Volume 14, Issue 1 (Journal of Control, V.14, N.1 Spring 2020)                   JoC 2020, 14(1): 73-91 | Back to browse issues page

XML Persian Abstract Print


Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Abooee A, Ahmadzadeh H R, Haeri M, Arefi M M. Designing Robust Finite-Time Nonlinear Torques for a n-DOF Robot Manipulator with Uncertainties, Sector and Dead-Zone Nonlinearities. JoC. 2020; 14 (1) :73-91
URL: http://joc.kntu.ac.ir/article-1-520-en.html
Abstract:   (1408 Views)
In this paper, a complete dynamical model is presented for an uncertain -DOF robot manipulator containing description of sector and dead-zone nonlinearities. Next, robust finite-time tracking problem of desired trajectories is declared and formulated for the aforementioned robot manipulator. By defining innovative nonlinear sliding manifolds and developing the nonsingular terminal sliding mode control, several types of input torques are designed to exactly reach configuration variables of robot's joints to desired paths within the finite times in the presence of uncertainties, sector and dead-zone nonlinearities. By utilizing some applicable lemmas and well-known inequalities, for each class of the proposed input torques, the global finite-time stability of the closed-loop robot system is proven analytically. Also, several new formulas are extracted for determining the convergence finite times of the closed-loop system. These formulas demonstrate that mentioned times are dependent on robot's initial conditions and optional parameters of the suggested torques. Finally, by using MATLAB software, all classes of the designed torques are numerically simulated onto the SCARA industrial robot manipulator and obtained results show the acceptable performance of the suggested control scheme.
Full-Text [PDF 1107 kb]   (74 Downloads)    
Type of Article: Research paper | Subject: Special
Received: 2017/09/4 | Accepted: 2019/01/7 | Published: 2020/06/11

References
1. [1] N. Adhikary and C. Mahanta, "Inverse dynamics based robust control method for position commanded servo actuators in robot manipulators," Control Engineering Practice, vol. 66, no. 1, pp. 146-155, 2017. [DOI:10.1016/j.conengprac.2017.07.001]
2. [2] Z. Ma and G. Sun, "Dual terminal sliding mode control design for rigid robotic manipulator," Journal of the Franklin Institute, doi: 10.1016/j.jfranklin.2017.01.034, Available online 4 February, 2017. [DOI:10.1016/j.jfranklin.2017.01.034]
3. [3] M. Galicki, "Finite-time trajectory tracking control in a task space of robotic manipulator," Automatica, vol. 67, no. 1, pp. 165-170, 2016. [DOI:10.1016/j.automatica.2016.01.025]
4. [4] M. D. Tran and H. J. Kang, "Adaptive terminal sliding mode control of uncertain robotic manipulator based on local approximation of a dynamic system," Nerocomputing, vol. 228, no. 1, pp. 231-240, 2017. [DOI:10.1016/j.neucom.2016.09.089]
5. [5] K. Kaltsoukalas, S. Makris, and G. Chryssolouris, "On generating the motion of industrial robot manipulators," Robotics and Computer-Integrated Manufacturing, vol. 32, no. 1, pp. 65-71, 2015. [DOI:10.1016/j.rcim.2014.10.002]
6. [6] G. Rigatos, P. Siano, and G. Raffo, "An H-infinity nonlinear control approach for multi-DOF robotic manipulator," IFAC-Paper Online, vol. 49, no. 12, pp. 1406-1411, 2016. [DOI:10.1016/j.ifacol.2016.07.766]
7. [7] S. I. Han and J. Lee, "Finite-time sliding surface constrained control for a robot manipulator with an unknown dead-zone and disturbance," ISA Transactions, vol. 65, no. 1, pp. 307-318, 2016. [DOI:10.1016/j.isatra.2016.07.013]
8. [8] A. Abooee, M. Moravej Khorasani, and M. Haeri, "Finite Time Control of Robotic Manipulators with Position Output Feedback," International Journal of Robust and Nonlinear Control, vol. 27, no. 16, pp. 2982-2999, 2017. [DOI:10.1002/rnc.3721]
9. [9] A. Mohammadi, M. Tavakoli, H. J. Marquez, and F. Hashemzadeh, "Nonlinear disturbance observer design for robotic manipulators," Control Engineering Practice, vol. 21, no. 3, pp. 253-267, 2013. [DOI:10.1016/j.conengprac.2012.10.008]
10. [10] X. Wang and J. Zhao, "Autonomous switched control of load shifting robot manipulators," IEEE Transactions on Industrial Electronics, vol. 64, no. 9, pp. 7161-7170, 2017. [DOI:10.1109/TIE.2017.2688958]
11. [11] M. Wang and A. Yang, "Dynamic learning from adaptive neural control of robot manipulators with prescribed performance," IEEE Transactions on Systems Man, and Cybernetics: Systems, vol. 47, no. 8, pp. 2244-2255, 2017. [DOI:10.1109/TSMC.2016.2645942]
12. [12] J. Lee, P. H. Chang, and M. Jin, "Adaptive integral sliding mode control with time-delay estimation for robot manipulators," IEEE Transactions on Industrial Electronics, vol. 64, no. 8, pp. 6796-6804, 2017. [DOI:10.1109/TIE.2017.2698416]
13. [13] G. Paolo, I. A. Ferrara, and L. Magni, "MPC for robot manipulators with integral sliding mode generation," IEEE/ASME Transactions on Mechatronics, vol. 22, no. 3, pp. 1299-1307, 2017. [DOI:10.1109/TMECH.2017.2674701]
14. [14] H. Wang, "Adaptive control of robot manipulators with uncertain kinematics and dynamics," IEEE Transactions on Automatics Control, vol. 62, no. 2, pp. 948-954, 2017. [DOI:10.1109/TAC.2016.2575827]
15. [15] Y. Wang, L. Gu, Y. Xu, and X. Cao, "Practical tracking control of robot manipulators with continuous fractional-order nonsingular terminal sliding mode," IEEE Transactions on Industrial Electronics, vol. 63, no. 10, pp. 6194-6204, 2016. [DOI:10.1109/TIE.2016.2569454]
16. [16] J. Baek, M. Jin, and S. Han, "A new adaptive sliding-mode control scheme for application to robot manipulators," IEEE Transactions on Industrial Electronics, vol. 63, no. 6, pp. 3628-3637, 2016. [DOI:10.1109/TIE.2016.2522386]
17. [17] D. Nojavanzadeh and M. Badamchizadeh, "Adaptive fractional-order non-singular fast terminal sliding mode control for robot manipulators," IET Control Theory and Applications, vol. 10, no. 13, pp. 1565-1572, 2016. [DOI:10.1049/iet-cta.2015.1218]
18. [18] B. Baigzadehnoe, Z. Rahmani, A. Khosravi, and B. Rezaie, "On position/force tracking control problem of cooperative robot manipulators using adaptive fuzzy backstepping approach," ISA Transactions, vol. 70, no. 1, pp. 432-446, 2017. [DOI:10.1016/j.isatra.2017.07.029]
19. [19]علي ابويي، مسعود مروج خراسانی و محمد حائری، "رديابي زمان محدود سرتاسري كلاس جامعي از سيستم هاي غيرخطي با استفاده از كنترل تطبيقي-لغزشي ترمينال غيرتكين" مجله علمي و پژوهشي کنترل و ابزار دقيق، جلد 9، شماره 4، تابستان 1394، صفحات 39-27.
20. [20] D. J. López-Araujo, A. Zavala-Río, V. Santibáñez, and F. Reyes, "Global adaptive regulation of robot manipulators with bounded inputs," IFAC Proceedings Volume, vol. 45, no. 22, pp. 881-888, 2012. [DOI:10.3182/20120905-3-HR-2030.00008]
21. [21] J. Wilson, M. Charest, and R. Dubay, "Non-linear model predictive control schemes with application on a 2-link vertical robot manipulator," Robotics and Computer-Integrated Manufacturing, vol. 41, no. 1, pp. 23-30, 2016. [DOI:10.1016/j.rcim.2016.02.003]
22. [22] P. R. Ouyang, W. J. Zhang, and M. M. Gupta, "An adaptive switching learning control method for trajectory tracking of robot manipulators," Mechatronics, vol. 16, no. 1, pp. 51-61, 2006. [DOI:10.1016/j.mechatronics.2005.08.002]
23. [23] T. Sun, H. Pei, Y. Pan, H. Zhou, and C. Zhang, "Neural network-based sliding mode adaptive control for robot manipulators," Neurocomputing, vol. 74, no. 14, pp. 2377-2384, 2011. [DOI:10.1016/j.neucom.2011.03.015]
24. [24] P. Tomei, "Adaptive PD controller for robot manipulators," IEEE Transactions on Robotics and Automation, vol. 7, no. 4, pp. 565-570, 1991. [DOI:10.1109/70.86088]
25. [25] A. Zavala-Rio and V. Santibanez, "A natural saturating extension of the PD-with-desired-gravity-compensation control law for robot manipulators with bounded inputs," IEEE Transactions on Robotics, vol. 23, no. 2, pp. 386-391, 2007. [DOI:10.1109/TRO.2007.892224]
26. [26] A. Zavala-Rio and V. Santibanez, "Simple extensions of the PD-with-gravity-compensation control law for robot manipulators with bounded inputs," IEEE Transactions on Control Systems Technology, vol. 14, no. 5, pp. 958-965, 2006. [DOI:10.1109/TCST.2006.876932]
27. [27] R. Kelly, "Global positioning of robot manipulators via PD control plus a class of nonlinear integral actions," IEEE Transactions on Automatic Control, vol. 43, no. 7, pp. 934-938, 1998. [DOI:10.1109/9.701091]
28. [28] F. Temurtas, H. Temurtas, and N. Yumusak, "Application of neural generalized predictive control to robotic manipulators with a cubic trajectory and random disturbances," Robotics and Autonomous Systems, vol. 54, no. 1, pp. 74-83, 2006. [DOI:10.1016/j.robot.2005.09.013]
29. [29] W. He, D. O. Amoateng, C. Yang, and D. Gong, "Adaptive neural network control of a robotic manipulator with unknown backlash-like hysteresis," IET Control Theory and Applications, vol. 11, no. 4, pp. 567-575, 2017. [DOI:10.1049/iet-cta.2016.1058]
30. [30] C. Sun, W. He, and J. Hong, "Neural network control of a flexible robotic manipulator using the lumped spring-mass model," IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 47, no. 8, pp. 1863-1874, 2017. [DOI:10.1109/TSMC.2016.2562506]
31. [31] R. J. Wai and R. Muthusamy, "Design of fuzzy-neural-network-inherited backstepping control for Robot manipulator including actuator dynamics," IEEE Transactions on Fuzzy Systems, vol. 22, no. 4, pp. 709-722, 2014. [DOI:10.1109/TFUZZ.2013.2270010]
32. [32] M. R. Soltanpour, P. Otadolajam, M. H. Khooban, "Robust control strategy for electrically driven robot manipulators: adaptive fuzzy sliding mode," IET Science, Measurement and Technology, vol. 9, no. 3, pp. 322-334, 2015. [DOI:10.1049/iet-smt.2013.0265]
33. [33] Z. Li, C. Yang, C. Y. Su, S. Deng, F. Sun, and W. Zhang, "Decentralized fuzzy control of multiple cooperating robotic manipulators with impedance interaction," IEEE Transactions on Fuzzy Systems, vol. 23, no. 4, pp. 1044-1056, 2015. [DOI:10.1109/TFUZZ.2014.2337932]
34. [34] Z. Zhang, L. Zheng, J. Yu, Y. Li, and Z. Yu, "Three recurrent neural networks and three numerical methods for solving a repetitive motion planning scheme of redundant robot manipulators," IEEE/ASME Transactions on Mechatronics, vol. 22, no. 3, pp. 1423-1434, 2017. [DOI:10.1109/TMECH.2017.2683561]
35. [35] M. Vijay and D. Jena. "PSO based neuro fuzzy sliding mode control for a robot manipulator," Journal of Electrical Systems and Information Technology, vol. 4, no. 1, pp. 243-256, 2017. [DOI:10.1016/j.jesit.2016.08.006]
36. [36] P. Gierlak and M. Szuster, "Adaptive position/force control for robot manipulator in contact with a flexible environment," Robotics and Autonomous Systems, vol. 95, no. 1, pp. 80-101, 2017. [DOI:10.1016/j.robot.2017.05.015]
37. [37] N. Nikdel, M. A. Badamchizadeh, V. Azimirad, and M. A. Nazari, "Adaptive backstepping control for an n-degree of freedom robotic manipulator based on combined state augmentation," Robotics and Computer-Integrated Manufacturing, vol. 44, no. 1, pp. 129-143, 2017. [DOI:10.1016/j.rcim.2016.08.007]
38. [38] D. Zhang and B. Wei, "A review on model reference adaptive control of robotic manipulators," Annual Reviews in Control, vol. 43, no. 1, pp. 188-198, 2017. [DOI:10.1016/j.arcontrol.2017.02.002]
39. [39] S. H. Park and S. I. Han, "Robust-tracking control for robot manipulator with dead-zone and friction using backstepping and RFNN controller," IET Control Theory and Applications, vol. 5, no. 12, pp. 1397-1417, 2011. [DOI:10.1049/iet-cta.2010.0460]
40. [40] W. He, Y. Dong, and C. Sun, "Adaptive neural impedance control of a robotic manipulator with input saturation," IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 46, no. 3, pp. 334-344, 2016. [DOI:10.1109/TSMC.2015.2429555]
41. [41] E. Aguinaga-Ruiz, A. Zavala-Rio, V. Santibanez, and F. Reyes, "Global trajectory tracking through static feedback for robot manipulators with bounded inputs," IEEE Transactions on Control Systems Technology, vol. 17, no. 4, pp. 934-944, 2009. [DOI:10.1109/TCST.2009.2013938]
42. [42] V. Santibanez, R. Kelly, and M. A. Liama, "A novel global asymptotic stable set-point fuzzy controller with bounded torques for robot manipulators," IEEE Transactions on Fuzzy Systems, vol. 13, no. 3, pp. 362-372, 2005. [DOI:10.1109/TFUZZ.2004.841735]
43. [43] W. Deng, J. Yao, and D. Ma, "Robust adaptive asymptotic tracking control of a class of nonlinear systems with unknown input dead-zone," Journal of the Franklin Institute, vol. 352, no. 12, pp. 5686-5707, 2015. [DOI:10.1016/j.jfranklin.2015.09.013]
44. [44] S. Hasanzadeh, F. Janabi-Sharifi, and P. Keenan, "Backlash characterization and position control of a robotic catheter manipulator using experimentally-based kinematic model," Mechatronics, vol. 44, no. 1, pp. 94-106, 2017. [DOI:10.1016/j.mechatronics.2017.05.002]
45. [45] K. C. Hsu, W. Y. Wang, and P. Z. Lin, "Sliding mode control for uncertain nonlinear systems with multiple inputs containing sector nonlinearities and dead-zones," IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 34, no. 1, pp. 374-380, 2004. [DOI:10.1109/TSMCB.2003.817029]
46. [46] B. K. Dinh, M. Xiloyannis, L. Cappello, C. W. Antuvan, S. C. Yen, and L. Masia, "Adaptive backlash compensation in upper limb soft wearable exoskeletons," Robotics and Autonomous Systems, vol. 92, no. 1, pp. 173-186, 2017. [DOI:10.1016/j.robot.2017.03.012]
47. [47] T. Yang, S. Yan, and Z. Han, "Nonlinear model of space manipulator joint considering time-variant stiffness and backlash," Journal of Sound and Vibration, vol. 341, no. 1, pp. 246-259, 2015. [DOI:10.1016/j.jsv.2014.12.028]
48. [48] A. Abooee and M. Haeri, "Stabilization of commensurate fractional order polytopic nonlinear differential inclusion subject to input nonlinearity and unknown disturbances," IET Control Theory & Applications, vol. 7, no. 12, pp. 1624-1633, 2013. [DOI:10.1049/iet-cta.2013.0038]
49. [49]علي ابويي و محمد حائری، "سنكرون‌سازي دو شمول‌ ديفرانسيلي لور با وجود پارامترهاي نامعلوم و غيرخطي‌ساز شعاعي در مسير ورودي‌هاي كنترلي" مجله علمي و پژوهشي کنترل و ابزار دقيق، جلد 7، شماره 2، تابستان 1392، صفحات 69-57.
50. [50] S. P. Bhat and D. S. Bernstein, "Continuous finite-time stabilization of the translational and rotational double integrators," IEEE Transactions on Automatic Control, vol. 43, no. 5, pp. 678-682, 1998. [DOI:10.1109/9.668834]
51. [51] Z. Zuo and L. Tie, "A new class of finite-time nonlinear consensus protocols for multi-agent systems," International Journal of Control, vol. 87, no. 2, pp. 363-370, 2016. [DOI:10.1080/00207179.2013.834484]
52. [52] A. Polyakov, D. Efimov, and W. Perruquetti, "Finite-time and fixed-time stabilization: Implicit Lyapunov function approach," Automatica, vol. 51, no. 1, pp. 332-340, 2015. [DOI:10.1016/j.automatica.2014.10.082]
53. [53] X. H. Zhang, K. Zhang, and X. J. Xie, "Finite-time output feedback stabilization of nonlinear high-order feed forward systems," International Journal of Robust and Nonlinear Control, vol. 26, no. 8, pp. 1794-1814, 2016. [DOI:10.1002/rnc.3384]
54. [54] S. E. Parsegov, A. E. Polyakov, and P. S. Shcherbakov, "Fixed-time consensus algorithm for multi-agent systems with integrator dynamics," IFAC Proceedings Volumes, vol. 46, no. 27, pp. 110-115, 2013. [DOI:10.3182/20130925-2-DE-4044.00055]
55. [55] Y. Feng, X. Yu, and F. Han, "On nonsingular terminal sliding-mode control of nonlinear systems," Automatica, vol. 49, no. 6, pp. 1715-1722, 2013. [DOI:10.1016/j.automatica.2013.01.051]
56. [56] Y. Zhang, G. Liu, and B. Luo, "Finite-time cascaded tracking control approach for mobile robots," Information Sciences, vol. 284, no. 1, pp. 31-43, 2014. [DOI:10.1016/j.ins.2014.06.037]
57. [57] S. Mondal and C. Mahanta, "Adaptive second order terminal sliding mode controller for robotic manipulators," Journal of the Franklin Institute, vol. 351, no. 4, pp. 2356-2377, 2014. [DOI:10.1016/j.jfranklin.2013.08.027]
58. [58] Z. Zuo, "Nonsingular fixed-time consensus tracking for second-order multi-agent networks," Automatica, vol. 54, no. 1, pp. 305-309, 2015. [DOI:10.1016/j.automatica.2015.01.021]
59. [59] A. Abooee, M. Moravej Khorasani, and M. Haeri "Global Finite Time Stabilization of a Class of Uncertain MIMO Nonlinear Systems," Journal of Dynamic Systems, Measurement, and Control, vol. 138, no. 2, pp 021007 (1-9), 2016. [DOI:10.1115/1.4032065]
60. [60] H. Liu, T. Zhang, and X. Tian, "Continuous output-feedback finite-time control for a class of second-order nonlinear systems with disturbances," International Journal of Robust and Nonlinear Control, vol. 26, no. 2, pp. 218-234, 2016. [DOI:10.1002/rnc.3305]
61. [61] S. P. Bhat and D. S. Bernstein, "Geometric homogeneity with applications to finite-time stability," Mathematics of Control, Signals and Systems, vol. 17, no. 2, pp. 101-127, 2005. [DOI:10.1007/s00498-005-0151-x]
62. [62] S. P. Bhat and D. S. Bernstein, "Finite-time stability of continuous autonomous systems," SIAM Journal on Control and Optimization, vol. 38, no. 3, pp. 751-766, 2000. [DOI:10.1137/S0363012997321358]
63. [63] M. Defoort, A. Polyakov, G. Demesure, M. Djemai, and K. Veluvolu, "Leader-follower fixed-time consensus for multi-agent systems with unknown non-linear inherent dynamics," IET Control Theory and Applications, vol. 9, no. 14, pp. 2165-2170, 2015. [DOI:10.1049/iet-cta.2014.1301]
64. [64] A. Polyakov and A. Poznyak, "Lyapunov function design for finite-time convergence analysis: "Twisting" controller for second-order sliding mode realization," Automatica, vol. 45, no. 2, pp. 444-448, 2009. [DOI:10.1016/j.automatica.2008.07.013]

Add your comments about this article : Your username or Email:
CAPTCHA

Send email to the article author


© 2020 All Rights Reserved | Journal of Control

Designed & Developed by : Yektaweb