Fractional-order sliding mode control of robotic arms with boundary layer

LIU Shijie; HUANG Zhilai; YANG Mingxing; XU Peimin

Volume 35 Issue 4

Feb. 2022

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Article Navigation > Journal of Shanghai University of Engineering Science > 2021 > 35(4): 327-332

LIU Shijie, HUANG Zhilai, YANG Mingxing, XU Peimin. Fractional-order sliding mode control of robotic arms with boundary layer[J]. Journal of Shanghai University of Engineering Science, 2021, 35(4): 327-332.

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LIU Shijie, HUANG Zhilai, YANG Mingxing, XU Peimin. Fractional-order sliding mode control of robotic arms with boundary layer[J]. Journal of Shanghai University of Engineering Science, 2021, 35(4): 327-332.

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Fractional-order sliding mode control of robotic arms with boundary layer

LIU Shijie^{a, b
,},
HUANG Zhilai^{a, b
,
,},
YANG Mingxing^{a, b},
XU Peimin^{a, b}

a.
Anhui Province Key Laboratory of Special Heavy Load Robot
b.
School of Mechanical Engineering, Anhui University of Technology, Ma’anshan 243000, China

Received Date: 2021-08-31
Publish Date: 2022-02-23

Abstract

Abstract

For the robotic arm system with perturbation, the fractional-order calculus was introduced to construct a fractional-order sliding mode surface based on classical sliding mode control. While a boundary layer had set in the reaching law, and the sign function was replaced with the saturation function to weaken chattering phenomenon of the sliding mode surface to obtain a fractional-order sliding mode control of robotic arms with boundary layer, and its convergence had proved by the direct method of Lyapunov. Example with a two-degree-of-freedom robotic arm system as the controlled object, the simulation result shows that the fractional-order sliding mode control of robotic arms with boundary layer can achieve better convergence and accurate trajectory tracking by adjusting the differential order compared with the classical sliding mode control.
- sliding mode control,
- boundary layer method,
- saturation function,
- fractional-order calculus,
- robotic arm

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References(29)

References

[1]	BAGLEY R L. On the fractional calculus model of viscoelastic behavior[J] . Journal of Rheology,1998,30(1):133 − 155.
[2]	KOBER H. On fractional integrals and derivatives[J] . Quarterly Journal of Mathematics,1940(1):193 − 211.
[3]	IGOR P. Fractional-order systems and PIλDμ controllers[J] . IEEE Trans. Automatic Control,1996,44(1):208 − 214. doi: 10.1109/9.739144
[4]	WANG L N, CHANG H, LI Y. Dynamics analysis and chaotic control of a fractional-order three-species food-chain system[J] . Mathematics,2020,8(3):409 − 15. doi: 10.3390/math8030409
[5]	ERAY O, TOKAT S. The design of a fractional-order sliding mode controller with a time-varying sliding surface[J] . Transactions of the Institute of Measurement and Control,2020,42(16):3196 − 3215. doi: 10.1177/0142331220944626
[6]	LI Z Q, CHEN L Q, ZHENG Q, et al. Control of a path following caterpillar robot based on a sliding mode variable structure algorithm[J] . Biosystems Engineering,2019,186:293 − 306. doi: 10.1016/j.biosystemseng.2019.07.004
[7]	PILLONI A, PISANO A, USAI E. Robust finite-time frequency and voltage restoration of inverter-based microgrids via sliding-mode cooperative control[J] . IEEE Transactions on Industrial Electronics,2018,65(1):907 − 917. doi: 10.1109/TIE.2017.2726970
[8]	BOUKADIDA W, BENAMOR A, MESSAOUD H, et al. Metaheuristics-based multi-objective design of global robust optimal sliding mode control of discrete uncertain systems[J] . International Journal of Control, Automation and Systems,2019,17(6):1378 − 1392. doi: 10.1007/s12555-018-0486-y
[9]	ZHANG X, ZHANG J, LU W R, et al. Research on fractional sliding mode synchronous control of robotic ARMS under uncertain disturbance[J] . Automatic Control and Computer Sciences,2021,55(1):26 − 37. doi: 10.3103/S0146411621010107
[10]	DUC T M, HOA N V, DAO T P. Adaptive fuzzy fractional-order nonsingular terminal sliding mode control for a class of second-order nonlinear systems[J] . Journal of Computational and Nonlinear Dynamics,2018,13(3):031004.
[11]	WANG J, SHAO C, CHEN Y Q. Fractional order sliding mode control via disturbance observer for a class of fractional order systems with mismatched disturbance[J] . Mechatronics,2018,53:8 − 19. doi: 10.1016/j.mechatronics.2018.05.006
[12]	HUANG S H, XIONG L Y, WANG J, et al. Fixed-time fractional-order sliding mode controller for multimachine power systems[J] . IEEE Transactions on Power Systems,2021,36(4):2866 − 2876.
[13]	NGUYEN S D, LAM B D, NGO V H. Fractional-order sliding-mode controller for semi-active vehicle MRD suspensions[J] . Nonlinear Dynamics,2020,101(3):1 − 10.
[14]	MA H F, LIU C, LIU Y, et al. Sliding mode control for uncertain discrete-time systems based on fractional order reaching law[J] . IET Control Theory & Applications,2019,13(13):1963 − 1970.
[15]	BABAEI S M, YAHYAZADEH M, MARJ H F. Novel MPPT for linear-rotational sun-tracking system using fractional fuzzy grey-based sliding mode control[J] . Iranian Journal of Science and Technology, Transactions of Electrical Engineering,2020,44(4):1379 − 1401. doi: 10.1007/s40998-020-00324-6
[16]	RIGATOS G G. Control and disturbances compensation in underactuated robotic systems using the derivative-free nonlinear Kalman filter[J] . Robotica,2017,35(3):687 − 711. doi: 10.1017/S0263574715000776
[17]	TAVARES A, MADRUGA S P, BRITO A V, et al. Dynamic leader allocation in multi-robot systems based on nonlinear model predictive control[J] . Journal of Intelligent and Robotic Systems,2019,98(6):1 − 18.
[18]	SU H, HU Y B, KARIMI H R, et al. Improved recurrent neural network-based manipulator control with remote center of motion constraints: Experimental results[J] . Neural Networks,2020,131:291 − 299. doi: 10.1016/j.neunet.2020.07.033
[19]	DAI L, YU Y, ZHAI D H, et al. Robust model predictive tracking control for robot manipulators with disturbances[J] . IEEE Transactions on Industrial Electronics,2021,68(5):4288 − 4297. doi: 10.1109/TIE.2020.2984986
[20]	KOMIJANI H, MASOUMNEZHAD M, ZANJIREH M M, et al. Robust hybrid fractional order proportional derivative sliding mode controller for robot manipulator based on extended grey wolf optimizer[J] . Robotica,2020,38(4):605 − 616. doi: 10.1017/S0263574719000882
[21]	YIN C, CHENG Y H, ZHONG S M, et al. Fractional-order switching type control law design for adaptive sliding mode technique of 3D fractional-order nonlinear systems[J] . Complexity,2016,21(6):363 − 373. doi: 10.1002/cplx.21696
[22]	RAHIMKHANI P, ORDOKHANI Y, BABOLIAN E. A new operational matrix based on Bernoulli wavelets for solving fractional delay differential equations[J] . Numerical Algorithms,2017,74(1):223 − 245. doi: 10.1007/s11075-016-0146-3
[23]	MADDAHI A, SEPEHRI N, KINSNER W. Fractional-Order Control of Hydraulically Powered Actuators: Controller Design and Experimental Validation[J] . IEEE/ASME Transactions on Mechatronics,2019,24(2):796 − 807. doi: 10.1109/TMECH.2019.2894105
[24]	WANG Y Q, FENG Y T, ZHANG X G, et al. A new reaching law for antidisturbance sliding-mode control of PMSM speed regulation system[J] . IEEE Transactions on Power Electronics,2020,35(4):4117 − 4126. doi: 10.1109/TPEL.2019.2933613
[25]	BRAHMI B, LARAKI M H, BRAHMI A, et al. Improvement of sliding mode controller by using a new adaptive reaching law: Theory and experiment[J] . ISA Transactions,2020,97:261 − 268. doi: 10.1016/j.isatra.2019.08.010
[26]	HOU S X, CHU Y D, FEI J T. Robust intelligent control for a class of power-electronic converters using neuro-fuzzy learning mechanism[J] . IEEE Transactions on Power Electronics,2021,36(8):9441 − 9452. doi: 10.1109/TPEL.2021.3049553
[27]	TAHERI, FERDOWSI E, DANESH M H, et al. Design boundary layer thickness and switching gain in SMC algorithm for AUV motion control[J] . Robotica,2019,37(10):1785 − 1803. doi: 10.1017/S0263574719000262
[28]	CRISTOFAR A. Robust distributed control of quasilinear reaction-diffusion equations via infinite-dimensional sliding modes[J] . Automatica,2019,104:165 − 172. doi: 10.1016/j.automatica.2019.02.039
[29]	GUO Y, WOO P Y. An adaptive fuzzy sliding mode controller for robotic manipulators[J] . Systems Man & Cybernetics Part A Systems & Humans IEEE Transactions on,2003,33(2):149 − 159.