A self-adaption compensation control for hysteresis nonlinearity in piezo-actuated stages based on Pi-sigma fuzzy neural network

Piezo-actuated stages are widely applied in the high-precision positioning field nowadays. However, the inherent hysteresis nonlinearity in piezo-actuated stages greatly deteriorates the positioning accuracy of piezo-actuated stages. This paper first utilizes a nonlinear autoregressive moving average with exogenous inputs (NARMAX) model based on the Pi-sigma fuzzy neural network (PSFNN) to construct an online rate-dependent hysteresis model for describing the hysteresis nonlinearity in piezo-actuated stages. In order to improve the convergence rate of PSFNN and modeling precision, we adopt the gradient descent algorithm featuring three different learning factors to update the model parameters. The convergence of the NARMAX model based on the PSFNN is analyzed effectively. To ensure that the parameters can converge to the true values, the persistent excitation condition is considered. Then, a self-adaption compensation controller is designed for eliminating the hysteresis nonlinearity in piezo-actuated stages. A merit of the proposed controller is that it can directly eliminate the complex hysteresis nonlinearity in piezo-actuated stages without any inverse dynamic models. To demonstrate the effectiveness of the proposed model and control methods, a set of comparative experiments are performed on piezo-actuated stages. Experimental results show that the proposed modeling and control methods have excellent performance.

[1]  M. A. Janaideh,et al.  An inversion formula for a Prandtl–Ishlinskii operator with time dependent thresholds☆ , 2011 .

[2]  Santosh Devasia,et al.  Feedback-Linearized Inverse Feedforward for Creep, Hysteresis, and Vibration Compensation in AFM Piezoactuators , 2007, IEEE Transactions on Control Systems Technology.

[3]  Li-Min Zhu,et al.  Modeling and Identification of Piezoelectric-Actuated Stages Cascading Hysteresis Nonlinearity With Linear Dynamics , 2016, IEEE/ASME Transactions on Mechatronics.

[4]  Nan Nan,et al.  Strong Convergence Analysis of Batch Gradient-Based Learning Algorithm for Training Pi-Sigma Network Based on TSK Fuzzy Models , 2015, Neural Processing Letters.

[5]  J.A. De Abreu-Garcia,et al.  Tracking control of a piezoceramic actuator with hysteresis compensation using inverse Preisach model , 2005, IEEE/ASME Transactions on Mechatronics.

[6]  Wei Zhu,et al.  Hysteresis modeling and displacement control of piezoelectric actuators with the frequency-dependent behavior using a generalized Bouc–Wen model , 2016 .

[7]  Qingsong Xu,et al.  Model Predictive Discrete-Time Sliding Mode Control of a Nanopositioning Piezostage Without Modeling Hysteresis , 2012, IEEE Transactions on Control Systems Technology.

[8]  Okyay Kaynak,et al.  Robust and adaptive backstepping control for nonlinear systems using RBF neural networks , 2004, IEEE Transactions on Neural Networks.

[9]  Xiaobo Tan,et al.  Modeling and inverse compensation of hysteresis in vanadium dioxide using an extended generalized Prandtl-Ishlinskii model , 2014 .

[10]  Yonghong Tan,et al.  Modeling hysteresis in piezoelectric actuators using NARMAX models , 2009 .

[11]  John S. Baras,et al.  Adaptive identification and control of hysteresis in smart materials , 2005, IEEE Transactions on Automatic Control.

[12]  谭永红,et al.  Modeling the dynamic sandwich system with hysteresis using NARMAX model , 2014 .

[13]  Micky Rakotondrabe,et al.  Bouc–Wen Modeling and Inverse Multiplicative Structure to Compensate Hysteresis Nonlinearity in Piezoelectric Actuators , 2011, IEEE Transactions on Automation Science and Engineering.

[14]  Rudolf Seethaler,et al.  An improved electromechanical model and parameter identification technique for piezoelectric actuators , 2013 .

[15]  Liang Deng,et al.  Modeling the dynamic sandwich system with hysteresis using NARMAX model , 2014, Math. Comput. Simul..

[16]  Long Li,et al.  A modified gradient-based neuro-fuzzy learning algorithm and its convergence , 2010, Inf. Sci..

[17]  S. O. Reza Moheimani,et al.  Control of a piezoelectrically actuated high-speed serial-kinematic AFM nanopositioner , 2014 .

[18]  Qingsong Xu,et al.  Adaptive Sliding Mode Control With Perturbation Estimation and PID Sliding Surface for Motion Tracking of a Piezo-Driven Micromanipulator , 2010, IEEE Transactions on Control Systems Technology.

[19]  Tianyou Chai,et al.  Nonlinear Control of Systems Preceded by Preisach Hysteresis Description: A Prescribed Adaptive Control Approach , 2016, IEEE Transactions on Control Systems Technology.

[20]  Hwee Choo Liaw,et al.  Neural Network Motion Tracking Control of Piezo-Actuated Flexure-Based Mechanisms for Micro-/Nanomanipulation , 2009, IEEE/ASME Transactions on Mechatronics.

[21]  Li-Min Zhu,et al.  High-Speed Tracking of a Nanopositioning Stage Using Modified Repetitive Control , 2017, IEEE Transactions on Automation Science and Engineering.

[22]  Ian R. Petersen,et al.  Creep, Hysteresis, and Cross-Coupling Reduction in the High-Precision Positioning of the Piezoelectric Scanner Stage of an Atomic Force Microscope , 2013, IEEE Transactions on Nanotechnology.

[23]  Bijan Shirinzadeh,et al.  Enhanced sliding mode motion tracking control of piezoelectric actuators , 2007 .

[24]  Jiao Luo,et al.  The fuzzy neural network model of flow stress in the isothermal compression of 300M steel , 2012 .

[25]  Ulrich Gabbert,et al.  Hysteresis and creep modeling and compensation for a piezoelectric actuator using a fractional-order Maxwell resistive capacitor approach , 2013 .

[26]  Y. Cao,et al.  A Novel Discrete ARMA-Based Model for Piezoelectric Actuator Hysteresis , 2012, IEEE/ASME Transactions on Mechatronics.

[27]  M. Al Janaideh,et al.  Inverse Rate-Dependent Prandtl–Ishlinskii Model for Feedforward Compensation of Hysteresis in a Piezomicropositioning Actuator , 2013, IEEE/ASME Transactions on Mechatronics.

[28]  Yangmin Li,et al.  Modeling and High Dynamic Compensating the Rate-Dependent Hysteresis of Piezoelectric Actuators via a Novel Modified Inverse Preisach Model , 2013, IEEE Transactions on Control Systems Technology.

[29]  Sung Hoon Ha,et al.  Accurate position control of a flexible arm using a piezoactuator associated with a hysteresis compensator , 2013 .

[30]  Junzhi Yu,et al.  An Inversion-Free Predictive Controller for Piezoelectric Actuators Based on a Dynamic Linearized Neural Network Model , 2016, IEEE/ASME Transactions on Mechatronics.

[31]  Long Zhang,et al.  A New Extension of Newton Algorithm for Nonlinear System Modelling Using RBF Neural Networks , 2013, IEEE Transactions on Automatic Control.

[32]  Hassan K. Khalil,et al.  Design and Analysis of Sliding Mode Controller Under Approximate Hysteresis Compensation , 2015, IEEE Transactions on Control Systems Technology.

[33]  Wei Li,et al.  A Monolithic Self-Sensing Precision Stage: Design, Modeling, Calibration, and Hysteresis Compensation , 2015, IEEE/ASME Transactions on Mechatronics.

[35]  Yan Liu,et al.  A Modifled Gradient-Based Neuro-Fuzzy Learning Algorithm for Pi-Sigma Network Based on First-Order Takagi-Sugeno System , 2014 .

[36]  Hassan K. Khalil,et al.  Control of systems with hysteresis via servocompensation and its application to nanopositioning , 2010, Proceedings of the 2010 American Control Conference.

[37]  M. Kamlah,et al.  Ferroelectric and ferroelastic piezoceramics – modeling of electromechanical hysteresis phenomena , 2001 .

[38]  Qingsong Xu,et al.  Digital Integral Terminal Sliding Mode Predictive Control of Piezoelectric-Driven Motion System , 2016, IEEE Transactions on Industrial Electronics.

[39]  Shengyuan Xu,et al.  Observer-Based Adaptive Neural Network Control for Nonlinear Stochastic Systems With Time Delay , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[40]  Wei Li,et al.  Compensation of hysteresis in piezoelectric actuators without dynamics modeling , 2013 .