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A Generalized Input-output-based Digital Sliding-mode Control for Piezoelectric Actuators with Non-minimum Phase Property

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Abstract

In this paper, a generalized input-output-based digital sliding-mode control (GIODSMC) is developed for piezoelectric actuators (PEA) with non-minimum phase (NMP) property. First, the instability mechanism of the traditional input-output-based digital sliding-mode control (IODSMC) for NMP systems is analyzed. Then, a generalized approximate input-output model is established to cancel the effect of unstable zeros in NMP systems. The generalized model can be transformed into different forms, which represents a class of approximate models suitable for this situation. Based on this model, a controller, called the GIODSMC, is presented. Unlike existing works, the developed controller ensures precision motion control for PEA with NMP property. Moreover, additional control parameters are not required to stabilize the NMP systems, and neither a hysteresis model nor a state observer is needed for the developed method. Stability of the closed-loop system is theoretically analyzed. At last, the presented method is tested through numerical simulations and experimental investigations on a piezoelectric actuator device.

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References

  1. H. Habibullah, H. Pota, and I. Petersen, “Reduction of phase error between sinusoidal motions and vibration of a tube scanner during spiral scanning using an AFM,” Int. J. Control Autom. Syst., vol. 14, no. 2, pp. 505–513, April 2016.

    Article  Google Scholar 

  2. T. Dinh and K. Ahn, “Radial basis function neural network based adaptive fast nonsingular terminal sliding mode controller for piezo positioning stage,” Int. J. Control Autom. Syst., vol. 15, no. 6, pp. 2892–2905, December 2017.

    Article  Google Scholar 

  3. R. Seifabadi, S. Rezaei, and S. Ghidary, “A teleoperation system for micro positioning with haptic feedback,” Int. J. Control Autom. Syst., vol. 11, no. 4, pp. 768–775, August 2013.

    Article  Google Scholar 

  4. G. Gu and L. Zhu, “Motion control of piezoceramic actuators with creep, hysteresis and vibration compensation,” Sens. Actuators A Phys., vol. 197, pp. 76–87, 2013.

    Article  Google Scholar 

  5. V. Phan, N. Goo, and H. Park, “Vibration suppression of a flexible robot manipulator with a lightweight piezocomposite actuator,” Int. J. Control Autom. Syst., vol. 7, no. 2, pp. 243–251, April 2009.

    Article  Google Scholar 

  6. P. Ge and M. Jouaneh, “Tracking control of a piezoceramic actuator,” IEEE Trans. Control Syst. Technol., vol. 4, no. 3, pp. 209–216, May 1996.

    Article  Google Scholar 

  7. P. Yen, M. Yan, and Y. Chen, “Hysteresis compensation and adaptive controller design for a piezoceramic actuator system in atomic force microscopy,” Asian J. Control, vol. 14, no. 4, pp. 1012–1027, July 2012.

    Article  MathSciNet  MATH  Google Scholar 

  8. Z. Chi, M. Jia, and Q. Xu, “Fuzzy PID feedback control of piezoelectric actuator with feedforward compensation,” Math. Probl. Eng., vol. 14, pp. 1–14, 2014.

    MathSciNet  Google Scholar 

  9. M. Ohka, K. Esumi, and Y. Sawamoto, “Two-axial piezoelectric actuator control using a multi-layer artificial neural network featuring feedback connection for tactile displays,” Adv. Rob, vol. 26, no. 1–2, pp. 219–232, 2012.

    Article  Google Scholar 

  10. M. Tsai and J. Chen, “Robust tracking control of a piezo actuator using a new approximate hysteresis mode,” J. Dyn. Syst. Meas. Control Trans. ASME, vol. 125, no. 1, pp. 96–102, 2003.

    Article  Google Scholar 

  11. B. Chen, T. Lee, C. Hang, and Y. Guo, “An H∞ almost disturbance decoupling robust controller design for a piezoelectric bimorph actuator with hysteresis,” IEEE Trans. Control Syst. Technol., vol. 7, no. 2, pp. 160–174, May 1999.

    Article  Google Scholar 

  12. Y. Wei, J. Park, J. Qiu, L. Wu, and H. Jung, “Sliding mode control for semi-Markovian jump systems via output feedback,” Automatica, vol. 81, pp. 133–141, July 2017.

    Article  MathSciNet  MATH  Google Scholar 

  13. S. Huang, K. Tan, and T. Lee, “Adaptive sliding-mode control of piezoelectric actuators,” IEEE Trans. Ind. Electron., vol. 56, no. 9, pp. 3514–3522, 2009.

    Article  Google Scholar 

  14. Y. Alipouri, J. Poshtan, and M. Zarch, “Generalized sliding mode with integrator controller design using a discrete linear model,” Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng., vol. 228, no. 9, pp. 677–689, October 2014.

    Article  Google Scholar 

  15. Y. Chen, J. Chang, and S. Chu, “PC-based sliding-mode control applied to parallel-type double inverted pendulum system,” Mechatronics, vol. 9, no. 5, pp. 553–564, August 1999.

    Article  Google Scholar 

  16. W. Gao, Y. Wang, and A. Homaifa, “Discrete-time variable structure control systems,” IEEE Trans. Ind. Electron., vol. 42, no. 2, pp. 117–122, April 1995.

    Article  Google Scholar 

  17. H. Ma, J. Wu, and Z. Xiong, “Discrete-time sliding-mode control with improved quasi-sliding-mode domain,” IEEE Trans. Ind. Electron., vol. 63, no. 10, pp. 6293–6304, October 2016.

    Article  Google Scholar 

  18. H. Ma, J. Wu, and Z. Xiong, “A novel exponential reaching law of discrete-time sliding-mode control,” IEEE Trans. Ind. Electron., vol. 64, no. 5, pp. 3840–3850, May 2017.

    Article  Google Scholar 

  19. P. Korondi, H. Hashimoto, and V. Utkin, “Direct torsion control of flexible shaft in an observer-based discrete-time sliding mode,” IEEE Trans. Ind. Electron., vol. 45, no. 2, pp. 291–296, April 1998.

    Article  Google Scholar 

  20. K. Abidi, J. Xu, and X. Yu, “On the discrete-time integral sliding mode control,” IEEE Trans. Autom. Control, vol. 52, no. 4. pp. 709–715, April 2007.

    Article  MathSciNet  MATH  Google Scholar 

  21. J. Xu, and K. Abidi, “Discrete-time output integral slidingmode control for a piezomotor-driven linear motion stage,” IEEE Trans. Ind. Electron., vol. 55, no. 11, pp. 3917–3926, 2008.

    Article  Google Scholar 

  22. L. Cao, and X. Chen, “Input-output linearization minimum sliding mode error feedback control for synchronization of chaotic system,” Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng., vol. 229, no. 8, pp. 352–368, September 2015.

    Article  Google Scholar 

  23. D. Sha and V. Bajic, “Robust discrete adaptive inputoutput-based sliding mode controller,” Int. J. Syst. Sci., vol. 31, no. 12, pp. 1601–1614, December 2000.

    Article  MATH  Google Scholar 

  24. X. Chen, T. Fukuda, and K. Young, “Adaptive quasisliding-mode tracking control for discrete uncertain inputoutput systems,” IEEE Trans. Ind. Electron., vol. 48, no. 1, pp. 216–224, February 2001.

    Article  Google Scholar 

  25. S. Janardhanan and B. Bandyopadhyay, “Multirate output feedback based robust quasi-sliding mode control of discrete-time system,” IEEE Trans. Autom. Control, vol. 52, no. 3, pp. 499–503, March 2007.

    Article  MathSciNet  MATH  Google Scholar 

  26. X. Yu, B. Wang, and X. Li, “Computer-controlled variable structure systems: The state-of-the-art,” IEEE Trans. Ind. Inf., vol. 8, no. 2, pp. 197–205, May 2012.

    Article  Google Scholar 

  27. Q. Xu, “Digital sliding-mode control of piezoelectric micropositioning system based on input-output model,” IEEE Trans. Ind. Electron., vol. 61, no. 10, pp. 5517–5526, October 2014.

    Article  Google Scholar 

  28. J. Butterworth, L. Pao, and D. Y. Abramovitch, “A discretetime single-parameter combined feedforward/feedback adaptive-delay algorithm with applications to piezo-based raster tracking Control,” IEEE Trans. Control Syst. Technol., vol. 20, no. 2, pp. 416–423, March 2012.

    Article  Google Scholar 

  29. M. Tomizuka, “Zero phase error tracking algorithm for digital control,” IJ. Dyn. Syst. Meas. Control Trans. ASME, vol. 109, no. 1, pp. 65–68, May 1987.

    Article  MATH  Google Scholar 

  30. J. Butterworth, L. Pao, and D. Abramovitch, “Analysis and comparison of three discrete-time feedforward modelinverse control techniques for nonminimum-phase systems,” Mechatronics, vol. 22, no. 5, pp. 577–587, August 2012.

    Article  Google Scholar 

  31. S. Yeh and P. Hsu, “Analysis and design of the integrated controller for precise motion systems,” IEEE Trans. Control Syst. Technol., vol. 7, no. 6, pp. 706–717, November 1999.

    Article  Google Scholar 

  32. N. Schapiro, Z. Palmor, and A. Steinberg, “Robust output feedback stabilizing control of discrete uncertain SISO systems,” IEEE Trans. Autom. Control, vol. 41, no. 9, pp. 1377–1381, September 1996.

    Article  MathSciNet  MATH  Google Scholar 

  33. Y. Wei, H. Yu, H. R. Karimi, and Y. H. Joo, “New approach to fixed-order output-feedback control for piecewise-affine systems,” IEEE Trans. Circuits Syst. Regul. Pap., vol. 65, no. 9, pp. 2961–2969, September 2018.

    Article  MathSciNet  Google Scholar 

  34. Y. Wei, J. Qiu, and H. K. Lam, “A new approach to reliable output feedback control of fuzzy-affine systems with time delays and sensor faults,” IEEE Trans. Fuzzy Syst., vol. 25, no. 6, pp. 1808–1823, December 2017.

    Article  Google Scholar 

  35. H. Ma, H. Liang, Q. Zhou, and C. K. Ahn, “Adaptive dynamic surface control design for uncertain nonlinear strictfeedback systems with unknown control direction and disturbances,” IEEE Trans. Syst., Man Cybern. Syst., 2018. DOI: 10.1109/TSMC.2018.2855170

    Google Scholar 

  36. Y. Zhang, H. Liang, H. Ma, Q. Zhou, and Z. Yu, “Distributed adaptive consensus tracking control for nonlinear multi-agent systems with state constraints,” Appl. Math. Comput., vol. 326, pp. 16–32, June 2018.

    MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Haifeng Ma & Zhenhua Xiong

  2. The Hong Kong Polytechnic University, Department of Industrial and Systems Engineering, Kowloon, Hong Kong

    Haifeng Ma & Yangmin Li

  3. Tianjin University of Technology, Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, Tianjin, China

    Yangmin Li

Authors
  1. Haifeng Ma
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  2. Yangmin Li
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  3. Zhenhua Xiong
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Corresponding author

Correspondence to Yangmin Li.

Additional information

Recommended by Editor Hamid Reza Karimi. This work is supported by the National Science Foundation of China under Grant (51805327, 51575544), by the Hong Kong Scholars Program under Grant (XJ2017022), the research committee of the Hong Kong Polytechnic University under Grant (G-YZ1G, 1-ZE97), and in part by Tianjin Natural Science Foundation (16JCZDJC38000).

Haifeng Ma received the B.E. and M.E. degrees in mechanical engineering from Southwest Jiaotong University, Chengdu, China, in 2010 and 2013, respectively, and the Ph.D. degree in mechatronics from Shanghai Jiao Tong University, Shanghai, China, in 2017. He is currently a "Hong Kong Scholar" and a postdoctoral fellow in The Hong Kong Polytechnic University, Kowloon, Hong Kong. He is also a postdoctoral fellow with the State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai, China. His research interests include sliding-mode control (SMC) theory and applications, vibration control and intelligent manufacturing.

Yangmin Li received the B.S. and M.S. degrees from Jilin University, Changchun, China, in 1985 and 1988, respectively, and the Ph.D. degree from Tianjin University, Tianjin, China, in 1994, all in mechanical engineering. He is currently a Full Professor of the Department of Industrial and Systems Engineering of The Hong Kong Polytechnic University. He has authored and coauthored 407 scientific papers in journals and conferences. His research interests include micro/nanomanipulation, compliant mechanism, precision engineering,robotics, multibody dynamics and control. Dr. Li is a Member of the ASME. He is an Associate Editor of the IEEE Trans. Auto. Sci. Eng., Associate Editor of Mechatronics, Associate Editor of the International Journal of Control, Automation,and Systems, and Associate Editor of IEEE Access.

Zhenhua Xiong received the B.E. and M.E. degrees from the Department of Aircraft Design, Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 1995 and 1998, respectively, and the Ph.D. degree from the Electrical and Electronics Engineering Department, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, in 2002. He is currently a Professor with the School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China. His research interests include servo motion control and intelligent manufacturing.

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Ma, H., Li, Y. & Xiong, Z. A Generalized Input-output-based Digital Sliding-mode Control for Piezoelectric Actuators with Non-minimum Phase Property. Int. J. Control Autom. Syst. 17, 773–782 (2019). https://doi.org/10.1007/s12555-018-9451-z

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  • DOI: https://doi.org/10.1007/s12555-018-9451-z

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