Abstract
In this paper, a sliding mode control with perturbation estimation (SMCPE) coupled with an inverse hysteresis compensator is proposed for the motion tracking control of a microposition system with piezoelectric actuation. The inverse hysteresis compensator is employed to cancel the hysteresis nonlinearity, thus reducing the nonlinear system to a linear system with an inversion error. Then, a SMCPE controller is adopted to deal with all the unmodeled dynamics and disturbances, aiming at improving the dynamic performance and the robustness of system. An experiment of a piezoelectric actuator is presented to demonstrate the feasibility and effectiveness of the proposed control scheme. The result shows that for a fast-rate control input, the proposed method is capable of leading to a good performance of system behavior.
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References
Ge P and Jouaneh M, Tracking control of a piezoceramic actuator, IEEE Trans. Control Syst. Technol, 1996, 4(3): 209–216.
Bashash S and Jalili N, Robust multiple frequency trajectory tracking control of piezoelectrically driven micro/nanopositioning systems, IEEE Trans. Control Syst. Technol, 2007, 15(5): 867–878.
Wei T A, Garmon F A, Khosla P K et al., Modeling rate-dependent hysteresis in piezoelectric actuators, Proceedings of the 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2003, 1975–1980.
Edardar M, Tan X B, and Khalil H K, Sliding-mode tracking control of piezo-actuated nanopositioners, American Control Conference, Montreal, QC, 2012, 3825–3830.
Lin C J and Lin P T, Tracking control of a biaxial piezo-actuated positioning stage using generalized Duhem model, Computers and Mathematics with Applications, 2012, 64(5): 766–787.
Guo W P, Liu D T, and Wang W, Neural network hysteresis modeling with an improved Preisach model for piezoelectric actuators, Engineering Computations, 2012, 29(3): 248–259.
Wang D H, Zhu W, and Yang Q, Linearization of stack piezoelectric ceramic actuators based on Bouc-Wen model, Intelligent Material Systems and Structures, 2011, 22(5): 401–413.
Xiao S L and Li Y M, Modeling and high dynamic compensating the rate-dependent hysteresis of piezoelectric actuators via a novel modified inverse preisach model, IEEE Trans. Control Syst. Technol, 2013, 21(5): 1549–1557.
Liu W and Shi W K, Experimental modeling of magneto-rheological damper and PID neural network controller design, Sixth International Conference on Natural Computation, 2010, 1674–1678.
Boukhnifer M and Ferreira A, Loop shaping bilateral controller for a two-fingered telemicromanipulation system, IEEE Trans. Control Syst. Technol, 2007, 15(5): 891–905.
Xu Q S, Adaptive discrete-time sliding mode impedance control of a piezoelectric microgripper, IEEE Trans. Robotics, 2013, 29(3): 663–673.
Ghafarirad H, Rezaei S M, Abdullah A, et al., Observer-based sliding mode control with adaptive perturbation estimation for micropositioning actuators, Precision Engineering, 2011, 35(2): 271–281.
Xiao S L and Li Y M, Dynamic compensation and H ∞ control for piezoelectric actuators based on the inverse Bouc-Wen model, Robotics and Computer-Integrated Manufacturing, 2014, 30(1): 47–54.
Wang Z Y, Zhang Z, et al., Precision tracking control of piezoelectric actuator based on Bouc-Wen hysteresis compensator, Electronics Letters, 2012, 48(23): 1459–1460.
Mohammad S S, Seyed M R, et al., Hysteresis-observer based robust tracking control of piezoelectric actuators, American Control Conference, Baltimore, MD, USA, 2010.
Bouc R, Forced vibration of mechanical systems with hysteresis, Proc. Conf. Nonlinear Oscillation, Prague, 1967, 32–39.
Wen Y K, Method for random vibration of hysteresis systems, J. Eng. Mech. Div., 1976, 102(2): 249–263.
Low T S and Guo W, Modeling of a three-layer piezoelectric bimorph beam with hysteresis, J. Microelectromech. Syst., 1995, 4(4): 230–237.
Rakotondrabe M, Bouc-Wen modeling and inverse multiplicative structure to compensate hysteresis nonlinearity in piezoelectric actuators, IEEE Trans. Autom. Sci. Eng., 2011, 8(2): 428–431.
Lin C J and Lin P T, Particle swarm optimization based feedforward controller for a XY PZT positioning stage, Mechatronics, 2012, 22(5): 614–628.
Rakotondrabe M, Lutz P, et al., Complete open loop control of hysteretic, creeped and oscillating piezoelectric cantilevers, IEEE Trans. Autom. Sci. Eng., 2010, 7(3): 440–450.
Elmali H and Olgac N, Theory and implementation of sliding mode control with perturbation estimation (SMCPE), Proceedings of the 1992 IEEE Intemrtiond Confemme on Robotics and Automation, Nice, France, 1992.
Elmali H and Olgac N, Sliding mode control with perturbation estimation (SMCPE): A new approach, Int. J. Control, 1992, 56: 923–941.
Elmali H and Olgac N, Implementation of sliding mode control with perturbation estimation (SMCPE), IEEE Trans. Control Syst. Technol., 1996, 4(1): 79–85.
Xu Q S and Li Y M, Sliding mode control of a piezo-driven micropositioning system using extended kalman filter, Proceedings of the 2010 IEEE International Conference on Automation and Logistics, Hong Kong and Macau, 2010, 16–20.
Chen M, Chen W H, and Wu Q X, Adaptive fuzzy tracking control for a class of uncertain MIMO nonlinear systems using disturbance observer, Science China Information Sciences, 2014, 57(1): 1–13.
Tong S C and Li Y M, Observer-based adaptive fuzzy backstepping control of uncertain nonlinear pure-feedback systems, Science China Information Sciences, 2014, 57(1): 1–14.
Wang H Q, Chen B, and Lin C, Approximation-based adaptive fuzzy control for a class of nonstrict-feedback stochastic nonlinear systems, Science China Information Sciences, 2014, 57(3): 1–16.
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This research was supported by National Science Foundation of China under Grant No. 61304097 and Foundation for Innovative Research Groups of the National Natural Science Foundation of China under Grant No. 61321002 and Program for Changjiang Scholars and Innovative Research Team in University under Grant No. IRT1208.
This paper was recommended for publication by Editor LIU Guoping.
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Gan, M., Qiao, Z. & Li, Y. Sliding Mode Control with Perturbation Estimation and Hysteresis Compensator Based on Bouc-Wen Model in Tackling Fast-Varying Sinusoidal Position Control of a Piezoelectric Actuator. J Syst Sci Complex 29, 367–381 (2016). https://doi.org/10.1007/s11424-016-5127-z
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DOI: https://doi.org/10.1007/s11424-016-5127-z