Abstract
A new motion controller ensuring finite-time stability for permanent-magnet linear motor (PMLM) system is investigated in this paper via second-order sliding mode (SOSM) control technique. Firstly, by choosing position error as sliding mode variable, the position dynamic error system is derived for PMLM system. Then, by appropriate assumption that the lumped disturbance is bounded by a positive function, a new SOSM controller is constructed by using the adding power integrator technique. Strict mathematical analysis is provided to show that the proposed SOSM controller could steer the current position of PMLM to the desired position in finite time. Finally, the claimed performance of the proposed control strategy is illustrated by simulation results.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Lin, F.J., Teng, L.T., Chu, H.: Modified Elman neural network controller with improved particle swarm optimization for linear synchronous motor drive. IET Ele. Pow. Appl. 2(3), 201–214 (2008). https://doi.org/10.1049/iet-epa:20070368
Su, W.T., Liaw, C.M.: Adaptive positioning control for a LPMSM drive based on adapted inverse model and robust disturbance observer. IEEE Trans. Pow. Ele. 21(2), 505–517 (2006). https://doi.org/10.1109/TPEL.2005.869729
Tan, K.K., Huang, S.N., Lee, T.H: Robust adaptive numerical compensation for friction and force ripple in permanent-magnet linear motors. IEEE Trans. Magn. 38(1), 221–228 (2002). https://doi.org/10.1109/20.990111
Chen, S.L., Tan, K.K., Huang, S., Teo, C.S.: Modeling and compensation of ripples and friction in permanent-magnet linear motor using a hysteretic relay. IEEE/ASME Trans. Mech. 15(4), 586–594 (2010). https://doi.org/10.1109/TMECH.2009.2030794
Ahn, H.S., Chen, Y.Q., Dou, H.F.: State-periodic adaptive compensation of cogging and coulomb friction in permanent-magnet linear motors. IEEE Trans. Magn. 41(1), 90–98 (2005). https://doi.org/10.1109/TMAG.2004.840182
Du, H.B., Chen, X.P., Wen, G.H., Yu, X.H., Lv, J.H.: Discrete-time fast terminal sliding mode control for permanent magnet linear motor. IEEE Trans. Ind. Ele. 65(12), 9916–9927 (2018). https://doi.org/10.1109/TIE.2018.2815942
Liu, H.X., Li, S.H.: Speed control for PMSM servo system using predictive functional control and extended state observer. IEEE Trans. Ind. Ele. 59(2), 1171–1183 (2012). https://doi.org/10.1109/TIE.2011.2162217
Tan, K.K., Lee, T.H., Dou, H.F., Chin, S.J., Zhao, S.: Precision motion control with disturbance observer for pulse width modulated driven permanent magnet linear motors. IEEE Trans. Magn. 39(9), 1813–1818 (2003). https://doi.org/10.1109/TMAG.2003.810617
Yan, M.T., Shiu, Y.J.: Theory and application of a combined feedback feedforward control and disturbance observer in linear motor drive wire-EDM machines. Int. J. Mach. Tolls. Manu. 48, 388–401 (2008). https://doi.org/10.1016/j.ijmachtools.2007.09.006
Cupertino, F., Naso, D., Mininno, E., Turchiano, B.: Sliding mode control with double boundary layer for robust compensation of payload mass and friction in linear motors. IEEE Trans. Ind. App. 45(5), 1688–1676 (2009). https://doi.org/10.1109/TIA.2009.2027521
Lin, F.J., Hwang, J.C., Chou, P.H., Hung, Y.C.: FPGA-Based intelligent-complementary sliding-mode control for PMLSM srevo-drive system. IEEE Trans. Power Ele. 25(10), 2573–2587 (2010). https://doi.org/10.1109/TPEL.2010.2050907
Armstrong-Helouvry, B., Dupont, P., DeWit, C.C.: A survey of models, analysis tools and compensation methods for the control machines with friction. Automatic 30(7), 1083–1138 (1994). https://doi.org/10.1016/0005-1098(94)90209-7
Mo, X.H., Lan, Q.X.: Finite-time integral sliding mode control for motion control of permanent-magnet linear motor. Math. Prob. Eng. 2013, Article ID 567610, 7. https://doi.org/10.1155/2013/567610
Gao, W., Chen, X.P., Du, H.B., Bai, S.: Position tracking control for permanent magnet linear motor via continuous-time fast terminal sliding model control. J. Cont. Sci. Eng. 2018, Article ID 3813624, 6. https://doi.org/10.1155/2018/3813624
Lan, Q.X., Li, S.H., Khoo, S.Y., Shi, P.: Global finite-time stabilization for a class of stochastic nonlinear systems by output feedback. Int. J. Cont. 88(3), 494–506 (2015). https://doi.org/10.1080/00207179.2014.962766
Bhar, S.P., Bernstein, D.S.: Geometric homogeneity with applications to finite-time stability. Math. Cont. Sig. Syst. 17, 101–127 (2005). https://doi.org/10.1007/s00498-005-0151-x
Hong, Y.G., Wang, J.K., Cheng, D.Z.: Adaptive finite time control of nonlinear system with parameter uncertainty. IEEE Trans. Autom. Cont. 51(5), 858–862 (2006). https://doi.org/10.1109/TAC.2006.875006
Feng, Y., Yu, X.H., Man, Z.H.: Continuous finite-time control for robotic manipulators with terminal sliding mode. Automatic 38, 2159–2167 (2002). https://doi.org/10.1016/j.automatica.2005.07.001
Yang, J., Ding, Z.T., Li, S.H., Zhang, C.L.: Continuous finite-time oupt regulation of nonlinear systems with unmatched time-varying disturbance. IEEE Contr. Syst. Lett. 2(1), 97–102 (2018). https://doi.org/10.1109/LCSYS.2017.2755363
Lan, Q.X., Li, S.H., Yang, J.: Finite-time tracking control for a class of nonlinear systems with multiple mismatched disturbances. Int. J. Robust. Non. Contr. (2020). https://doi.org/10.1002/rnc.4989
Yu, S.H., Yu, X.H., Shirinzadeh, B., Man, Z.H.: Non-singular terminal sliding mode control of rigid manipulators. Automatic 41, 1957–1964 (2005). https://doi.org/10.1016/s0005-1098(02)00147-4
Lan, Q.X., Li, S.H., Yang, J., Sun, H.B.: Finite-time control for 6DOF spacecraft formation flying system. J. Aero. Eng. 28(5), 040140137 (2015). https://doi.org/10.1061/(ASCE)AS.1943-5525.0000476
Li, S.H., Liu, H.X., Ding, S.H.: A speed control for a PMSM using finite-time feedback control and disturbance compensation. Trans. Inst. Meas. Cont. 32(2), 170–187 (2010). https://doi.org/10.1177/0142331209339860
Guermouche, M.S., Ali, A., Langlois, N.: Super-twisting algorithm for dc motor position control via disturbance observer. IFAC-Papers on line 48(30), 043–048 (2015). https://doi.org/10.1016/j.ifacol.2015.12.351
Kwon, S., Chung, W.K.: A discrete-time design and analysis of perturbation observer for motion control applications. IEEE Trans. Cont. Sys. Tech. 11(3), 399–407 (2003). https://doi.org/10.1109/TCST.2003.810398
Barabanov, N., Ortega, R.: Necessary and sufficient conditions for passivity of the LuGre friction model. IEEE Trans. Auto. Cont. 45(4), 830–832 (2000). https://doi.org/10.1109/9.847131
Qian, C.J., Lin, W.: A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Trans. Auto. Cont. 46(7), 1061–1079 (2001). https://doi.org/10.1109/9.935058
Ding, S.H., Li, S.H.: Second-order sliding mode controller design subject to mismatched term. Automatic 77, 388–392 (2017). https://doi.org/10.1016/j.automatica.2016.07.038
Acknowledgements
This work was supported in part by the Key Research and Development and Promotion of Special Project of Henan Province under Grant 202102210142.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Cao, W., Lan, Q., Ma, T. (2022). Second-Order Sliding Mode Controller Design for Motion Control of PMLM System. In: Yan, L., Duan, H., Yu, X. (eds) Advances in Guidance, Navigation and Control . Lecture Notes in Electrical Engineering, vol 644. Springer, Singapore. https://doi.org/10.1007/978-981-15-8155-7_176
Download citation
DOI: https://doi.org/10.1007/978-981-15-8155-7_176
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-8154-0
Online ISBN: 978-981-15-8155-7
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)