Fractional-order super-twisting nonsingular terminal sliding mode control of 2-DOF robotics manipulators

Authors

Shahrood University of Technology

Abstract

In this study, a super-twisting algorithm, using the sliding surface as a fractional-order non-singular terminal sliding mode (NTSM), is presented. In robust control, one of the important problem is the reduction of system error and reduce the chattering. One of the most common applications of sliding mode controllers is about the reduction of chattering. Also, utilizing the fractional calculus in controller design brings more accuracy and reduces system errors. Utilizing a higher-order sliding mode controller using the super-twisting algorithm and the fractional-order non-single terminal sliding mode for the two-link serial robot is the novelty of the presented research. The design of the suggested controller is such that it is independent of the robotic manipulators model and is based on the system errors. Stability analysis of the close-loop system has performed using Lyapunov's method. The simulation results show high accuracy, fast convergence, and high robustness of the proposed fractional-order super-twisting nonsingular terminal sliding mode control.

Keywords

References

[1] Das S (2008) Functional fractional calculus for system identification and controls. Springer, Berlin, Heidelberg.
[2] Capelas de Oliveira E (2019) Solved Exercises in fractional calculus. Springer.
[3] David S, Balthazar J.M, Julio B, Oliveira C (2012) The fractional-nonlinear robotic manipulator: Modeling and dyn. sim., AIP pp. 298-305.
[4] Coronel-Escamilla A,Torres F, Gómez-Aguilar J, Escobar-Jiméne R, Guerrero-Ramírez R (2018) On the trajectory tracking control for an SCARA robot manipulator in a fractional model driven by induction motors with PSO tuning. Multibody Syst Dyn 43(3) 257-277.
[5] Goodwine B (2014) Modeling a multi-robot system with fractional-order differential equations. (ICRA), IEEE 1763-1768.
[6] Wensong J, Zhongyu W, Mourelatos Z.P (2016) Application of nonequidistant fractional-order accumulation model on trajectory prediction of space manipulator. IEEE ASME Trans Mechatron 21(3): 1420-1427.
[7] Al-Saggaf UM, Bettayeb M, Djennoune S (2017) Super-twisting algorithm-based sliding-mode observer for Synchronization of nonlinear incommensurate fractional-order chaotic systems Subject to unknown inputs. Arab J Sci Eng 42(7): 3065-3075.
[8] Mujumdar A, Tamhane B, Kurode S (2014) Fractional order modeling and control of a flexible manipulator using sliding modes. IEEE 2011-2016.
[9] Chen H, Chen W, Chen B (2013) Robust synchronization of incommensurate fractional-order chaotic systems via second-order sliding mode technique. IEEE 3147-3151.
[10] Bettayeb R.F.M ,Rahman M.H (2018) Control of serial link manipulator using a fraction al order controller. IREACO 11(1).
[11] Mohammed RH, Bendary F, Elserafi K (2016) Trajectory tracking control for robot manipulator using fractional order-fuzzy-PID controller. Int J Comput Appl 134(15): 8887.
[12] Moreno AR, Sandoval VJ (2013) Fractional order PD and PID position control of an angular manipulator of 3DOF. IEEE 89-94.
[13] Angel L, Viola J (2018) Fractional order PID for tracking control of a parallel robotic manipulator type delta. ISA Trans 79 172-188.
[14] Dumlu A (2018) Practical position tracking control of a robotic manipulator based on fractional order sliding mode controller. Elektronika ir Elektrotechnika 24(5): 19-25.
[15] Rahmani M, Rahman M.H (2019) A new adaptive fractional sliding mode control of a MEMS gyroscope. Microsyst Technol 2(9): 3409-3416.
[16] Mujumdar A, Kurode S, Tamhane B (2013) Fractional order sliding mode control for single link flexible manipulator, (CCA). IEEE 288-293.
[17] Ghasemi I, Ranjbar Noei A, Sadati J (2018) Sliding mode based fractional-order iterative learning control for a nonlinear robot manipulator with bounded disturbance. Meas Control 40(1): 49-60.
[18] Senejohnny D, Faieghi M, Delavari H (2017) Adaptive second-order fractional sliding mode controlwith application to water tanks level control.
[19] Muñoz-Vázquez AJ, Sánchez-Torres DJ, Parra-Vega V, Sánchez-Orta A, Martínez-Reyes F (2020) A fractional super-twisting control of electrically driven mechanical systems. Meas Control 42(3): 485-492.
[20] Caponetto R, Graziani S, Tomasello V, Pisano A (2015) Identification and fractional super-twisting robust control of IPMC actuators. Fract Calc Appl Anal 18(6): 1358.
[21] Levant A (1993) Sliding order and sliding accuracy in sliding mode control; Int J Control 58(6): 1247-1263.
[22] Patel A (2018) Observer based fractional second-oreder nonsingular terminal multisegment sliding mode control of SRM position regulation system. IAEME.
[23] Yu S, Yu X, Shirinzadeh B, Man Z (2005) Continuous finite-time control for robotic manipulators with terminal sliding mode. Automatica 41(11): 1957-1964.
[24] Wang YY, Chen JW, LGu LY, Li XD  (2015) Time delay control of hydraulic manipulators with continuous nonsingular terminal sliding mode. J Cent South Univ 22(12): 4616-4624.
[25] Ma X, Zhao Y, Di Y (2020) Trajectory Tracking control of robot manipulators based on U-model. Math Probl Eng 2020(8): 1-10.
[26] Divandari M, Rezaie B, Ranjbar Noei A (2019) Speed control of switched reluctance motor via fuzzy fast terminal sliding-mode control. Comput Electr Eng 80: 106472.
[27] Baek J, Kwon W, Kang C (2020) A new widely and stably adaptive sliding-mode control with nonsingular terminal sliding variable for robot manipulators. IEEE 43443-43454.
[28] Babaie M, Rahmani Z, Rezaie B (2019) Designing a switching controller based on control performance assessment index and a fuzzy supervisor for perturbed discrete-time systems subject to uncertainty. Autom Control Comp S 53: 116-126.
[29] Wang Y, Gu L, Gao M, Zhu K (2016) Multivariable output feedback adaptive terminal sliding mode control for underwater vehicles. Asian J Control 18: 247-265(1).
[30] Nguyen S.D, Vo HD, Seo TI (2017) Nonlinear adaptive control based on fuzzy sliding mode technique and fuzzy-based compensator. ISA Trans 70: 309-321.
[31] Wang Y, Jiang S, Chen B, Wu H (2018) A new continuous fractional-order nonsingular terminal sliding mode control for cable-driven manipulators. Adv Eng Softw 119: 21-29.
[32] Deng W, Yao J, Ma D (2017) Robust adaptive precision motion control of hydraulic actuators with valve dead-zone compensation. ISA Trans 70: 269-278.
[33] Sadeghi R, Madani SM, Ataei M, Kashkooli MA, Ademi S (2018) Super-twisting sliding mode direct power control of a brushless doubly fed induction generator. IEEE Trans Indus Electronics 65(11): 9147-9156.
[34] Jin M, Lee J, Chang PH, Choi C (2009) Practical nonsingular terminal sliding-mode control of robot manipulators for high-accuracy tracking control IEEE Trans Indus Electronics 56(9): 3593-3601.
[35] Kali Y, Saad M, Benjelloun K, Khairallah C (2018) Super-twisting algorithm with time delay estimation for uncertain robot manipulators. Nonlinear Dyn 93(2): 557-569.
[36] Kilbas AA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. elsevier.
[37] Rivera J, Garcia L, Mora M, Raygoza J, Ortega S (2011) Super-twisting sliding mode in motion control systems. Sliding Mode Control 237-254.
[38] Sabatier J, Lanusse P, Melchior P, Oustaloup A  (2015) Fractional order differentiation and robust control design. Springer, Dordrecht.
Journal of Solid and Fluid Mechanics
Volume 11, Issue 2
May and June 2021
Pages 41-56

Files

Share

How to cite

Statistics