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Fast nonsingular terminal sliding mode control for permanent-magnet linear motor via ELM

  • Extreme Learning Machine and Deep Learning Networks
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Abstract

In this paper, a novel fast nonsingular terminal sliding mode (FNTSM) control strategy using extreme learning machine (ELM) is proposed for permanent-magnet linear motor systems. It is shown that the developed FNTSM controller is composed of an equivalent control via ELM technique, a compensation control and a reaching control. Distinguished from the traditional ELM for pattern classification, output weights of the proposed ELM are adaptively adjusted by the adaptive law in Lyapunov sense from the global stability point of view, such that the equivalent control of the proposed controller can be flexibly estimated via ELM. Not only can the strong robustness and the faster convergence rate of the closed-loop control be guaranteed, but also the dependence of system dynamics can be further alleviated in the controller design due to the implementation of the ELM. Comparative simulation results are given to validate the robust control performance of the developed controller for both step tracking and sinusoidal tracking purposes.

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References

  1. Tan KK, Huang SN, Lee TH (2002) Robust adaptive numerical compensation for friction and force ripple in permanent-magnet linear motors. IEEE Trans Magn 38:221–228

    Article  Google Scholar 

  2. Kim J, Choi S, Cho K, Nam K (2016) Position estimation using linear hall sensors for permanent magnet linear motor systems. IEEE Trans Ind Electron 63:7644–7652

    Article  Google Scholar 

  3. Zhang DL, Chen YP, Zhou ZD et al (2007) Robust adaptive motion control of permanent magnet linear motors based on disturbance compensation. IET Electr Power Appl 1:543–548

    Article  Google Scholar 

  4. Chen C-H, Cheng M-Y (2005) Design and implementation of a cost-effective position control system for an ironless linear motor. IEE Proc Electr Power Appl 152:1223–1232

    Article  Google Scholar 

  5. Tan KK, Lee TH, Dou HF et al (2003) Precision motion control with disturbance observer for pulsewidth-modulated-driven permanent-magnet linear motors. IEEE Trans Magn 39:1813–1818

    Article  Google Scholar 

  6. Basak A (1996) Permanent-magnet DC linear motors. Clarendon Press, New York

    Google Scholar 

  7. Tang KZ, Huang SN, Tan KK, Lee TH (2004) Combined PID and adaptive nonlinear control for servo mechanical systems. Mechatronics 14:701–714

    Article  Google Scholar 

  8. Tan KK, Lee TH, Dou H, Lim SY (2005) Adaptive ripple suppression/compensation apparatus for permanent magnet linear motors. US Patent 6,853,158

  9. Chen S-L, Tan KK, Huang S, Teo CS (2010) Modeling and compensation of ripples and friction in permanent-magnet linear motor using a hysteretic relay. IEEE/ASME Trans Mechatron 15:586–594

    Article  Google Scholar 

  10. Utkin VI (2013) Sliding modes in control and optimization. Springer, New York

    Google Scholar 

  11. Edwards C, Spurgeon S (1998) Sliding mode control: theory and applications. CRC Press, London

    Book  Google Scholar 

  12. Cupertino F, Naso D, Mininno E, Turchiano B (2009) Sliding-mode control with double boundary layer for robust compensation of payload mass and friction in linear motors. IEEE Trans Ind Appl 45:1688–1696

    Article  Google Scholar 

  13. Lin F-J, Hwang J-C, Chou P-H et al (2010) FPGA-based intelligent-complementary sliding-mode control for PMLSM servo-drive system. IEEE Trans Power Electron 25:2573–2587

    Article  Google Scholar 

  14. Zhihong M, Yu XH (1997) Terminal sliding mode control of MIMO linear systems. IEEE Trans Circuits Syst I Fundam Theory Appl 44:1065–1070

    Article  MathSciNet  Google Scholar 

  15. Yang L, Yang J (2011) Nonsingular fast terminal sliding-mode control for nonlinear dynamical systems. Int J Robust Nonlinear Control 21:1865–1879

    Article  MathSciNet  Google Scholar 

  16. Du H, Chen X, Wen G et al (2018) Discrete-time fast terminal sliding mode control for permanent magnet linear motor. IEEE Trans Ind Electron 65:9916–9927

    Article  Google Scholar 

  17. Gao W, Chen X, Du H, Bai S (2018) Position tracking control for permanent magnet linear motor via continuous-time fast terminal sliding mode control. J Control Sci Eng 2018:1–6

    MathSciNet  MATH  Google Scholar 

  18. Wang H, Shi L, Man Z et al (2018) Continuous fast nonsingular terminal sliding mode control of automotive electronic throttle systems using finite-time exact observer. IEEE Trans Ind Electron 65:7160–7172

    Article  Google Scholar 

  19. Wang H, Man Z, Kong H et al (2016) Design and implementation of adaptive terminal sliding-mode control on a steer-by-wire equipped road vehicle. IEEE Trans Ind Electron 63:5774–5785

    Article  Google Scholar 

  20. Huang C, Liu B (2019) New studies on dynamic analysis of inertial neural networks involving non-reduced order method. Neurocomputing 325:283–287

    Article  Google Scholar 

  21. Huang C, Zhang H (2019) Periodicity of non-autonomous inertial neural networks involving proportional delays and non-reduced order method. Int J Biomath 12:1950016

    Article  MathSciNet  Google Scholar 

  22. Wang H, Xu Z, Do MT et al (2015) Neural-network-based robust control for steer-by-wire systems with uncertain dynamics. Neural Comput Appl 26:1575–1586

    Article  Google Scholar 

  23. Huang G-B, Zhu Q-Y, Siew C-K (2006) Extreme learning machine: theory and applications. Neurocomputing 70:489–501

    Article  Google Scholar 

  24. Elkoteshy Y, Jiao LC, Chen W (2014) ELM-based adaptive backstepping neural control for a class of uncertain MIMO nonlinear systems with predefined tracking accuracy. Int J Control 87:1047–1060

    Article  MathSciNet  Google Scholar 

  25. Zhang Y, Fang Z, Li H (2015) Extreme learning machine assisted adaptive control of a quadrotor helicopter. Math Probl Eng 2015:1–12

    Google Scholar 

  26. Rong H-J, Zhao G-S (2013) Direct adaptive neural control of nonlinear systems with extreme learning machine. Neural Comput Appl 22:577–586

    Article  Google Scholar 

  27. Tan KK, Zhao S (2002) Adaptive force ripple suppression in iron-core permanent magnet linear motors. In: Proceedings of the 2002 IEEE international symposium on intelligent control, pp 266–269

  28. Ahn H-S, Chen Y, Dou H (2005) State-periodic adaptive compensation of cogging and coulomb friction in permanent magnet linear motors. In: Proceedings of the 2005 American control conference, pp 3036–3041

  29. Krishnamurthy P, Khorrami F (2001) Adaptive control of stepper motors without current measurements. In: Proceedings of the 2001 American Control Conference, pp 1563–1568

  30. Huang G-B (2003) Learning capability and storage capacity of two-hidden-layer feedforward networks. IEEE Trans Neural Netw 14:274–281

    Article  Google Scholar 

  31. Rao CR (1971) Generalized inverse of matrices and its applications. Wiley, New York

    MATH  Google Scholar 

  32. Huang G-B, Chen L, Siew CK et al (2006) Universal approximation using incremental constructive feedforward networks with random hidden nodes. IEEE Trans Neural Netw 17:879–892

    Article  Google Scholar 

  33. Khalil HK, Grizzle JW (2002) Nonlinear systems. Prentice hall, New York

    Google Scholar 

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Authors and Affiliations

  1. Hefei University of Technology, Hefei, 230009, China

    Jie Zhang & Ming Yu

  2. Murdoch University, Perth, WA, 6150, Australia

    Hai Wang, Amirmehdi Yazdani & Farhad Shahnia

  3. Swinburne University of Technology, Melbourne, VIC, 3122, Australia

    Zhenwei Cao & Jinchuan Zheng

Authors
  1. Jie Zhang
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  2. Hai Wang
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  3. Zhenwei Cao
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  4. Jinchuan Zheng
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  5. Ming Yu
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  6. Amirmehdi Yazdani
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  7. Farhad Shahnia
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Correspondence to Hai Wang.

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Zhang, J., Wang, H., Cao, Z. et al. Fast nonsingular terminal sliding mode control for permanent-magnet linear motor via ELM. Neural Comput & Applic 32, 14447–14457 (2020). https://doi.org/10.1007/s00521-019-04502-4

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  • DOI: https://doi.org/10.1007/s00521-019-04502-4

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