SECOND ORDER SLIDING MODE CONTROLLERS OF MICROPOSITIONING STAGE PIEZOELECTRIC ACTUATOR WITH COLMAN-HODGDON MODEL PARAMETERS
Keywords:
Colman-Hodgdon model, Identification particle swarm optimization PSO approach, Second order sliding mode controllers (SOSMC), Piezo-positioning mechanismAbstract
This paper presents the second-order sliding mode controller (SOSMC) of a micro-positioning stage piezoelectric model actuator (PEA), where the C-H model parameters are adopted to describe the hysteresis behavior and identified through particle swarm optimization. In this technique, two control algorithms are developed. The first one is the so-called twisting algorithm (TA). The control appears explicitly in the second surface derivative, and in a discontinuous control action that ensures a sliding regime mode. The second one, the super twisting algorithms (STA) has been developed and analyzed for systems. The use of both algorithms gives a significant reduction in chattering as compared to the standard sliding mode control. It is shown that the STA case offers better performances than TA. Simulation results are presented to demonstrate the advantage of SOSMC over SMC.
References
(1) G. Wan, G. Chen, H. Zhou, F. Bai, Modeling and Tracking Control for Piezoelectric Actuator Based on a New Asymmetric Hysteresis model, IEEE/CAA Journal of Automatica Sinica, 4, 4, pp. 782–791 (2017).
(2) A. Nicolaide, An approach to the mathematical modeling of the hysteresis curves of magnetic materials: the minor curves, Rev. Roum. Sci. Techn. – Électrotechn. et Énerg., 52, 3, pp. 301–310, (2007).
(3) L. Petrescu, Comparison between frequently used hysteresis models, Rev. Roum. Sci. Techn.– Électrotechn. et Énerg., 52, 3, pp. 311–320 (2007).
(4) G Y.Gu, L.-M. Zhu, C.-Y. Su, H. Ding, S. Fatikow, Modeling and control of piezo-actuated nanopositioning stages: a survey, IEEE Transactions on Automation Science and Engineering, 13, 1, pp. 313–332 (2016).
(5) A. Giustiniani, A. Masi, M. Biggio, M. Butcher, M. Storace, Memory characteristics of hysteresis and creep in multi-layer piezoelectric actuators: An experimental analysis, Physica B: Condensed Matter, 435, pp. 40–43, (2014).
(6) V. Paltanea, G. Paltanea, P. Minciunescu, F.I. Hantila, M. Maricaru, P.C. Andrei, C. Grumeza, Static hysteresis determination using a new laboratory apparatus, Rev. Roum. Sci. Techn.-Electrotechn. et Energ. 63, 4, pp. 353–357 (2018).
(7) A. Ladjimi, A. Barouri, Modeling of frequency effects in a Jiles- Atherton magnetic hysteresis model, Rev. Roum. Sci. Techn-Electrotechn. et Energ., 61, 3, pp. 217–220 (2016).
(8) C. Y. Glu, G. Kavuran, Sliding mode controller design fractional order differentiation: applications for unstable time delay systems, Turk. J. Elec. Eng. & Comp. Sci. 22, pp. 1270 –1286 (2014).
(9) N. Kapoor, J. Ohri, Improved PSO tuned Classical Controllers (PID and SMC) for Robotic Manipulator, I. J. Modern Education and Computer Science, 1, pp. 47–54 (2015).
(10) M. A. Salai Kumutha, M. Vasugi, R. Dharmaprakash, Voltage Ripple Reduction of Buck Converter Using Sliding Mode Control Technique, Middle-East Journal of Scientific Research (Sensing, Signal Processing and Security), 23, pp. 83–88 (2015).
(11) F. Cupertino, D. Naso, E. Mininno, B. Turchiano, Sliding-Mode with Double Boundary Layer for Robust Compensation of Payload Mass and Friction in Linear Motors, IEEE Transactions on Industry Applications, 45, 5, pp. 1688–1695 (2009).
(12) E. Kose, H. Kizmaz, K. Abaci, S. Aksoy, Control of SVC based on the sliding mode control method, Turk. J. Elec. Eng. & Comp. Sci. 22, 3, pp. 605–619 (2014).
(13) J. Li, L. Yang, Adaptive PI-Based Sliding Mode Control for Nano positioning of Piezoelectric Actuators, Mathematical Problems in Engineering, 2014, pp. 1–10, (2014).
(14) L. Mandache, D. Topan, K. Al-Haddad, Modeling of nonlinear ferromagnetic cores, Rev. Roum. Sci. Techn. – Électrotechn. et Énerg., 53, 4, pp. 403–412 (2008).
(15) Z. Qiao, T. Shi, Y. Wang, Y. Yan, C. Xia, X. He, New Sliding-Mode Observer for Position Sensorless Control of Permanent-Magnet Synchronous Motor, IEEE Transactions on Industry Applications, 60, 2, pp. 710–719 (2013).
(16) V. Goyal, V. K. Deolia, T. N. Sharma, Robust Sliding Mode Control for Nonlinear Discrete-Time Delayed Systems Based on Neural Network, Intelligent Control and Automation, 6, 1, pp. 75–83, (2015).
(17) S. Qu, X. Xia, J. Zhang, Dynamics of Discrete-Time Sliding-Mode-Control Uncertain Systems with a Disturbance Compensator, IEEE Transactions on Industry Applications, 61, 7, pp. 3502 – 3510 (2013).
(18) A. Yazdanpanah, A. Rezaee, A. Faraahi, Robot Control Using Intelligent Gain Sliding Mode, International Journal of Hybrid Information Technology, 8, 1, pp. 227–236 (2015).
(19) S. Kamal, B. Bandyopadhyay, Arbitrary higher order sliding mode control based on control Lyapunov approach, Variable Structure Systems (VSS), pp. 446 – 451 (2012).
(20) R. Ling, M. Wu, Y. Dong, Y. Chai, High Order Sliding-Mode Control for uncertain nonlinear systems with relative degree three, Communications in Nonlinear Science and Numerical Simulation 17, 8, pp. 3406–3416 (2012).
(21) G. Bartolini, A. Pisano, E. Punta, E. Usai, A survey of applications of second-order sliding mode control to mechanical systems, International Journal of Control, 76, 9–10, pp. 875–892 (2003).
(22) J. Li, L. Yan, Finite-Time Terminal Sliding Mode Tracking Control for Piezoelectric Actuators, 2014, pp. 1–9 (2014).
(23) J. Liu, G. Ding, Z. S. Zhao, Design Higher Order Sliding Mode Controller for a Class of SISO Uncertain Nonlinear System, Applied Mechanics and Materials, 397–400, pp. 1442–1445 (2013).
(24) V. Ionita, E. Cazacu, Magnetic hysteresis modeling based on magneto-optical Kerr effect, Rev. Roum. Sci. Techn. – Électrotechn. et Énerg., 53, 4, pp. 455–462 (2008).
(25) A. Yazdanpanah, A. Rezaee, A. Faraahi, Robot Control Using Intelligent Gain Sliding Mode, International Journal of Hybrid Information Technology, 8, 1, pp. 227–236 (2015).
(26) M. Furat, I. Eker, Experimental Evaluation of Sliding-Mode Control Techniques, Çukurova University Journal of the Faculty of Engineering and Architecture, 27, 1, pp. 23–37 (2012).
(27) S. Kamal, B. Bandyopadhyay, Higher Order Sliding Mode Control: A Control Lyapunov Function Based Approach, WSEAS Transactions on Systems and Control, 9, pp. 38–46 (2014).
(28) A. Levant, A. Pridor, R. Gitizadeh, I. Yaech, J. Z .Ben-Asher, Aircraft pitch control via second-order sliding technique, Journal of Guidance, Control and Dynamics, 23, 4, pp. 586–594 (2000).
(29) A. Levant, Robust exact differentiation via sliding mode technique, Automatica, 34, pp. 379–384 (1998).
(30) S. M. Redha, T. Abdelhalim, A new Algorithm Observer Of Higher Order Sliding Mode Applied To Series Multicells Converter, Rev. Roum. Sci. Techn.-Electrotechn. et Energ., 61, 2, pp. 126 –130 (2016).
(31) B. D. Colman, M.L.Hodgdon, On a class of constitutive relations for ferromagnetic hysteresis, Archive for Rational Mechanics and Analysis, 99, 4, pp. 375–396 (1987).
(32) B. D. Colman, M. L. Hodgdon, A constitutive relation for rate-independent hysteresis in ferromagnetically soft materiels, Int. J. Engng. Sci., 24, 6, pp. 897–919 (1986).
(33) J. Vörös, Modeling and Identification of Discrete-Time Dynamic Cascade Systems with Input Hysteresis, Mathematical Problems in Engineering, 2015, pp.1–8 (2015).
(34) A. Ounissi, K. Yakoub, A. Kaddouri, R. Abdessemed, Robust Adaptive Displacement Tracking Control of Piezo-Actuated Stage, International Conference on Systems and Control, University of Batna 2, Algeria, pp. 297–302, 2017.
(35) L. Fridman, A. Levant, Higher-order sliding modes. Sliding mode control in engineering, Ed. Marcel Dekker, 2002.
(36) B. Koo, Y. Yoo, S. Won, Super-twisting algorithm based sliding mode controller for a refrigeration system, Proceedings of 12th International Conference on Control, Automation and Systems (ICCAS), Jeju Island, pp. 34–38, 2012.
(37) E. S. Elyoussef, E. R. D. Pieri, M. Jungers, U. F. Moren, Super- twisting sliding modes tracking control of a nonholonomic wheeled mobile robot, Int. IFAC. Symp. on Robot Control, pp. 429–434, 2012.
(38) J. Davila, L.Fridman, Observation and identification of mechanical systems via second order sliding modes, 8th International workshop on variables structure systems, September, 2004.
(39) J. A. Morino, M. Osorio, A Lyapunov approach to second-order sliding mode controllers and observer, The 47th IEEE conference on decision and control, pp 2856-2861, 2008.
