closed-loop system can be proved.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 24 , Special Issue 5: Mathematical Method in Intelligent Computing and Automation , October 2014 , e240504
Copyright
Copyright © Cambridge University Press 2014 

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References

Corradini, M. L. and Orlando, G. (2002) Robust stabilization of nonlinear uncertain plants with backlash or dead zone in the actuator. IEEE Transactions on Control Systems Technology 10 (1)158–166.CrossRefGoogle Scholar
Jang, J. O., Son, M. K. and Chung, H. T. (2004) Friction and output backlash compensation of systems using neural networks and fuzzy logic. Proceedings of the 2004 American Control Conference 1758–1763.CrossRefGoogle Scholar
Krstic, M., Kanellakopoulos, I. and Kokotovic, P. V. (1995) Nonlinear and adaptive control design, Wiley.Google Scholar
Pare, T. E. and How, J. P. (1998) Robust stability and performance analysis of systems with hysteresis nonlinearities. In: Proceedings of the 1998 American Control Conference 1904–1908.CrossRefGoogle Scholar
Su, C. Y., Stepanenko, Y. and Svoboda, J. (2000) Robust adaptive control of a class of nonlinear systems with unknown backlash-like hysteresis. IEEE Transactions on Automatic Control 45 (12)2427–2432.CrossRefGoogle Scholar
Sun, X., Zhang, W. and Jin, Y. (1992) Stable adaptive control of backlash nonlinear systems with bounded disturbance. Proceedings of the 31th IEEE Conference on Decision and Control 274–275.CrossRefGoogle Scholar
Tao, G. and Kokotovic, P. V. (1995a) Adaptive control of plants with unknown hysteresis. IEEE Transactions on Automatic Control 40 (2)200–212.CrossRefGoogle Scholar
Tao, G. and Kokotovic, P. V. (1995b) Adaptive control of systems with unknown output backlash. IEEE Transactions on Automatic Control 40 (2)326–330.CrossRefGoogle Scholar
Tao, G. and Kokotovic, P. V. (1995c) Continuous-time adaptive control of systems with unknown backlash. IEEE Transactions on Automatic Control 40 (6)1083–1087.Google Scholar
Tao, G. and Kokotovic, P. V. (1996) Adaptive control of systems with actuator and sensor nonlinearities, Wiley.Google Scholar
Wen, C. and Zhou, J. (2007) Decentralized adaptive stabilization in the presence of unknown backlash-like hysteresis. Automatica 43 (3)426–440.CrossRefGoogle Scholar
Zhou, J., Wen, C. and Zhang, Y. (2004a) Adaptive backstepping control of a class of uncertain nonlinear systems with unknown backlash-like hysteresis. IEEE Transactions on Automatic Control 49 (10)1751–1757.CrossRefGoogle Scholar
Zhou, J.Wen, C. and Zhang, Y. (2004b) Adaptive output feedback control of linear systems preceded by unknown backlash-like hysteresis. In: Proceedings of the 2004 IEEE Conference on Cybernetics and Intelligent Systems 12–17.Google Scholar
Zhou, J., Zhang, Y. and Wen, C. (2007a) Robust adaptive output control of uncertain nonlinear plants with unknown backlash nonlinearity. IEEE Transactions on Automatic Control 52 (3)503–509.CrossRefGoogle Scholar
Zhou, J., Wen, C. and Zhang, C. (2007b) Adaptive output control of uncertain nonlinear systems with unknown backlash. In: Proceedings of the 2007 American Control Conference 498–503.CrossRefGoogle Scholar