Adaptive wavelet neural network control with hysteresis estimation for piezo-positioning mechanism

An adaptive wavelet neural network (AWNN) control with hysteresis estimation is proposed in this study to improve the control performance of a piezo-positioning mechanism, which is always severely deteriorated due to hysteresis effect. First, the control system configuration of the piezo-positioning mechanism is introduced. Then, a new hysteretic model by integrating a modified hysteresis friction force function is proposed to represent the dynamics of the overall piezo-positioning mechanism. According to this developed dynamics, an AWNN controller with hysteresis estimation is proposed. In the proposed AWNN controller, a wavelet neural network (WNN) with accurate approximation capability is employed to approximate the part of the unknown function in the proposed dynamics of the piezo-positioning mechanism, and a robust compensator is proposed to confront the lumped uncertainty that comprises the inevitable approximation errors due to finite number of wavelet basis functions and disturbances, optimal parameter vectors, and higher order terms in Taylor series. Moreover, adaptive learning algorithms for the online learning of the parameters of the WNN are derived based on the Lyapunov stability theorem. Finally, the command tracking performance and the robustness to external load disturbance of the proposed AWNN control system are illustrated by some experimental results.

[1]  Yves Bernard,et al.  Dynamic hysteresis modeling based on Preisach model , 2002 .

[2]  Carlos Canudas de Wit,et al.  A new model for control of systems with friction , 1995, IEEE Trans. Autom. Control..

[3]  Dongwoo Song,et al.  Modeling of piezo actuator’s nonlinear and frequency dependent dynamics , 1999 .

[4]  Yih-Guang Leu,et al.  Observer-based direct adaptive fuzzy-neural control for nonaffine nonlinear systems , 2005, IEEE Trans. Neural Networks.

[5]  T. Low,et al.  Modeling of a three-layer piezoelectric bimorph beam with hysteresis , 1995 .

[6]  David W. L. Wang,et al.  Stability of control for the Preisach hysteresis model , 1997, Proceedings of International Conference on Robotics and Automation.

[7]  Ping Ge,et al.  Tracking control of a piezoceramic actuator , 1996, IEEE Trans. Control. Syst. Technol..

[8]  Karl Johan Åström,et al.  Adaptive Control , 1989, Embedded Digital Control with Microcontrollers.

[9]  Stephen A. Billings,et al.  A new class of wavelet networks for nonlinear system identification , 2005, IEEE Transactions on Neural Networks.

[10]  Gang Tao,et al.  Adaptive control of plants with unknown hystereses , 1995 .

[11]  Jason M. Kinser,et al.  Inherent features of wavelets and pulse coupled networks , 1999, IEEE Trans. Neural Networks.

[12]  Junmin Li,et al.  Adaptive neural control for a class of nonlinearly parametric time-delay systems , 2005, IEEE Transactions on Neural Networks.

[13]  Jean-Jacques E. Slotine,et al.  Space-frequency localized basis function networks for nonlinear system estimation and control , 1995, Neurocomputing.

[14]  M. Gafvert.  Dynamic model based friction compensation on the Furuta pendulum , 1999, Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328).

[15]  P. Kokotovic,et al.  Adaptive nonlinear design with controller-identifier separation and swapping , 1995, IEEE Trans. Autom. Control..

[16]  Seung-Woo Kim,et al.  Improvement of scanning accuracy of PZT piezoelectric actuators by feed-forward model-reference control , 1994 .

[17]  Bernard Friedland,et al.  Implementation of a friction estimation and compensation technique , 1996, Proceeding of the 1996 IEEE International Conference on Control Applications IEEE International Conference on Control Applications held together with IEEE International Symposium on Intelligent Contro.

[18]  Gi Sang Choi,et al.  A study on position control of piezoelectric actuators , 1997, ISIE '97 Proceeding of the IEEE International Symposium on Industrial Electronics.

[19]  Yih-Guang Leu,et al.  Robust adaptive fuzzy-neural controllers for uncertain nonlinear systems , 1999, IEEE Trans. Robotics Autom..

[20]  David L. Elliott,et al.  Neural Systems for Control , 1997 .

[21]  Woonchul Ham,et al.  Adaptive fuzzy sliding mode control of nonlinear system , 1998, IEEE Trans. Fuzzy Syst..

[22]  Bernard Delyon,et al.  Accuracy analysis for wavelet approximations , 1995, IEEE Trans. Neural Networks.

[23]  Zhi Wang,et al.  Robust adaptive friction compensation in servo-drives using position measurement only , 2000, Proceedings of the 2000. IEEE International Conference on Control Applications. Conference Proceedings (Cat. No.00CH37162).

[24]  Gérard Dreyfus,et al.  Training wavelet networks for nonlinear dynamic input-output modeling , 1998, Neurocomputing.

[25]  E. Della Torre,et al.  Fast Preisach-based magnetization model and fast inverse hysteresis model , 1998 .

[26]  Frank L. Lewis,et al.  Multilayer neural-net robot controller with guaranteed tracking performance , 1996, IEEE Trans. Neural Networks.

[27]  Ye-Hwa Chen,et al.  Piezomechanics using intelligent variable-structure control , 2001, IEEE Trans. Ind. Electron..

[28]  Qinghua Zhang,et al.  Wavelet networks , 1992, IEEE Trans. Neural Networks.

[29]  C. Canudas de Wit,et al.  Adaptive friction compensation for systems with generalized velocity/position friction dependency , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[30]  Isaak D. Mayergoyz,et al.  Dynamic Preisach models of hysteresis , 1988 .

[31]  Yagyensh C. Pati,et al.  Analysis and synthesis of feedforward neural networks using discrete affine wavelet transformations , 1993, IEEE Trans. Neural Networks.

[32]  Darren M. Dawson,et al.  Adaptive control techniques forfrictioncompensation , 1999 .

[33]  K.J. Astrom,et al.  Observer-based friction compensation , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[34]  Patrick J. Moyer,et al.  Near-Field Optics: Theory, Instrumentation, and Applications , 1996 .

[35]  Reinder Banning,et al.  Modeling piezoelectric actuators , 2000 .

[36]  Romeo Ortega,et al.  An Adaptive Friction Compensator for Global Tracking in Robot Manipulators , 1997 .

[37]  Bernard Friedland,et al.  On adaptive friction compensation , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[38]  Chia-Hsiang Menq,et al.  Hysteresis compensation in electromagnetic actuators through Preisach model inversion , 2000 .

[39]  C. F. Chen,et al.  Wavelet approach to optimising dynamic systems , 1999 .

[40]  Qinghua Zhang,et al.  Using wavelet network in nonparametric estimation , 1997, IEEE Trans. Neural Networks.

[41]  Kok Kiong Tan,et al.  Adaptive motion control using neural network approximations , 2002, Autom..

[42]  Darren M. Dawson,et al.  Adaptive control techniques for friction compensation , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[43]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[44]  Frank L. Lewis,et al.  Neural net robot controller with guaranteed tracking performance , 1993, Proceedings of 8th IEEE International Symposium on Intelligent Control.

[45]  Michael Goldfarb,et al.  Modeling Piezoelectric Stack Actuators for Control of Mlcromanlpulatlon , 2022 .

[46]  Jonq-Jer Tzen,et al.  Modeling of piezoelectric actuator for compensation and controller design , 2003 .

[47]  Chih-Lyang Hwang,et al.  A reinforcement discrete neuro-adaptive control for unknown piezoelectric actuator systems with dominant hysteresis , 2003, IEEE Trans. Neural Networks.