The Design and Comparison of Backstepping Fuzzy Control and Fuzzy Sliding Mode Control for Controlling Underactuated Mechanical Systems with Two Degrees of Freedom

Document Type : Dynamics, Vibrations, and Control

Authors

1 Department of Electrical Engineering, Khatam Al-Anbiya University, Tehran, Iran

2 Department of Electrical Engineering, Shahid Sattari Aeronautical University of Science and Technology, Tehran, Iran

Abstract

In this paper, two control methods are presented to control a class of underactuated systems with two degrees of freedom. The design method of the proposed controllers and how to prove the stability of the closed-loop system using solutions such as backstepping control, sliding mode control, fuzzy logic and their combinations are presented in details. Mathematical proof shows that the closed-loop system under the proposed scheme has a global asymptotic stability in the presence of structural and un-structural uncertainties. Then, the advantages and disadvantages of the proposed controls are examined and then some criteria such as simplicity in practical implementation, the control input calculations volume, the adjustment of the control input coefficients, and the amplitude of the control input are used to make comparisons between the suggested controllers. Finally, to evaluate the performance of the proposed controllers, simulations are implemented on the cart-position system with a single-link inverted pendulum. The simulation results confirm the performance of the proposed solutions.

Keywords

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References

  1. Saptarshi Bandyopadhyay, Soon-Jo Chung, and Fred Y. Hadaegh.  "Nonlinear Attitude Control of Spacecraft with a Large Captured Object", Journal of Guidance, Control, and Dynamics, Vol. 39, No. 4 (2016), pp. 754-769.##
  2. Young-Cheol Choi, Hyo-Sung Ahn, Nonlinear Control of Quadrotor for Point Tracking: Actual Implementation and Experimental Tests. IEEE/ASME Transactions on Mechatronics ( Volume: 20, Issue: 3,pp. 1179 – 1192,  June 2015 )##
  3. Khassanov Alisher, Krupenkin Alexander, Borgul Alexandr, Control of the Mobile Robots with ROS in Robotics Courses. Procedia Engineering, Volume 100, 2015, Pages 1475-1484.##
  4. F.Peza-Solís, G.Silva-Navarro, N.R.Castro-Linares, Trajectory Tracking Control in a Single Flexible-Link Robot using Finite Differences and Sliding Modes. Journal of Applied Research and Technology, Volume 13, Issue 1, February 2015, Pages 70-78.##
  5. Jie Huang, Zan Liang, Qiang Zang, Dynamics and swing control of double-pendulum bridge cranes with distributed-mass beams. Mechanical Systems and Signal Processing, Volumes 54–55, March 2015, Pages 357-366.##
  6. ChenY-F,Huang A-C. Controller design for a class of underactuated mechanical systems.IET Control Theory Applications, 2012;6(1):103–10.##
  7. Man W-S,LinJ-S. Nonlinear control design for a class of underactuated systems.In IEEE international conference on control applications(CCA), 2010.p.1439–44.##
  8. Olfati-Saber R. Nonlinear control of underactuated mechanical systems with application to robotics and aerospace vehicles. PhD thesis. 2001.##
  9. Reyhanoglu M, van der Schaft A, McClamroch N, Kolmanovsky I. Nonlinear control of a class of underactuated systems. In Proceedings of the 35th IEEE conference on decision and control, vol.2,1996.p.1682–7.##
  10. Spong MW. Underactuated mechanical systems. In: Control problems in robotics and automation. Springer-Verlag; 1998.##
  11. Utkin V. Sliding modes in control and optimization. Berlin: Springer-Verlag; 1992.##
  12. Utkin V. Variable structure systems with sliding modes.IEEE Transactions on Automatic Control, 1977; 22(2):212–22.##
  13. H. Khooban and M. R. Soltanpour (2013), “Swarm Optimization Tuned Fuzzy Sliding Mode Control Design for a Class of Nonlinear Systems in Presence of Uncertainties,” Journal of Intelligent and Fuzzy Systems, Vol. 24, No. 2, pp. 383-394.##
  14. R. Soltanpour, B. Zolfaghari, M. Soltani and M. H. Khooban (2013), “Fuzzy Sliding Mode Control Design for a Class of Nonlinear Systems with Structured and Unstructured Uncertainties,” International Journal of Innovative Computing, Information and Control, Vol. 9, No. 7, pp. 2713-2726.##
  15. R. Soltanpour, M. H. Khooban and Mahmoodreza Soltani (2014), “Robust Fuzzy Sliding Mode Control for Tracking the Robot Manipulator in Joint Space and in Presence of Uncertainties,” Journal of Robotica, Vol. 32, No. 3, pp. 433-446.##
  16. Veysi, Mohammad Reza Soltanpour (2016), “Voltage-Base Control of Robot Manipulator Using Adaptive Fuzzy Sliding Mode Control,” Accepted for Publication in International Journal of Fuzzy Systems.##
  17. Sankaranarayanan V, Mahindrakar AD (2009) Control of a class of underactuated mechanical systems using sliding modes. IEEE Transactions on Robotics 25(2): 459–467.##
  18. Su SF, Hsueh YC, Tseng CP, Chen SS, Lin YS (2015) Direct adaptive fuzzy sliding mode control for Under-actuated Uncertain Systems. International Journal of Fuzzy Logic and Intelligent Systems 15(4): 240-250.##
  19. Baklouti F, Aloui S, Chaari A (2016) Adaptive fuzzy sliding mode tracking control of uncertain underactuated nonlinear systems: a comparative study. Journal of Control Science and Engineering 3(13): 110-122.##
  20. Moussaoui S, Boulkroune A, Vaidyanathan S (2016) Fuzzy adaptive sliding-mode control scheme for uncertain underactuated systems. Advances and Applications in Nonlinear Control Systems, Part of the Studies in Computational Intelligence book series (SCI, volume 635): 351-367.##
  21. Lo J. C., Kuo Y. H. (1998) Decoupled fuzzy sliding-mode control. IEEE Transactions on Fuzzy Systems 6(3): 426-435.##
  22. Marton L, Hodel AS, Lantos B, Hung JY (2008) Underactuated robot control: comparing LQR, subspace stabilization, and combined error metric approaches. IEEE Transactions on Industrial Electronics 55(10): 3724-3730.##
  23. Park MS, Chwa D, Hong SK (2006) Decoupling control of a class of underactuated mechanical systems based on sliding mode control. SI. CE. Korea: 806-810.##
  24. Lin CM, Mon YJ, (2005) Decoupling control by hierarchical fuzzy sliding-mode controller. IEEE Transactions on Control Systems Technology 13(4): 593-598.##
  25. Shin SY, Lee JY, Sugisaka M, Lee JJ (2010) Decoupled fuzzy adaptive sliding mode control for underactuated systems with mismatched uncertainties. Proc. IEEE Int. Conf. Info. Auto. China: 599-604.##
  26. Hung LC, Chung HY (2007) Decoupled sliding-mode with fuzzy-neural network controller for nonlinear systems. International Journal of Approximate Reasoning 46(1): 74-97.##
  27. Din S. U., Khan Q., Rehman F. U., Akmeliawati R. (2016) Robust Control of Underactuated Systems: Higher Order Integral Sliding Mode Approach. Mathematical Problems in Engineering, 8(2): 12-21.##
  28. Shah I., Rehman F. U. (2017) Smooth Higher-Order Sliding Mode Control of a Class of Underactuated Mechanical Systems. Accepted for Publication in Arab Journal of Science Engineering.##
  29. Din S. U., Khan Q., Rehmani F. U., Akmeliawanti R. (2017) A Comparative Experimental Study of Robust Sliding Mode Control Strategies for Underactuated Systems. Accepted for publication in IEEE Access.##
  30. Khalil HK (2002) Nonlinear systems. 3rd edn. Prentice Hall, 2002.##
  31. R. Soltanpour, M. H. Khooban and T. Niknam (2014) , “ A Robust and New Simple Control Strategy for a Class of Nonlinear Mechanical Systems: Induction and Servo motors,” Accepted for Publication in Journal of Vibration and Control.##
  32. Ahmadnezhad and Mohammad Reza Soltanpour(2015) , “Tracking Performance Evaluation of Robust Back-Stepping Control Design for a Nonlinear Electro hydraulic Servo System,”. International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, Vol. 9, No. 7, pp. 1146-1152.##

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History

  • Receive Date: 20 November 2020
  • Revise Date: 01 March 2021
  • Accept Date: 18 December 2021
  • Publish Date: 23 October 2021

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