Skip to main content
SpringerLink
Log in

Sampled-data Fuzzy Control of Two-wheel Inverted Pendulums Based on Passivity Theory

  • Regular Papers
  • Intelligent Control and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

In this paper, an aperiodically sampled-data control scheme is detailed for the two-wheel inverted pendulum using Takagi-Sugeno (T-S) fuzzy models. The passivity theory is applied in the presence of the disturbances in the actuator channel. A two-rule fuzzy model is utilized to represent the two-wheel inverted pendulum. By using the pendulum angle as the antecedent variable of the fuzzy rule, a passive sampled-data controller is established using the pendulum inclination angle and the mean value of the rim motors’ rotary angles. A Lyapunov-like function based on the two fuzzy rules is constructed to develop criteria of passivity, by the utilization of very-strict passivity in terms of the pendulum angle. Then a solution to the gains of sampled-data controller is synthesized to ensure the very-strict passivity of the pendulum system. By the illustrative examples, the effectiveness of the variable-sampling control scheme is validated for the two-wheel inverted pendulum.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

D :

Distance between the two wheels

f L :

Force from the left rim motor

f R :

Force from the right rim motor

g :

Gravitational acceleration

l :

Length between wheel axle and gravitational center of the pendulum

M :

Mass of the pendulum

m :

Mass of the cart

r :

Radius of the wheel

θ :

Mean value of the rim motors’ rotary angles

θ L :

Rotary angle of the left rim motor

θ R :

Rotary angle of the right rim motor

ψ :

Cart Yaw steering angle

ϕ :

Pendulum inclination angle

References

  1. S. Kim and S. Kwon, “Nonlinear optimal control design for underactuated two–wheeled inverted pendulum mobile platform,” IEEE/ASME Transactions on Mechatronics, vol. 22, no. (6), pp. 2803–2808, 2017.

    Article  Google Scholar 

  2. C.-H. Huang, W.-J. Wang, and C.-H. Chiu, “Design and implementation of fuzzy control on a two–wheel inverted pendulum,” IEEE Transactions on Industrial Electronics, vol. 58, no. (7), pp. 2988–3001, 2011.

    Article  Google Scholar 

  3. V. T. Yen, W. Y. Nan, P. Van Cuong, N. X. Quynh, and V. H. Thich, “Robust adaptive sliding mode control for industrial robot manipulator using fuzzy wavelet neural networks,” International Journal of Control, Automation and Systems, vol. 15, no. (6), pp. 2930–2941, 2017.

    Article  Google Scholar 

  4. H. Li and Y. Shi, “Event–triggered robust model predictive control of continuous–time nonlinear systems,” Automatica, vol. 50, no. (5), pp. 1507–1513, 2014.

    Article  MathSciNet  MATH  Google Scholar 

  5. H. R. Karimi, “A sliding mode approach to h∞ synchronization of master–slave time–delay systems with Markovian jumping parameters and nonlinear uncertainties,” Journal of the Franklin Institute, vol. 349, no. (4), pp. 1480–1496, 2012.

    Article  MathSciNet  MATH  Google Scholar 

  6. Y. H. Joo, L. Q. Tien, P. X. Duong, et al., “Adaptive neural network second–order sliding mode control of dual arm robots,” International Journal of Control, Automation and Systems, vol. 15, no. (6), pp. 2883–2891, 2017.

    Article  Google Scholar 

  7. J. O. Pedro, M. Dangor, O. A. Dahunsi, and M. M. Ali, “Intelligent feedback linearization control of nonlinear electrohydraulic suspension systems using particle swarm optimization,” Applied Soft Computing, vol. 24, pp. 50–62, 2014.

    Article  Google Scholar 

  8. H. Li, Y. Gao, P. Shi, and X. Zhao, “Output–feedback control for T–S fuzzy delta operator systems with time–varying delays via an input–output approach,” IEEE Transactions on Fuzzy systems, vol. 23, no. (4), pp. 1100–1112, 2015.

    Article  Google Scholar 

  9. G. B. Koo, J. B. Park, and Y. H. Joo, “Intelligent digital redesign for sampled–data fuzzy control systems based on state–matching error cost function approach,” International Journal of Control, Automation and Systems, vol. 16, no. (1), pp. 350–359, 2018.

    Article  Google Scholar 

  10. T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 15, pp. 116–132, February 1985.

    Article  MATH  Google Scholar 

  11. J.-H. Park, G.-T. Park, S.-H. Kim, and C.-J. Moon, “Output–feedback control of uncertain nonlinear systems using a self–structuring adaptive fuzzy observer,” Fuzzy Sets and Systems, vol. 151, no. (1), pp. 21–42, 2005.

    Article  MathSciNet  MATH  Google Scholar 

  12. H. D. Choi, C. K. Ahn, P. Shi, L. Wu, and M. T. Lim, “Dynamic output–feedback dissipative control for T–S fuzzy systems with time–varying input delay and output constraints,” IEEE Transactions on Fuzzy Systems, vol. 25, no. (3), pp. 511–526, 2017.

    Article  Google Scholar 

  13. E. Kim, “Output feedback tracking control of robot manipulators with model uncertainty via adaptive fuzzy logic,” IEEE Transactions on Fuzzy Systems, vol. 12, no. (3), pp. 368–378, 2004.

    Article  MathSciNet  Google Scholar 

  14. H. S. Kim, J. B. Park, and Y. H. Joo, “Sampled–data control of fuzzy systems based on the intelligent digital redesign technique: an input–delay approach,” International Journal of Control, Automation and Systems, vol. 16, no. (1), pp. 327–334, 2018.

    Article  Google Scholar 

  15. J. Qiu, Y. Wei, H. R. Karimi, and H. Gao, “Reliable control of discrete–time piecewise–affine time–delay systems via output feedback,” IEEE Transactions on Reliability, vol. 67, no. (1), pp. 79–91, 2018.

    Article  Google Scholar 

  16. J. Qiu, Y. Wei, and L. Wu, “A novel approach to reliable control of piecewise affine systems with actuator faults,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 64, no. (8), pp. 957–961, 2017.

    Article  Google Scholar 

  17. H. Li, Y. Gao, P. Shi, and H. K. Lam, “Observer–based fault detection for nonlinear systems with sensor fault and limited communication capacity,” IEEE Transactions on Automatic Control, vol. 61, no. (9), pp. 2745–2751, 2016.

    Article  MathSciNet  MATH  Google Scholar 

  18. J. P. Hwang and E. Kim, “Robust tracking control of an electrically driven robot: adaptive fuzzy logic approach,” IEEE Transactions on Fuzzy systems, vol. 14, no. (2), pp. 232–247, 2006.

    Article  Google Scholar 

  19. H. Li, Y. Gao, L. Wu, and H. K. Lam, “Fault detection for T–S fuzzy time–delay systems: delta operator and input–output methods,” IEEE Transactions on Cybernetics, vol. 45, no. (2), pp. 229–241, 2015.

    Article  Google Scholar 

  20. C.-H. Chiu and C.-C. Chang, “Wheeled human transportation vehicle implementation using output recurrent fuzzy control strategy,” IET Control Theory & Applications, vol. 8, no. (17), pp. 1886–1895, 2014.

    Article  Google Scholar 

  21. J. Huang, M. Ri, D. Wu, and S. Ri, “Interval type–2 fuzzy logic modeling and control of a mobile two–wheeled inverted pendulum,” IEEE Transactions on Fuzzy Systems, 2017.

    Google Scholar 

  22. S. Miyakoshi, “Omnidirectional two–parallel–wheel–type inverted pendulum mobile platform using mecanum wheels,” Proc. of IEEE International Conference on Advanced Intelligent Mechatronics (AIM), pp. 1291–1297, IEEE, 2017.

    Google Scholar 

  23. K. Pathak, J. Franch, and S. K. Agrawal, “Velocity and position control of a wheeled inverted pendulum by partial feedback linearization,” IEEE Transactions on Robotics, vol. 21, no. (3), pp. 505–513, 2005.

    Article  Google Scholar 

  24. H. Fukushima, K. Muro, and F. Matsuno, “Sliding–mode control for transformation to an inverted pendulum mode of a mobile robot with wheel–arms,” IEEE Transactions on Industrial Electronics, vol. 62, no. (7), pp. 4257–4266, 2015.

    Article  Google Scholar 

  25. H. Lee and S. Jung, “Balancing and navigation control of a mobile inverted pendulum robot using sensor fusion of low cost sensors,” Mechatronics, vol. 22, no. (1), pp. 95–105, 2012.

    Article  Google Scholar 

  26. T. Chen and L. Qiu, “H∞ design of general multirate sampled–data control systems,” Automatica, vol. 30, no. (7), pp. 1139–1152, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  27. E. Fridman, A. Seuret, and J. Richard, “Robust sampleddata stabilization of linear systems: an input delay approach,” Automatica, vol. 40, no. (8), pp. 1441–1446, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  28. H. Gao and T. Chen, “Stabilization of nonlinear systems under variable sampling: a fuzzy control approach,” IEEE Transactions on Fuzzy Systems, vol. 15, no. (5), pp. 972–983, 2007.

    Article  Google Scholar 

  29. H. Gao, T. Chen, and T. Chai, “Passivity and passification for networked control systems,” SIAM Journal on Control and Optimization, vol. 46, p. 1299, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  30. P. Shi, Y. Zhang, M. Chadli, and R. K. Agarwal, “Mixed Hinfinity and passive filtering for discrete fuzzy neural networks with stochastic jumps and time delays,” IEEE Transactions on Neural Networks And Learning Systems, vol. 27, no. (4), pp. 903–909, 2016.

    Article  MathSciNet  Google Scholar 

  31. L. Wu and W. Zheng, “Passivity–based sliding mode control of uncertain singular time–delay systems,” Automatica, vol. 45, no. (9), pp. 2120–2127, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  32. J. Liu, S. Vazquez, L. Wu, A. Marquez, H. Gao, and L. G. Franquelo, “Extended state observer based sliding mode control for three–phase power converters,” IEEE Transactions on Industrial Electronics, vol. 64, no. (1), pp. 22–31, 2017.

    Article  Google Scholar 

  33. B. Brogliato, O. Egeland, R. Lozano, and B. Maschke, Dissipative systems analysis and control: theory and applications. second ed., Springer–Verlag, London, UK, 2007.

    Book  MATH  Google Scholar 

  34. J. Qiu, H. Tian, Q. Lu, and H. Gao, “Nonsynchronized robust filtering design for continuous–time T–S fuzzy affine dynamic systems based on piecewise Lyapunov functions,” IEEE Transactions on Cybernetics, vol. 43, no. (6), pp. 1755–1766, 2013.

    Article  Google Scholar 

  35. S. Wen, T. Huang, X. Yu, M. Z. Chen, and Z. Zeng, “Aperiodic sampled–data sliding–mode control of fuzzy systems with communication delays via the event–triggered method,” IEEE Transactions on Fuzzy Systems, vol. 24, no. (5), pp. 1048–1057, 2016.

    Article  Google Scholar 

  36. J. Araújo, M. Mazo, A. Anta, P. Tabuada, and K. H. Johansson, “System architectures, protocols and algorithms for aperiodic wireless control systems,” IEEE Transactions on Industrial Informatics, vol. 10, no. (1), pp. 175–184, 2014.

    Article  Google Scholar 

  37. M. S. Mahmoud and A. M. Memon, “Aperiodic triggering mechanisms for networked control systems,” Information Sciences, vol. 296, pp. 282–306, 2015.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Measure-Control Technology and Communication Engineering, Harbin University of Science and Technology, Harbin, 150040, China

    Rongjun Liu & Junfeng Wu

  2. Heilongjiang University of Science and Technology, Harbin, 150022, China

    Junfeng Wu

  3. College of Automation, Harbin Engineering University, Harbin, 150001, China

    Dan Wang

Authors
  1. Rongjun Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Junfeng Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Junfeng Wu.

Additional information

Recommended by Associate Editor Ohmin Kwon under the direction of Editor Euntai Kim. This work was partially supported by the Harbin Applied Technology Research and Development Project (excellent academic leader) (No. 2014RFXYJ051), China.

Rongjun Liu received the M.E. degree in Agricultural Electrification and Automation from Northeast Agricultural University, Harbin, China, in 2009. He is pursuing the Ph.D. degree in Measuring and Testing Technologies and Instruments from Harbin University of Science and Technology, Harbin, China. His current research interests include sampleddata control, nonlinear control.

Junfeng Wu received the B.E. degree in Automatic Control from the Harbin University of Science and Technology, the M.E. degree in Automatic Control, and the Ph.D. degree in Material Processing Engineering from the Harbin Institute of Technology, Harbin, China, in 1982, 1987, and 2003, respectively. From 2004 to 2006, he was a Post-Doctoral Researcher with the College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin, China. He is currently a Professor with the College of Measure-Control Technology and Communication Engineering, Harbin University of Science and Technology, and is also the Secretary of the Party Committee of the Heilongjiang University of Science and Technology, Harbin, China. His current research interests include sampled-data control, nonlinear control.

Dan Wang received the B.E. degree in Electronic Information Engineering, and the M.E. degree in Agricultural Electrification and Automation, both from Northeast Agricultural University, Harbin, China, in 2010 and 2013, respectively. She is pursuing the Ph.D. degree in Precision Instrument Machinery from Harbin Engineering University, Harbin, China. Her current research interests include particle swarm optimization, robust control, sliding mode control.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, R., Wu, J. & Wang, D. Sampled-data Fuzzy Control of Two-wheel Inverted Pendulums Based on Passivity Theory. Int. J. Control Autom. Syst. 16, 2538–2548 (2018). https://doi.org/10.1007/s12555-018-0063-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-018-0063-4

Keywords

Search

Navigation