Document Type : Article

**Authors**

^{1}
Department of Mechatronics, SZABIST, Karachi, Pakistan

^{2}
Department of Electrical and Computer Engineering, COMSATS University, Lahore, Pakistan

**Abstract**

This paper establishes a model-free finite-time tracking control of nonlinear robotic manipulator systems. The proposed controller incorporates both time delay estimation (TDE) and an enhanced terminal sliding mode control (TSMC). The improved TSMC scheme is devised using fractional-order TSMC (FOTSMC) and proportional-integral-derivative (PID) control to obtain robust tracking and high control performance. The TDE is designed to estimate the unknown nonlinear dynamics of robotic manipulators including the Stribeck friction and the external disturbances. Due to Stribeck friction, the effect of TDE error may fail to obtain the desired error performance; thus, another TDE loop is devised to compensate for TDE error generated by non-smooth frictions. The Lyapunov criterion is used to investigate the finite-time stability to analyze the behavior of the designed approach. Finally, computer simulations of the proposed method on PUMA 560 robotic manipulators are performed in contrast with FOTSMC and adaptive fractional-order nonsingular terminal sliding mode control (AFONTSM).

**Keywords**

References:

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27. Bina, M.A., Gitizadeh, M., and Mahmoudian, M. "High-accuracy power sharing in parallel inverters in an islanded microgrid using modified sliding mode control approach", Scientia Iranica, 27, pp. 3128-3139 (2020).

28. Van, M. "An enhanced robust fault tolerant control based on n adaptive fuzzy pid-nonsingular fast terminal sliding mode control for uncertain nonlinear systems", IEEE/ASME Transactions on Mechatronics, 23, pp. 1362-1371 (2018).

29. Ahmed, S., Wang, H., and Tian, Y. "Adaptive fractional high-order terminal sliding mode control for nonlinear robotic manipulator under alternating loads", Asian Journal of Control, 23, pp. 1900-1910 (2021).

30. Wang, Y., Jiang, S., Chen, B., et al. "A new continuous fractional-order nonsingular terminal sliding mode control for cable-driven manipulators", Advances in Engineering Software, 119, pp. 21-29 (2018).

31. Ahmed, S., Wang, H., and Tian, Y. "Fault tolerant control using fractional-order terminal sliding mode control for robotic manipulators", Studies in Informatics and Control, 27, pp. 55-64 (2018).

32. Ahmed, S., Ahmed, A., Mansoor, I., et al. "Output feedback adaptive fractional-order supertwisting sliding mode control of robotic manipulator", Iranian Journal of Science and Technology, Transactions of Electrical Engineering, 45, pp. 335-347 (2021).

33. Youcef-Toumi, K. and Ito, O. "A time delay controller for systems with unknown dynamics", Journal of Dynamic Systems, Measurement, and Control, 112, pp. 133-142 (1990).

34. Podlubny, I., Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and Some of their Applications, Academic Press, Elsevier, 198 (1998).

35. Tang, Y. "Terminal sliding mode control for rigid robots", Automatica, 34, pp. 51-56 (1998).

36. Zaare, S. and Soltanpour, M.R. "The position control of the ball and beam system using statedisturbance observe-based adaptive fuzzy sliding mode control in presence of matched and mismatched uncertainties", Mechanical Systems and Signal Processing, 150, 107243 (2021).

37. Zaare, S. and Soltanpour, M.R. "Continuous fuzzy nonsingular terminal sliding mode control of flexible joints robot manipulators based on nonlinear finite time observer in the presence of matched and mismatched uncertainties", Journal of the Franklin Institute, 357, pp. 6539-6570 (2020).

38. Ma, Z. and Sun, G. "Dual terminal sliding mode control design for rigid robotic manipulator", Journal of the Franklin Institute, 355, pp. 9127-9149 (2018).

39. Armstrong, B., Khatib, O., and Burdick, J. "The explicit dynamic model and inertial parameters of the puma 560 arm", In Proceedings IEEE International Conference on Robotics and Automation, 3, pp. 510- 518 (1986).

2. Guo, Y., Zhang, S., Ritter, A., et al. "A case study on a capsule robot in the gastrointestinal tract to teach robot programming and navigation", IEEE Transactions on Education, 57, pp. 112-121 (2013).

3. Lukic, M., Barnawi, A., and Stojmenovic, I. "Robot coordination for energy-balanced matching and sequence dispatch of robots to events", IEEE Transactions on Computers, 64, pp. 1416-1428 (2014).

4. Mohan, R.E., Wijesoma, W.S., Acosta Calderon, C.A., et al. "False alarm metrics for human-robot interactions in service robots", Advanced Robotics, 24, pp. 1841-1859 (2010).

5. Ouyang, P., Acob, J., and Pano, V. "Pd with sliding mode control for trajectory tracking of robotic system", Robotics and Computer-Integrated Manufacturing, 30, pp. 189-200 (2014).

6. Marton, L. and Lantos, B. "Control of mechanical systems with stribeck friction and backlash", Systems & Control Letters, 58, pp. 141-147 (2009).

7. Selmic, R.R. and Lewis, F.L. "Neural-network approximation of piecewise continuous functions: application to friction compensation", IEEE Transactions on Neural Networks, 13, pp. 745-751 (2002).

8. Sami, M. and Patton, R.J. "A multiple-model approach to fault tolerant tracking control for nonlinear systems", In Mediterranean Conference on Control & Automation, pp. 498-503 (2012).

9. Wang, H., Vasseur, C., and Koncar, V. "Friction compensation of an XY robot using a recursive model free controller", In International Conference on Industrial Technology, pp. 355-360 (2010).

10. Soleymani, F., Rezaei, S.M., Rahimi, A., et al. "Multiple-surface sliding mode control of pneumatic actuator with mismatched uncertainties", In RSI International Conference on Robotics and Mechatronics, pp. 133-138 (2015).

11. Tsai, Y.-C. and Huang, A.-C. "Multiple-surface sliding controller design for pneumatic servo systems", Mechatronics, 18, pp. 506-512 (2008).

12. Hidalgo, M.C. and Garcia, C. "Friction compensation in control valves: Nonlinear control and usual approaches", Control Engineering Practice, 58, pp. 42-53 (2017).

13. Korayem, M. and Yousefzadeh, M. "Adaptive control of a cable-actuated parallel manipulator mounted on a platform with differential wheels under payload uncertainty", Scientia Iranica, 27, pp. 273-286 (2020).

14. Ahmed, S., Wang, H., and Tian, Y. "Model-free control using time delay estimation and fractionalorder nonsingular fast terminal sliding mode for uncertain lower-limb exoskeleton", Journal of Vibration and Control, 24, pp. 5273-5290 (2018).

15. Wang, H., Ye, X., Tian, Y., et al. "Model-free-based terminal smc of quadrotor attitude and position", IEEE Transactions on Aerospace and Electronic Systems, 52, pp. 2519-2528 (2016).

16. Jin, M., Lee, J., Chang, P.H., et al. "Practical nonsingular terminal sliding-mode control of robot manipulators for high-accuracy tracking control", IEEE Transactions on Industrial Electronics, 56, pp. 3593- 3601 (2009).

17. Jin, M., Kim, J., Lee, J., et al. "Improving timedelay control for robot manipulators using tsk fuzzy logic control systems", In International Conference on Advanced Intelligent Mechatronics, pp. 1743-1748 (2017).

18. Zhang, X., Wang, H., Tian, Y., et al. "Modelfree based neural network control with time-delay estimation for lower extremity exoskeleton", Neurocomputing, 272, pp. 178-188 (2018).

19. Ahmed, S., Wang, H., and Tian, Y. "Adaptive highorder terminal sliding mode control based on time delay estimation for the robotic manipulators with backlash hysteresis", IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51, pp. 1128-1137 (2019).

20. Jin, M., Kang, S.H., Chang, P.H., et al. "Robust control of robot manipulators using inclusive and enhanced time delay control", IEEE/ASME Transactions on Mechatronics, 22, pp. 2141-2152 (2017).

21. Chang, P.H. and Park, S.H. "On improving timedelay control under certain hard nonlinearities", Mechatronics, 13, pp. 393-412 (2003).

22. Feng, Y., Yu, X., and Man, Z. "Non-singular terminal sliding mode control of rigid manipulators", Automatica, 38, pp. 2159-2167 (2002).

23. Samanfar, A., Shakarami, M.R., Soltani, J., et al. "Adaptive sliding mode control for multi-machine power systems under normal and faulted conditions", Scientia Iranica, 29(5), pp. 2526-2536 (2020).

24. Yu, X. and Zhihong, M. "Fast terminal slidingmode control design for nonlinear dynamical systems", IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 49, pp. 261-264 (2002).

25. Mobayen, S. and Tchier, F. "Nonsingular fast terminal sliding-mode stabilizer for a class of uncertain nonlinear systems based on disturbance observer", Scientia Iranica, 24, pp. 1410-1418 (2017).

26. Torabi, M., Sharifi, M., and Vossoughi, G. "Robust adaptive sliding mode admittance control of exoskeleton rehabilitation robots", Scientia Iranica, 25, pp. 2628-2642 (2018).

27. Bina, M.A., Gitizadeh, M., and Mahmoudian, M. "High-accuracy power sharing in parallel inverters in an islanded microgrid using modified sliding mode control approach", Scientia Iranica, 27, pp. 3128-3139 (2020).

28. Van, M. "An enhanced robust fault tolerant control based on n adaptive fuzzy pid-nonsingular fast terminal sliding mode control for uncertain nonlinear systems", IEEE/ASME Transactions on Mechatronics, 23, pp. 1362-1371 (2018).

29. Ahmed, S., Wang, H., and Tian, Y. "Adaptive fractional high-order terminal sliding mode control for nonlinear robotic manipulator under alternating loads", Asian Journal of Control, 23, pp. 1900-1910 (2021).

30. Wang, Y., Jiang, S., Chen, B., et al. "A new continuous fractional-order nonsingular terminal sliding mode control for cable-driven manipulators", Advances in Engineering Software, 119, pp. 21-29 (2018).

31. Ahmed, S., Wang, H., and Tian, Y. "Fault tolerant control using fractional-order terminal sliding mode control for robotic manipulators", Studies in Informatics and Control, 27, pp. 55-64 (2018).

32. Ahmed, S., Ahmed, A., Mansoor, I., et al. "Output feedback adaptive fractional-order supertwisting sliding mode control of robotic manipulator", Iranian Journal of Science and Technology, Transactions of Electrical Engineering, 45, pp. 335-347 (2021).

33. Youcef-Toumi, K. and Ito, O. "A time delay controller for systems with unknown dynamics", Journal of Dynamic Systems, Measurement, and Control, 112, pp. 133-142 (1990).

34. Podlubny, I., Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and Some of their Applications, Academic Press, Elsevier, 198 (1998).

35. Tang, Y. "Terminal sliding mode control for rigid robots", Automatica, 34, pp. 51-56 (1998).

36. Zaare, S. and Soltanpour, M.R. "The position control of the ball and beam system using statedisturbance observe-based adaptive fuzzy sliding mode control in presence of matched and mismatched uncertainties", Mechanical Systems and Signal Processing, 150, 107243 (2021).

37. Zaare, S. and Soltanpour, M.R. "Continuous fuzzy nonsingular terminal sliding mode control of flexible joints robot manipulators based on nonlinear finite time observer in the presence of matched and mismatched uncertainties", Journal of the Franklin Institute, 357, pp. 6539-6570 (2020).

38. Ma, Z. and Sun, G. "Dual terminal sliding mode control design for rigid robotic manipulator", Journal of the Franklin Institute, 355, pp. 9127-9149 (2018).

39. Armstrong, B., Khatib, O., and Burdick, J. "The explicit dynamic model and inertial parameters of the puma 560 arm", In Proceedings IEEE International Conference on Robotics and Automation, 3, pp. 510- 518 (1986).

January and February 2024

Pages 137-148