Adaptive non-singular fast terminal sliding mode based on prescribed performance for robot manipulators. (English) Zbl 07889225
Summary: A fast convergent non-singular terminal sliding mode adaptive control law based on prescribed performance is formulated to solve the uncertainties and external disturbances of robot manipulators. First, the tracking error of robot manipulators is transformed by using the prescribed performance function, which improves the transient behaviors and steady-state accuracy of robot manipulators. Then, a novel fast convergent non-singular terminal sliding mode surface is brought up according to the transformed error, and the control law is derived to meet the stability requirements of robot manipulators. In practice, the upper boundary of the lumped disturbances cannot be accurately obtained. Therefore, an adaptive prescribed performance control (PPC) controller to lumped disturbances is brought up to ensure the stability and finite-time convergence of robot manipulators. Finally, the system stability of robot manipulators is proved by the Lyapunov theorem. Simulation results and comparative analysis demonstrate the superiority and robustness of the raised strategy.
©2023Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd.
©2023Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd.
MSC:
| 93-XX | Systems theory; control |
Keywords:
finite-time; non-singular terminal sliding mode; prescribed performance control; robot manipulatorsReferences:
| [1] | I.El Makrini, C.Rodriguez‐Guerrero, D.Lefeber, and B.Vanderborght, The variable boundary layer sliding mode control: A safe and performant control for compliant joint manipulators, IEEE Robot. Autom. Lett.2 (2017), no. 1, 187-192. |
| [2] | K.Mohamed, H.Elgamal, and A.Elsharkawy, Dynamic analysis with optimum trajectory planning of multiple degree‐of‐freedom surgical micro‐robot, Alex. Eng. J.57 (2018), no. 4, 4103-4112. |
| [3] | X.Chen, Y.Guo, D.Duanmu, J.Zhou, W.Zhang, and Z.Wang, Design and modeling of an extensible soft robotic arm, IEEE Robot. Autom. Lett.4 (2019), no. 4, 4208-4215. |
| [4] | B.Henze, R.Balachandran, M. A.Roa‐Garzon, C.Ott, and A.Albu‐Schaffer, Passivity analysis and control of humanoid robots on movable ground, IEEE Robot. Autom. Lett.3 (2018), no. 4, 3457-3464. |
| [5] | M. N.Huda, H.Yu, and S.Cang, Behaviour‐based control approach for the trajectory tracking of an underactuated planar capsule robot, IET Control. Theory Appl.9 (2015), no. 2, 163-175. |
| [6] | A. K.Khalaji, PID‐based target tracking control of a tractor‐trailer mobile robot, Proc. Inst. Mech. Eng. Pt. C J. Mechan. Eng. Sci.233 (2019), no. 13, 4776-4787. |
| [7] | H.Yang, M.Guo, Y.Xia, and L.Cheng, Trajectory tracking for wheeled mobile robots via model predictive control with softening constraints, IET Control. Theory Appl.12 (2018), no. 2, 206-214. |
| [8] | M. M.Fateh and S.Azargoshasb, Discrete adaptive fuzzy control for asymptotic tracking of robotic manipulators, Nonlinear Dyn.78 (2014), no. 3, 2195-2204. |
| [9] | Q.Yan, J.Cai, Y.Ma, and Y.Yu, Robust learning control for robot manipulators with random initial errors and iteration‐varying reference trajectories, Ieee Access7 (2019), 32628-32643. |
| [10] | A.Zahaf, S.Bououden, M.Chadli, and M.Chemachema, Robust fault tolerant optimal predictive control of hybrid actuators with time‐varying delay for industrial robot arm, Asian J. Control24 (2022), no. 1, 1-15. · Zbl 07886946 |
| [11] | D.‐T.Tran, H.‐V.‐A.Truong, and K. K.Ahn, Adaptive nonsingular fast terminal sliding mode control of robotic manipulator based neural network approach, Int. J. Precis. Eng. Manuf.22 (2021), no. 3, 417-429. |
| [12] | X.Lin, Y.Wang, and Y.Liu, Neural‐network‐based robust terminal sliding‐mode control of quadrotor, Asian J. Control24 (2022), no. 1, 427-438. · Zbl 07886980 |
| [13] | J.Hu, P.Wang, C.Xu, H.Zhou, and J.Yao, High accuracy adaptive motion control for a robotic manipulator with model uncertainties based on multilayer neural network, Asian J. Control24 (2022), no. 3, 1503-1514. · Zbl 07887071 |
| [14] | Z.Xu, C.Sun, M.Yang, and Q.Liu, Active disturbance rejection control for hydraulic systems with full‐state constraints and input saturation, IET Control. Theory Appl.16 (2022), no. 11, 1127-1136. |
| [15] | K.He, C.Dong, and Q.Wang, Active disturbance rejection adaptive control for uncertain nonlinear systems with unknown time‐varying dead‐zone input, Asian J. Control24 (2022), no. 3, 1209-1222. · Zbl 07887047 |
| [16] | T. T.Nguyen, Fractional‐order sliding mode controller for the two‐link robot arm, Int. J. Electr. Comput. Eng.10 (2020), no. 6, 5579. |
| [17] | Y.Mousavi, A.Zarei, and Z. S.Jahromi, Robust adaptive fractional‐order nonsingular terminal sliding mode stabilization of three‐axis gimbal platforms, ISA Trans.123 (2022), 98-109. |
| [18] | Y.Xie, X.Zhang, W.Meng, S.Zheng, L.Jiang, J.Meng, and S.Wang, Coupled fractional‐order sliding mode control and obstacle avoidance of a four‐wheeled steerable mobile robot, ISA Trans.108 (2021), 282-294. |
| [19] | X. H.Yu and Z. H.Man, Multi‐input uncertain linear systems with terminal sliding‐mode control, Automatica34 (1998), no. 3, 389-392. · Zbl 0915.93012 |
| [20] | Y.Feng, X. H.Yu, and Z. H.Man, Non‐singular terminal sliding mode control of rigid manipulators, Automatica38 (2002), no. 12, 2159-2167. · Zbl 1015.93006 |
| [21] | Z.Zuo, Nonsingular fixed‐time consensus tracking for second‐order multi‐agent networks, Automatica54 (2015), 305-309. · Zbl 1318.93010 |
| [22] | Y.Wang, L.Gu, Y.Xu, and X.Cao, Practical tracking control of robot manipulators with continuous fractional‐order nonsingular terminal sliding mode, IEEE Trans. Ind. Electron.63 (2016), no. 10, 6194-6204. |
| [23] | L.Chuanjiang, J.Boyan, Z.Qinghua, and Y.Chentao, Non‐singular Terminal Sliding Mode Controller for Spacecraft Attitude Stabilization. in 34th Chinese Control Conference (CCC). 2015. Hangzhou, PEOPLES R CHINA. |
| [24] | D.Zhao and Q.Zhu, Position synchronised control of multiple robotic manipulators based on integral sliding mode, Int. J. Syst. Sci.45 (2014), no. 3, 556-570. · Zbl 1307.93108 |
| [25] | S. H.Yu, X.Yu, B.Shirinzadeh, and Z.Man, Continuous finite‐time control for robotic manipulators with terminal sliding mode, Automatica41 (2005), no. 11, 1957-1964. · Zbl 1125.93423 |
| [26] | L. M.Capisani, A.Ferrara, and L.Magnani, Design and experimental validation of a second‐order sliding‐mode motion controller for robot manipulators, Int. J. Control82 (2009), no. 2, 365-377. · Zbl 1168.93321 |
| [27] | X.Deng, Z.Feng, and C.He, An adaptive reaching law of chattering‐free discrete‐time sliding mode control for systems with external disturbance, Asian J. Control (2022). https://doi.org/10.1002/asjc.2845 · Zbl 07889127 · doi:10.1002/asjc.2845 |
| [28] | L.Zhang and J.Yang, Continuous nonsingular terminal sliding mode control for nonlinear systems subject to mismatched terms, Asian J. Control24 (2022), no. 2, 885-894. · Zbl 07887020 |
| [29] | Q.Lei and W.Zhang, Adaptive non‐singular integral terminal sliding mode tracking control for autonomous underwater vehicles, IET Control. Theory Appl.11 (2017), no. 8, 1293-1306. |
| [30] | L.Qiao and W.Zhang, Trajectory tracking control of AUVs via adaptive fast nonsingular integral terminal sliding mode control, IEEE Trans. Industr. Inform.16 (2020), no. 2, 1248-1258. |
| [31] | J.Zhang, X.Liu, Y.Xia, Z.Zuo, and Y.Wang, Disturbance observer‐based integral sliding‐mode control for systems with mismatched disturbances, IEEE Trans. Ind. Electron.63 (2016), no. 11, 7040-7048. |
| [32] | J.Yang, S.Li, and X.Yu, Sliding‐mode control for systems with mismatched uncertainties via a disturbance observer, IEEE Trans. Ind. Electron.60 (2013), no. 1, 160-169. |
| [33] | J.Wang, S.Li, J.Yang, B.Wu, and Q.Li, Extended state observer‐based sliding mode control for PWM‐based DC‐DC buck power converter systems with mismatched disturbances, IET Control. Theory Appl.9 (2015), no. 4, 579-586. |
| [34] | R.Cui, L.Chen, C.Yang, and M.Chen, Extended state observer‐based integral sliding mode control for an underwater robot with unknown disturbances and uncertain nonlinearities, IEEE Trans. Ind. Electron.64 (2017), no. 8, 6785-6795. |
| [35] | C. L. P.Chen, C.‐E.Ren, and T.Du, Fuzzy observed‐based adaptive consensus tracking control for second‐order multiagent systems with heterogeneous nonlinear dynamics, IEEE Trans. Fuzzy Syst.24 (2016), no. 4, 906-915. |
| [36] | H.Liu and H. K.Khalil, Output feedback stabilization using super‐twisting control and high‐gain observer, Int. J. Robust Nonlinear Control29 (2019), no. 3, 601-617. · Zbl 1411.93150 |
| [37] | J.Lee, P. H.Chang, and M.Jin, Adaptive integral sliding mode control with time‐delay estimation for robot manipulators, IEEE Trans. Ind. Electron.64 (2017), no. 8, 6796-6804. |
| [38] | J.Baek, S.Cho, and S.Han, Practical time‐delay control with adaptive gains for trajectory tracking of robot manipulators, IEEE Trans. Ind. Electron.65 (2018), no. 7, 5682-5692. |
| [39] | T.Song, L.Fang, and H.Wang, Model‐free finite‐time terminal sliding mode control with a novel adaptive sliding mode observer of uncertain robot systems, Asian J. Control24 (2022), no. 3, 1437-1451. · Zbl 07887064 |
| [40] | S.Roy, J.Lee, and S.Baldi, A new adaptive‐robust design for time delay control under state‐dependent stability condition, IEEE Trans. Control Syst. Technol.29 (2021), no. 1, 420-427. |
| [41] | Q.Yao, Adaptive trajectory tracking control of a free‐flying space manipulator with guaranteed prescribed performance and actuator saturation, Acta Astronaut.185 (2021), 283-298. |
| [42] | H.Yang, B.Jiang, H.Yang, and H. H. T.Liu, Synchronization of multiple 3‐DOF helicopters under actuator faults and saturations with prescribed performance, ISA Trans.75 (2018), 118-126. |
| [43] | G.Xu, Y.Xia, D. H.Zhai, and B.Cui, Adaptive sliding mode disturbance observer‐based funnel trajectory tracking control of quadrotor with external disturbances, IET Control. Theory Appl.15 (2021), no. 13, 1778-1788. |
| [44] | S.Wang, J.Na, X.Ren, H.Yu, and J.Yu, Unknown input observer‐based robust adaptive funnel motion control for nonlinear servomechanisms, Int. J. Robust Nonlinear Control28 (2018), no. 18, 6163-6179. · Zbl 1405.93068 |
| [45] | S.Wang, H.Yu, J.Yu, J.Na, and X.Ren, Neural‐network‐based adaptive funnel control for servo mechanisms with unknown dead‐zone, IEEE Trans. Cybern.50 (2020), no. 4, 1383-1394. |
| [46] | J.Bao, H.Wang, and P.Xiaoping Liu, Adaptive finite‐time tracking control for robotic manipulators with funnel boundary, Int. J. Adapt. Control Signal Process.34 (2020), no. 5, 575-589. · Zbl 1467.93171 |
| [47] | H.Wang, L.Fang, M.Hu, T.Song, and J.Xu, Adaptive funnel fast nonsingular terminal sliding mode control for robotic manipulators with dynamic uncertainties, Proc. Inst. Mech. Eng. Pt. C J. Mechan. Eng. Sci.235 (2021), no. 18, 3678-3693. |
| [48] | S.Hao, L.Hu, and P. X.Liu, Second‐order adaptive integral terminal sliding mode approach to tracking control of robotic manipulators, IET Control. Theory Appl.15 (2021), no. 17, 2145-2157. |
| [49] | M.Boukattaya, N.Mezghani, and T.Damak, Adaptive nonsingular fast terminal sliding‐mode control for the tracking problem of uncertain dynamical systems, ISA Trans.77 (2018), 1-19. |
| [50] | A.‐M.Zou, K. D.Kumar, Z.‐G.Hou, and X.Liu, Finite‐time attitude tracking control for spacecraft using terminal sliding mode and Chebyshev neural network, IEEE Trans. Syst. Man Cybern. B Cybern.41 (2011), no. 4, 950-963. |
| [51] | S.Mondal and C.Mahanta, Adaptive second order terminal sliding mode controller for robotic manipulators, J. Frankl. Inst.‐Eng. Appl. Math.351 (2014), no. 4, 2356-2377. · Zbl 1372.93065 |
| [52] | D.Nojavanzadeh and M.Badamchizadeh, Adaptive fractional‐order non‐singular fast terminal sliding mode control for robot manipulators, IET Control. Theory Appl.10 (2016), no. 13, 1565-1572. |
| [53] | M.Van and S. S.Ge, Adaptive fuzzy integral sliding‐mode control for robust fault‐tolerant control of robot manipulators with disturbance observer, IEEE Trans. Fuzzy Syst.29 (2021), no. 5, 1284-1296. |
| [54] | R.Chang, Y.Fang, L.Liu, and J.Li, Decentralized prescribed performance adaptive tracking control for Markovian jump uncertain nonlinear systems with input saturation, Int. J. Adapt. Control Signal Process.31 (2017), no. 2, 255-274. · Zbl 1358.93005 |
| [55] | F.Plestan, Y.Shtessel, V.Brégeault, and A.Poznyak, New methodologies for adaptive sliding mode control, Int. J. Control83 (2010), no. 9, 1907-1919. · Zbl 1213.93031 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
