Inversion-free force tracking control of piezoelectric actuators using fast finite-time integral terminal sliding-mode

Abstract The major hurdles to control the force created by piezoelectric actuators (PEAs) are originated from its strong nonlinear behaviors which include hysteresis, creep, and vibration dynamics. To achieve an accurate, fast and robust force tracking performance without using complicated modeling and parameter identification of PEAs, this paper presents a practical direct force control scheme. The proposed controller is based on two core approaches: 1) fast finite-time integral terminal sliding mode (FFI-TSM) which allows fast convergence and high accuracy to the closed-loop system without control chattering; and 2) an inverse-model-free compensation, named force-based time-delayed estimation (FBTDE) which offers significant robustness with minimum use of plant dynamics information. The finite-time stability of the overall closed-loop system is proven through the Lyapunov’s method. The proposed force tracking controller is implemented on the PEA system driving a variable physical damping actuator mechanism. The overall accuracy, convergence speed, and robustness of the proposed controller are validated under various experimental scenarios. Comparative experimental results are particularly presented to verify the effectiveness of the FFI-TSM term and the FBTDE term.

[1]  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.

[2]  R. Ben Mrad,et al.  On the classical Preisach model for hysteresis in piezoceramic actuators , 2003 .

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

[4]  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.

[5]  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.

[6]  Chintae Choi,et al.  Practical Nonsingular Terminal Sliding-Mode Control of Robot Manipulators for High-Accuracy Tracking Control , 2009, IEEE Transactions on Industrial Electronics.

[7]  Yanfang Liu,et al.  Modelling and compensation of hysteresis in piezoelectric actuators based on Maxwell approach , 2016 .

[8]  Wei Zhang,et al.  Model and Control of a Compact Long-Travel Accurate-Manipulation Platform , 2017, IEEE/ASME Transactions on Mechatronics.

[9]  Wei Tech Ang,et al.  Feedforward Controller With Inverse Rate-Dependent Model for Piezoelectric Actuators in Trajectory-Tracking Applications , 2007, IEEE/ASME Transactions on Mechatronics.

[10]  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.

[11]  Wu-Chung Su,et al.  An Boundary Layer in Sliding Mode for Sampled-Data Systems , 2000 .

[12]  Si-Lu Chen,et al.  Development of an Approach Toward Comprehensive Identification of Hysteretic Dynamics in Piezoelectric Actuators , 2013, IEEE Transactions on Control Systems Technology.

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

[14]  Hewon Jung,et al.  Creep characteristics of piezoelectric actuators , 2000 .

[15]  Micky Rakotondrabe,et al.  Further Results on Hysteresis Compensation of Smart Micropositioning Systems With the Inverse Prandtl–Ishlinskii Compensator , 2016, IEEE Transactions on Control Systems Technology.

[16]  Jinhao Qiu,et al.  Self-sensing force control of a piezoelectric actuator , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[17]  Qingsong Xu,et al.  Hysteresis modeling and compensation of a piezostage using least squares support vector machines , 2011 .

[18]  Gene F. Franklin,et al.  Digital control of dynamic systems , 1980 .

[19]  Chian-Song Chiu,et al.  Derivative and integral terminal sliding mode control for a class of MIMO nonlinear systems , 2012, Autom..

[20]  Hartmut Logemann,et al.  A class of differential-delay systems with hysteresis: Asymptotic behaviour of solutions☆ , 2008 .

[21]  Maolin Jin,et al.  Precise tracking control of shape memory alloy actuator systems using hyperbolic tangential sliding mode control with time delay estimation , 2013 .

[22]  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.

[23]  Filip Szufnarowski,et al.  Force control of a piezoelectric actuator based on a statistical system model and dynamic compensation , 2011 .

[24]  Linlin Li,et al.  Positive acceleration, velocity and position feedback based damping control approach for piezo-actuated nanopositioning stages , 2017 .

[25]  Nikolaos G. Tsagarakis,et al.  Development and control of a series elastic actuator equipped with a semi active friction damper for human friendly robots , 2014, Robotics Auton. Syst..

[26]  Sergej Fatikow,et al.  Modeling and Control of Piezo-Actuated Nanopositioning Stages: A Survey , 2016, IEEE Transactions on Automation Science and Engineering.

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

[28]  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.

[29]  Peiyue Li,et al.  Adaptive Fuzzy Hysteresis Internal Model Tracking Control of Piezoelectric Actuators With Nanoscale Application , 2016, IEEE Transactions on Fuzzy Systems.

[30]  T. A. Lasky,et al.  Robust independent joint controller design for industrial robot manipulators , 1991 .

[31]  Kamal Youcef-Toumi,et al.  A Time Delay Controller for Systems with Unknown Dynamics , 1988, 1988 American Control Conference.

[32]  M. Kreutzbruck,et al.  Nonlinear electromechanical response of the ferroelectret ultrasonic transducers , 2010 .

[33]  Woosoon Yim,et al.  Variable Structure Adaptive Force Tracking Control of a Cantilever Beam Using a Piezoelectric Actuator , 2000 .

[34]  Po-Ying Chen,et al.  Precision tracking control of a biaxial piezo stage using repetitive control and double-feedforward compensation , 2011 .

[35]  Philippe Lutz,et al.  Complete Open Loop Control of Hysteretic, Creeped, and Oscillating Piezoelectric Cantilevers , 2010, IEEE Transactions on Automation Science and Engineering.

[36]  Nikolaos G. Tsagarakis,et al.  Model-free force tracking control of piezoelectric actuators: Application to variable damping actuator , 2014, 2014 IEEE International Conference on Robotics and Automation (ICRA).

[37]  Vahid Hassani,et al.  A hysteresis model for a stacked-type piezoelectric actuator , 2017 .

[38]  Chun-Yi Su,et al.  Development of the rate-dependent Prandtl–Ishlinskii model for smart actuators , 2008 .

[39]  Maolin Jin,et al.  Robust Control of Robot Manipulators Using Inclusive and Enhanced Time Delay Control , 2017, IEEE/ASME Transactions on Mechatronics.

[40]  Yuansheng Chen,et al.  Tracking control of piezoelectric stack actuator using modified Prandtl–Ishlinskii model , 2013 .

[41]  John T. Wen,et al.  Preisach modeling of piezoceramic and shape memory alloy hysteresis , 1997 .

[42]  D.H. Wang,et al.  Linearization of Stack Piezoelectric Ceramic Actuators Based on Bouc-Wen Model , 2011 .

[43]  Bijan Shirinzadeh,et al.  Development of a 4-DOF haptic micromanipulator utilizing a hybrid parallel-serial flexure mechanism , 2018 .

[44]  Santosh Devasia,et al.  A Survey of Control Issues in Nanopositioning , 2007, IEEE Transactions on Control Systems Technology.

[45]  Hamed Ghafarirad,et al.  Modified robust external force control with disturbance rejection with application to piezoelectric actuators , 2015 .

[46]  Clément Gosselin,et al.  Design, analysis and experimental validation of an ungrounded haptic interface using a piezoelectric actuator , 2017 .

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

[48]  Musa Jouaneh,et al.  Modeling hysteresis in piezoceramic actuators , 1995 .

[49]  Xinghuo Yu,et al.  Terminal sliding mode control of MIMO linear systems , 1997 .

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

[51]  Klaus Kuhnen,et al.  Modeling, Identification and Compensation of Complex Hysteretic Nonlinearities: A Modified Prandtl - Ishlinskii Approach , 2003, Eur. J. Control.

[52]  Thanh Nho Do,et al.  A survey on hysteresis modeling, identification and control , 2014 .

[53]  Micky Rakotondrabe,et al.  Internal model-based feedback control design for inversion-free feedforward rate-dependent hysteresis compensation of piezoelectric cantilever actuator , 2018 .

[54]  L. Xie,et al.  Integral terminal sliding mode cooperative control of multi-robot networks , 2009, 2009 IEEE/ASME International Conference on Advanced Intelligent Mechatronics.

[55]  Nikolaos G. Tsagarakis,et al.  Terminal sliding-mode based force tracking control of piezoelectric actuators for variable physical damping system , 2014, 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[56]  Pyung Hun Chang,et al.  Relative Impedance Control for Dual-Arm Robots Performing Asymmetric Bimanual Tasks , 2014, IEEE Transactions on Industrial Electronics.

[57]  Tingwen Huang,et al.  An Adaptive Takagi–Sugeno Fuzzy Model-Based Predictive Controller for Piezoelectric Actuators , 2017, IEEE Transactions on Industrial Electronics.

[58]  Zhihong Man,et al.  Continuous finite-time control for robotic manipulators with terminal sliding mode , 2003, Autom..

[59]  Young-Bae Kim,et al.  Robust Time-Delay Control for the DC–DC Boost Converter , 2014, IEEE Transactions on Industrial Electronics.

[60]  Hangil Joe,et al.  Time-Delay Controller Design for Position Control of Autonomous Underwater Vehicle Under Disturbances , 2016, IEEE Transactions on Industrial Electronics.

[61]  M. Zak.  Terminal attractors for addressable memory in neural networks , 1988 .

[62]  Philippe Lutz,et al.  Modelling and Robust Position/Force Control of a Piezoelectric Microgripper , 2007, 2007 IEEE International Conference on Automation Science and Engineering.

[63]  Seung-Bok Choi,et al.  Force Tracking Control of a Flexible Gripper Driven by Piezoceramic Actuators , 1997 .

[64]  Gangbing Song,et al.  A comprehensive model for piezoceramic actuators: modelling, validation and application , 2009 .

[65]  Wu-Chung Su,et al.  An O(T2) boundary layer in sliding mode for sampled-data systems , 2000, IEEE Trans. Autom. Control..

[66]  A. Sabanovic,et al.  Sliding-mode based force control of a piezoelectric actuator , 2004, Proceedings of the IEEE International Conference on Mechatronics, 2004. ICM '04..