Skip to main content

Sliding Mode Variable Structure-Based Chattering Avoidance Control for Mobile Wheeled Inverted Pendulums

  • Chapter
  • First Online:
Robust and Intelligent Control of a Typical Underactuated Robot

Abstract

Sever chattering appearing in the traditional sliding mode control may cause harm to physical systems. This chapter shows two typical chattering avoidance controllers based on the idea of sliding mode variable structure, including adaptive super-twisting control and terminal sliding mode control. By proceeding with the discontinuous term on the second-order time derivative and introducing an adaptive gain, the proposed adaptive super-twisting control can suppress the system input chattering and learn the upper bounds of the lumped disturbances, thereby performing a superior performance of balance control of the WMIP system and capacity to reduce chattering. On the other hand, the terminal sliding mode control solves the equations of the underactuated part and the dynamics on the sliding surface simultaneously, allowing the system to be self-stabilizing on the sliding surface. Various simulations, including balance and velocity control, are conducted, which verifies the effectiveness of the proposed chattering avoidance controllers.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Kim, S., & Kwon, S. (2017). Nonlinear optimal control design for underactuated two-wheeled inverted pendulum mobile platform. IEEE/ASME Transactions on Mechatronics, 22, 2803–2808.

    Article  Google Scholar 

  2. Hendzel, Z. (2007). An adaptive critic neural network for motion control of a wheeled mobile robot. Nonlinear Dynamics, 40, 849–855.

    Article  MATH  Google Scholar 

  3. Butt, C., & Rahman, M. A. (2004). Limitations of simplified fuzzy logic controller for IPM motor drive. In Proceedings of the Conference Record of the 2004 IEEE Industry Applications Conference (pp. 1891–1898), Seattle, WA, USA, 3–7 October 2004.

    Google Scholar 

  4. Huang, J., Ri, M., Wu, D., & Ri, S. (2017). Interval type-2 fuzzy logic modeling and control of a mobile two-wheeled inverted pendulum. IEEE Transactions on Fuzzy Systems, 26(4), 2030–2038.

    Article  Google Scholar 

  5. Lee, D., Kim, H. J., & Sastry, S. (2009). Feedback linearization vs. adaptive sliding mode control for a quadrotor helicopter. International Journal of control, Automation and Systems, 7, 419–428.

    Article  Google Scholar 

  6. Utkin, V. I. (1993). Sliding mode control design principles and applications to electric drives. IEEE Transactions on Industrial Electronics, 40, 23–36.

    Article  Google Scholar 

  7. Li, H., Shi, P., & Yao, D. (2017). Adaptive sliding-mode control of Markov Jump nonlinear systems with actuator faults. IEEE Transactions on Automatic Control, 62, 1933–1939.

    Article  MathSciNet  MATH  Google Scholar 

  8. Su, X., Liu, X., Shi, P., & Yang, R. (2017). Sliding mode control of discrete-time switched systems with repeated scalar nonlinearities. IEEE Transactions on Automatic Control, 62, 4604–4610.

    Article  MathSciNet  MATH  Google Scholar 

  9. Huang, J., Guan, Z., Matsuno, T., Fukuda, T., & Sekiyama, K. (2010). Sliding-mode velocity control of mobile-wheeled inverted-pendulum systems. IEEE Transactions on Robotics, 26, 750–758.

    Article  Google Scholar 

  10. Sankaranarayanan, V., & Mahindrakar, A. D. (2009). Control of a class of underactuated mechanical systems using sliding modes. IEEE Transactions on Robotics, 25, 459–467.

    Article  Google Scholar 

  11. Pupek, L., & Dubay, R. (2018). Velocity and position trajectory tracking through sliding mode control of two-wheeled self-balancing mobile robot. In Proceedings of the 2018 Annual IEEE International Systems Conference (SysCon) (pp. 1–5), Vancouver, BC, Canada, 23–26 April 2018.

    Google Scholar 

  12. Yang, J., Li, S., & Yu, X. (2013). Sliding-mode control for systems with mismatched uncertainties via a disturbance observer. IEEE Transactions on Industrial Electronics, 60, 160–169.

    Article  Google Scholar 

  13. Zhang, J., Liu, X., Xia, Y., Zuo, Z., & Wang, Y. (2016). Disturbance observer-based integral sliding-mode control for systems with mismatched disturbances. IEEE Transactions on Industrial Electronics, 63, 7040–7048.

    Article  Google Scholar 

  14. Huang, J., Zhang, M., Ri, S., Xiong, C., Li, Z., & Kang, Y. (2019). High-order disturbance-observer-based sliding mode control for mobile wheeled inverted pendulum systems. IEEE Transactions on Industrial Electronics. https://doi.org/10.1109/TIE.2019.2903778.

    Article  Google Scholar 

  15. Huang, J., Ri, S., Fukuda, T., & Wang, Y. (2019). A disturbance observer based sliding mode control for a class of underactuated robotic system with mismatched uncertainties. IEEE Transactions on Automatic Control, 64, 2480–2487. https://doi.org/10.1109/TAC.2018.2868026.

    Article  MathSciNet  MATH  Google Scholar 

  16. Ding, S., & Li, S. (2017). Second-order sliding mode controller design subject to mismatched term. Automatica, 77, 388–392.

    Article  MathSciNet  MATH  Google Scholar 

  17. Ling, R., Maksimovic, D., & Leyva, R. (2016). Second-order sliding-mode controlled synchronous buck DCDC converter. IEEE Transactions on Power Electronics, 31, 2539–2549.

    Article  Google Scholar 

  18. Tiwari, P. M., Janardhanan, S., & un Nabi, M. (2015). Rigid spacecraft attitude control using adaptive integral second order sliding mode. Aerospace Science and Technology, 4(2), 50–57.

    Google Scholar 

  19. Chalanga, A., Kamal, S., Fridman, L. M., Bandyopadhyay, B., & Moreno, J. A. (2016). Implementation of super-twisting control: Super-twisting and higher order sliding-mode observer-based approaches. IEEE Transactions on Industrial Electronics, 63, 3677–3685.

    Article  Google Scholar 

  20. Derafa, L., Benallegue, A., & Fridman, L. (2012). Super twisting control algorithm for the attitude tracking of a four rotors UAV. Journal of the Franklin Institute, 349, 685–699.

    Article  MathSciNet  MATH  Google Scholar 

  21. Wang, C., Mi, Y., Fu, Y., & Wang, P. (2018). Frequency control of an isolated micro-grid using double sliding mode controllers and disturbance observer. IEEE Transactions on Smart Grid, 9, 923–930.

    Article  Google Scholar 

  22. Jia, Z., Yu, J., Mei, Y., Chen, Y., Shen, Y., & Ai, X. (2017). Integral backstepping sliding mode control for quadrotor helicopter under external uncertain disturbances. Aerospace Science and Technology, 68, 299–307.

    Article  Google Scholar 

  23. Zak, M. (1989). Terminal attractors in neural networks. Neural Networks, 2(4), 259–274.

    Article  Google Scholar 

  24. Man, Z. H., & Yu, X. (1997). Terminal sliding mode control of MIMO linear systems. IEEE Transactions on Circuits and Systems, 44(11), 1065–1070.

    Article  MathSciNet  Google Scholar 

  25. Ding, F., Huang, J., Wang, Y., Gao, X., et al. (2009). Optimal braking control for UW-car using sliding mode. In Proceeding IEEE 2009 International Conference on Robotics and Biomimetics, pp. 117C122.

    Google Scholar 

  26. Park, K.-B., & Tsuji, T. (1999). Terminal sliding mode control of second-order nonlinear uncertain systems. International Journal of Robust and Nonlinear Control, 9(11), 769C780.

    Google Scholar 

  27. Man, Z. H., et al. (1994). A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators. IEEE Transaction on Automatic Control, 39(12), 2464C2470.

    Google Scholar 

  28. Chen, S.-Y., & Lin, F.-J. (2011). Robust nonsingular terminal sliding model control for nonlinear magnetic bearing system. IEEE Transaction on Control Systems Technology,19(3), 636C643.

    Google Scholar 

  29. Liu, H., & Li, J. F. (2009). Terminal sliding mode control for spacecraft formation flying. IEEE Transaction on Aerospace and Electronic Systems,45(3), 835C846.

    Google Scholar 

  30. Guo, Y. S., & Li, C. (2008). Terminal sliding mode control for coordinated motion of a space rigid manipulator with external disturbance. Applied Mathematics and Mechanics,29(5), 583C590.

    Google Scholar 

  31. Ge, W., & Ye, D. (2011). Sliding mode variable structure control of mobile manipulators. International Journal of Modelling, Identification and Control,12(1C2), 166C172.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jian Huang .

Rights and permissions

Reprints and permissions

Copyright information

© 2023 Huazhong University of Science and Technology Press

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Huang, J., Zhang, M., Fukuda, T. (2023). Sliding Mode Variable Structure-Based Chattering Avoidance Control for Mobile Wheeled Inverted Pendulums. In: Robust and Intelligent Control of a Typical Underactuated Robot. Research on Intelligent Manufacturing. Springer, Singapore. https://doi.org/10.1007/978-981-19-7157-0_4

Download citation

Publish with us

Policies and ethics