Abstract
This paper is concentrated on the rate-dependent hysteresis modeling and compensation for a piezoelectric actuator. A least squares support vector machines (LS-SVM) model is proposed and trained by introducing the current input value and input variation rate as the input data set to formulate a one-to-one mapping. After demonstrating the effectiveness of the presented model, a LS-SVM inverse model based feedforward control combined with a PID feedback control is designed to compensate the hysteresis nonlinearity. Simulation results show that the hybrid scheme is superior to either of the stand-alone controllers, and the rate-dependent hysteresis is suppressed to a negligible level, which validate the effectiveness of the constructed controller. Owing to the simple procedure, the proposed modeling and control approaches are expected to be extended to other types of hysteretic systems as well.
This is a preview of subscription content, log in via an institution to check access.
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
Tan, X., Baras, J.S.: Adaptive identification and control of hysteresis in smart materials. IEEE Trans. Automat. Contr. 50(6), 827–839 (2005)
Kuhnen, K.: Modeling, identification and compensation of complex hysteretic nonlinearities: A modified Prandtl-Ishlinskii approach. European J. Control 9(4), 407–421 (2003)
Xie, W.F., Fu, J., Su, C.Y.: Observer based control of piezoelectric actuators with classical Duhem modeled hysteresis. In: Proc. of American Control Conf., pp. 4221–4226 (2009)
Xu, Q., Li, Y.: Dahl model-based hysteresis compensation and precise positioning control of an XY parallel micromanipulator with piezoelectric actuation. J. Dyn. Syst. Meas. Control-Trans. ASME 132(4), 041011 (2010)
Yu, Y., Xiao, Z., Naganathan, N.G., Dukkipati, R.V.: Dynamic Preisach modelling of hysteresis for the piezoceramic actuator system. Mech. Mach. Theory 37(1), 75–89 (2002)
Ang, W.T., Khosla, P.K., Riviere, C.N.: Feedforward controller with inverse rate-dependent model for piezoelectric actuators in trajectory-tracking applications. IEEE/ASME Trans. Mechatron. 12(2), 134–142 (2007)
Yu, S., Alici, G., Shirinzadeh, B., Smith, J.: Sliding mode control of a piezoelectric actuator with neural network compensating rate-dependent hysteresis. In: Proc. of IEEE Int. Conf. on Robotics and Automation, pp. 3641–3645 (2005)
Dong, R., Tan, Y., Chen, H., Xie, Y.: A neural networks based model for rate-dependent hysteresis for piezoelectric actuators. Sens. Actuator A-Phys. 143(2), 370–376 (2008)
Wong, P.K., Vong, C.M., Tam, L.M., Li, K.: Data preprocessing and modelling of electronically-controlled automotive engine power performance using kernel principal components analysis and least-square support vector machines. Int. J. Vehicle Systems Modelling and Testing 3(4), 312–330 (2008)
Suykens, J.A.K.: Support vector machines: a nonlinear modeling and control perspective. European J. Control 7(2-3), 311–327 (2001)
Ji, H.W., Yang, S.X., Wu, Z.T., Yan, G.B.: Precision control of piezoelectric actuator using support vector regression nonlinear model and neural networks. In: Proc. of Int. Conf. on Machine Learning and Cybernetics, pp. 1186–1191 (2005)
Wang, B., Zhong, W., Pi, D., Sun, Y., Xu, C., Chu, S.: Support vector machine based modeling of nonlinear systems with hysteresis. In: Proc. of 6th World Congress on Intelligent Control and Automation, pp. 1722–1725 (2006)
Yang, X.F., Li, W., Wang, Y.Q., Su, X.P.: A multi-loop hysteresis model of piezo actuator based on LS-SVM. In: Proc. of 7th Int. Conf. on Asia Simulation Conf., pp. 1451–1454 (2008)
Wang, X., Ye, M.: Hysteresis and nonlinearity compensation of relative humidity sensor using support vector machines. Sens. Actuator A-Phys. 129(1), 274–284 (2008)
Lei, W., Mao, J., Ma, Y.: A new modeling method for nonlinear rate-dependent hysteresis system based on LS-SVM. In: Proc. of 10th Int. Conf. on Control, Automation, Robotics and Vision, pp. 1442–1446 (2008)
Li, Y., Xu, Q.: Adaptive sliding mode control with perturbation estimation and PID sliding surface for motion tracking of a piezo-driven micromanipulator. IEEE Trans. Contr. Syst. Technol. 18(4), 798–810 (2010)
Xu, Q., Li, Y.: Fuzzy sliding mode control with perturbation estimation for a piezoactuated micromanipulator. In: Zeng, Z., Wang, J. (eds.) Advances in Neural Network Research and Applications. Lecture Notes in Electrical Engineering, vol. 67, pp. 153–160. Springer, Heidelberg (2010)
De Brabanter, K., Karsmakers, P., Ojeda, F., Alzate, C., De Brabanter, J., Pelckmans, K., De Moor, B., Vandewalle, J., Suykens, J.A.K.: LS-SVMlab toolbox user’s guide version 1.7. Internal Report 10-146, ESAT-SISTA, K.U. Leuven, Leuven, Belgium (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Xu, Q., Wong, PK., Li, Y. (2011). Rate-Dependent Hysteresis Modeling and Compensation Using Least Squares Support Vector Machines. In: Liu, D., Zhang, H., Polycarpou, M., Alippi, C., He, H. (eds) Advances in Neural Networks – ISNN 2011. ISNN 2011. Lecture Notes in Computer Science, vol 6676. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21090-7_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-21090-7_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21089-1
Online ISBN: 978-3-642-21090-7
eBook Packages: Computer ScienceComputer Science (R0)