Advertisement

Control Algorithms of Magnetic Suspension Systems Based on the Improved Double Exponential Reaching Law of Sliding Mode Control

  • Jian Pan
  • Wei Li
  • Haipeng Zhang
Regular Papers Control Theory and Applications

Abstract

This paper proposes an improved double power reaching law integral SMC algorithm to overcome the chattering, large overshoot, slow response. This improved algorithm has two advantages. Firstly, the designed control law can reach the approaching equilibrium point quickly when it is away from or close to the sliding surface. The chattering and response speed problems can be resolved. Secondly, the proposed algorithm has a good anti-jamming performance, and can maintain a good dynamic quality under the condition of the uncertain external disturbance. Finally, the proposed algorithm is applied to the open-loop unstable magnetic suspension system. Theoretical analysis and Matlab simulation results show that the improved algorithm has better control performances than the traditional SMC and the power reaching law integral SMC algorithm, such as less chattering, smaller overshoots, and faster response speed.

Keywords

Improved double power reaching law integral sliding mode control magnetic suspension systems Matlab simulation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Y. Cao, P. Li, and Y. Zhang, “Parallel processing algorithm for railway signal fault diagnosis data based on cloud computing,” Future Generation Computer Systems, vol. 88, pp. 279–283, November 2018.Google Scholar
  2. [2]
    Y. Z. Zhang, Y. Cao, Y. H. Wen, L. Liang, and F. Zou, “Optimization of information interaction protocols in cooperative vehicle-infrastructure systems,” Chinese Journal of Electronics, vol. 27, no. 2, pp. 439–444, March 2018.Google Scholar
  3. [3]
    Y. Cao, L. C. Ma, S. Xiao, X. Zhang, and W. Xu, “Standard analysis for transfer delay in CTCS-3,” Chinese Journal of Electronics, vol. 26, no. 5, pp. 1057–1063, September 2017.Google Scholar
  4. [4]
    Y. Cao, Y. Wen, X. Meng, and W. Xu, “Performance evaluation with improved receiver design for asynchronous coordinated multipoint transmissions,” Chinese Journal of Electronics. vol. 25, no. 2, pp. 372–378, March 2016.Google Scholar
  5. [5]
    S. L. Shi, K. S. Kang, J. X. Li and Y. M. Fang, “Sliding mode control for continuous casting mold oscillatory system driven by servo motor,” International Journal of Control, Automation and Systems, vol. 15, no. 4, pp. 1669–1674, August 2017.Google Scholar
  6. [6]
    S. Islam, P. X. Liu, and A. E. Saddik, “Nonlinear robust adaptive sliding mode control design for miniature unmanned multirotor aerial vehicle,” International Journal of Control, Automation and Systems, vol. 15, no. 4, pp. 1661–1668, August 2017.Google Scholar
  7. [7]
    J. L. Chang, “Sliding mode control design for mismatched uncertain systems using output feedback,” International Journal of Control, Automation and Systems, vol. 14, no. 2, pp. 579–586, April 2016.Google Scholar
  8. [8]
    C. Pukdeboon, “Output feedback second order sliding mode control for spacecraft attitude and translation motion,” International Journal of Control, Automation and Systems, vol. 14, no. 2, pp. 411–424, April 2016.Google Scholar
  9. [9]
    F. Ding, “Decomposition based fast least squares algorithm for output error systems,” Signal Processing, vol. 93, no. 5, pp. 1235–1242, May 2013.Google Scholar
  10. [10]
    L. Xu, F. Ding, Y. Gu, A. Alsaedi, and T. Hayat, “A multiinnovation state and parameter estimation algorithm for a state space system with d-step state-delay,” Signal Processing, vol. 140, pp. 97–103, November 2017.Google Scholar
  11. [11]
    F. Ding, “Two-stage least squares based iterative estimation algorithm for CARARMA system modeling,” Applied Mathematical Modelling, vol. 37, no. 7, 4798–4808, April 2013.Google Scholar
  12. [12]
    Y. J. Liu, D. Q. Wang, and F. Ding, “Least squares based iterative algorithms for identifying Box-Jenkins models with finite measurement data,” Digital Signal Processing, vol. 20, no. 5, pp. 1458–1467, September 2010.Google Scholar
  13. [13]
    F. Ding, Y. J. Liu, and B. Bao, “Gradient based and least squares based iterative estimation algorithms for multiinput multi-output systems,” Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 226, no. 1, pp. 43–55, February 2012.Google Scholar
  14. [14]
    F. Ding, X. P. Liu, and G. Liu, “Gradient based and leastsquares based iterative identification methods for OE and OEMA systems,” Digital Signal Processing, vol. 20, no. 3, pp. 664–677, May 2010.Google Scholar
  15. [15]
    A. Qureshi and M. A. Abido, “Decentralized discretetime quasi-sliding mode control of uncertain linear interconnected systems,” International Journal of Control, Automation and Systems, vol. 12, no. 2, pp. 349–357, April 2014.Google Scholar
  16. [16]
    S. Mobayen, “An adaptive chattering-free PID sliding mode control based on dynamic sliding manifolds for a class of uncertain nonlinear systems,” Nonlinear Dynamics, vol. 82, no. 1–2, pp. 53–60, October 2015.MathSciNetzbMATHGoogle Scholar
  17. [17]
    Z. Belkhatir and T. M. Laleg-Kirati, “High-order sliding mode observer for fractional commensurate linear systems with unknown input,” Automatica, vol. 82, pp. 209–217, August 2017.MathSciNetzbMATHGoogle Scholar
  18. [18]
    J. Yang, J. Y. Su, S. H. Li, and X. H. Yu, “High-Order Mismatched Disturbance Compensation for Motion Control Systems Via a Continuous Dynamic Sliding-Mode Approach,” IEEE Transactions on Industrial Informatics, vol. 10, no. 1, pp. 604–614, February 2014.Google Scholar
  19. [19]
    S. Mobayen, D. Baleanu, and F. Tchier, “Second-order fast terminal sliding mode control design based on LMI for a class of non-linear uncertain systems and its application to chaotic systems,” Journal of Vibration and Control, vol. 23, no. 18, pp. 2912–2925, October 2017.MathSciNetzbMATHGoogle Scholar
  20. [20]
    S. Dadras and H. R. Momeni, “Adaptive sliding mode control of chaotic dynamical systems with application to synchronization,” Mathematics and Computers in Simulation, vol. 80, no. 12, pp. 2245–2257, August 2010.MathSciNetzbMATHGoogle Scholar
  21. [21]
    H. C. Gui and G. Vukovich, “Adaptive fault-tolerant spacecraft attitude control using a novel integral terminal sliding mode,” International Journal of Robust and Nonlinear Control, vol. 27, no. 16, pp. 3174–3196, November 2017.MathSciNetzbMATHGoogle Scholar
  22. [22]
    J. Pan, X. Jiang, X. K. Wan, and W. Ding, “A filtering based multi-innovation extended stochastic gradient algorithm for multivariable control systems,” International Journal of Control, Automation and Systems, vol. 15, no. 3, pp. 1189–1197, June 2017.Google Scholar
  23. [23]
    D. Ginoya, P. D. Shendge, and S. B. Phadke, “Sliding mode control for mismatched uncertain systems using an extended disturbance observer,” IEEE Transactions on Industrial Electronics, vol. 61, no. 4, pp. 1983–1992, April 2014.Google Scholar
  24. [24]
    X. S. Zhan, Z. H. Guan, X. H. Zhang, and F. S. Yuan, “Optimal tracking performance and design of networked control systems with packet dropout,” Journal of the Franklin Institute, vol. 350, no. 10, pp. 3205–3216, December 2013.MathSciNetzbMATHGoogle Scholar
  25. [25]
    X. S. Zhan, J.Wu, T. Jiang, and X.W. Jiang, “Optimal performance of networked control systems under the packet dropouts and channel noise,” ISA Transactions, vol. 58, no. 5, pp. 214–221, September 2015.Google Scholar
  26. [26]
    S. Dadras and H. R. Momeni, “Passivity-based fractionalorder integral sliding-mode control design for uncertain fractional-order nonlinear systems,” Mechatronics, vol. 23, no. 7, pp. 880–887, October 2013.Google Scholar
  27. [27]
    R. Galván-Guerra, L. Fridman, J. E. Velázquez-Velázquez, S. Kamal, and B. Bandyopadhyay, “Continuous output integral sliding mode control for switched linear systems,” Nonlinear Analysis: Hybrid Systems, vol. 22, pp. 284–305, November 2016.MathSciNetzbMATHGoogle Scholar
  28. [28]
    S. Chakrabarty and B. Bandyopadhyay, “A generalized reaching law for discrete time sliding mode control,” Automatica, vol. 52, pp. 83–86, February 2015.MathSciNetzbMATHGoogle Scholar
  29. [29]
    M. H. Rahman, M. Saad, J. P. Kenné, and P. S. Archambault, “Control of an exoskeleton robot arm with sliding mode exponential reaching law,” International Journal of Control, Automation and Systems, vol. 11, no. 1, pp. 92–104, February 2013.Google Scholar
  30. [30]
    Y. Q. Chen, Y. H. Wei, H. Zhong, and Y. Wang, “Sliding mode control with a second-order switching law for a class of nonlinear fractional order systems,” Nonlinear Dynamics, vol. 85, no. 1, pp. 633–643, July 2016.MathSciNetzbMATHGoogle Scholar
  31. [31]
    H. P. Wang, X. K. Zhao, and Y. Tian, “Trajectory Tracking Control of XY Table Using Sliding Mode Adaptive Control Based on Fast Double Power Reaching Law,” Asian Journal of Control, vol. 18, no. 6, pp. 2263–2271, November 2016.MathSciNetzbMATHGoogle Scholar
  32. [32]
    M. Van, S. S. Ge, and H. L. Ren, “Finite Time Fault Tolerant Control for Robot Manipulators Using Time Delay Estimation and Continuous Nonsingular Fast Terminal Sliding Mode Control,” IEEE Transactions on Cybernetics, vol. 47, no. 7, pp. 1681–1693, July 2017.Google Scholar
  33. [33]
    L. Xu, “A proportional differential control method for a time-delay system using the Taylor expansion approximation,” Applied Mathematics and Computation, vol. 236, pp. 391–399, June 2014.MathSciNetzbMATHGoogle Scholar
  34. [34]
    L. Xu, “Application of the Newton iteration algorithm to the parameter estimation for dynamical systems,” Journal of Computational and Applied Mathematics, vol. 288, pp. 33–43, November 2014.MathSciNetGoogle Scholar
  35. [35]
    L. Xu, L. Chen, and W. L. Xiong, “Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration,” Nonlinear Dynamics, vol. 79, no. 3, pp. 2155–2163, February 2015.MathSciNetGoogle Scholar
  36. [36]
    L. Xu, “The damping iterative parameter identification method for dynamical systems based on the sine signal measurement,” Signal Processing, vol. 120, pp. 660–667, March 2016.Google Scholar
  37. [37]
    L. Xu, and F. Ding, “Parameter estimation for control systems based on impulse responses,” International Journal of Control, Automation, and Systems, vol. 15, no. 6, pp. 2471–2479, December 2017.Google Scholar
  38. [38]
    L. Xu, “The parameter estimation algorithms based on the dynamical response measurement data,” Advances in Mechanical Engineering, vol. 9, no. 11, pp. 1–12, November 2017.Google Scholar
  39. [39]
    L. Xu and F. Ding, “Iterative parameter estimation for signal models based on measured data,” Circuits, Systems and Signal Processing, vol. 37, no. 7, pp. 3046–3069, July 2018.MathSciNetGoogle Scholar
  40. [40]
    L. Xu, W. L. Xiong, A. Alsaedi, and T. Hayat, “Hierarchical parameter estimation for the frequency response based on the dynamical window data,” International Journal of Control, Automation and Systems, vol. 16, no. 4, pp. 1756–1764, August 2018.Google Scholar
  41. [41]
    F. Ding and H. M. Zhang, “Gradient-based iterative algorithm for a class of the coupled matrix equations related to control systems,” IET Control Theory and Applications, vol. 8, no. 15, pp. 1588–1595, October 2014.MathSciNetGoogle Scholar
  42. [42]
    H. M. Zhang and F. Ding, “Iterative algorithms for X+A(T)X(-1)A=I by using the hierarchical identification principle,” Journal of the Franklin Institute, vol. 353, no. 5, pp. 1132–1146, March 2016.MathSciNetzbMATHGoogle Scholar
  43. [43]
    H. M. Zhang and F. Ding, “A property of the eigenvalues of the symmetric positive definite matrix and the iterative algorithm for coupled Sylvester matrix equations,” Journal of the Franklin Institute, vol. 351, no. 1, pp. 340–357, January 2014.MathSciNetzbMATHGoogle Scholar
  44. [44]
    X. Li and D. Q. Zhu, “An improved SOM neural network method to adaptive leader-follower formation control of AUVs,” IEEE Transactions on Industrial Electronics, vol. 65, no. 10, pp. 8260–8270, October 2018.Google Scholar
  45. [45]
    F. Z. Geng and S.P. Qian, “An optimal reproducing kernel method for linear nonlocal boundary value problems,” Applied Mathematics Letters, vol. 77, pp. 49–56, March 2018.MathSciNetzbMATHGoogle Scholar
  46. [46]
    X. Y. Li and B. Y. Wu, “A new reproducing kernel collocation method for nonlocal fractional boundary value problems with non-smooth solutions,” Applied Mathematics Letters, vol. 86, pp. 194–199, December 2018.MathSciNetGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Hubei Collaborative Innovation Center for High-efficiency Utilization of Solar EnergyHubei University of TechnologyWuhanP. R. China
  2. 2.Department of Control Science and EngineeringHubei Normal UniversityHuangshiChina
  3. 3.China Railway Major Bridge Engineering Group Limited CorporationWuhanP. R. China

Personalised recommendations