Model reference adaptive control based time delay estimation with RBF neural network for robot manipulators

Abstract

In this paper, model-reference adaptive control (MRAC) with neural network (NN) and time delay estimation (TDE) is proposed for controlling a robotic manipulator. With more than two degrees of freedom (DoF) of the robot, the formulation of a known regression matrix is tedious and also difficult to compute for the different robotic systems. Therefore, this work introduces MRAC based on TDE with NN (MRAC-NNTDE) to achieve high-control performance without prior knowledge of the regression matrix and offers a model-free scheme. Firstly, MRAC is applied to adjust the control gains, then TDE is implemented to estimate the unknown dynamical robotic system, and NN is employed to deal with the TDE estimation error. The overall stability of the robotic dynamics is investigated using the Lyapunov theorem. In the end, computer simulations are compared to validate the effectiveness of the proposed scheme.

Keywords

Model reference adaptive control / Time delay estimation / Neural network / Robotic manipulator

Funding

This work is funded by Prince Sultan University, Riyadh, Saudi Arabia.

Declaration of competing interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

References

[1] Ajel AR. Robust model reference adaptive control for tail-sitter vtol aircraft. Actuators. 2021; 10(7).

[2] Lavretsky E. Adaptive control: Introduction, overview, and applications. Lecture notes IEEE Robust Adapt. Control Workshop 208; 2008.

[3] Dan Z, Bin W. A review on model reference adaptive control of robotic manipulators. Annu Rev Control. 2017;43:188-198.

[4] Xiao Shunli LJ, Yangmin L. A model reference adaptive pid control for electromagnetic actuated micro-positioning stage. In 2012 IEEE International Conference on Automation Science and Engineering (CASE), IEEE, 2012;97-102.

[5] Goléa N, Goléa A, Kadjoudj M. Nonlinear model reference adaptive control using takagi-sugeno fuzzy systems. J Intell Fuzzy Syst. 2006; 17(1):47-57.

[6] Guo L, Parsa L. Model reference adaptive control of five-phase ipm motors based on neural network. IEEE Trans Ind Electron. 2011; 59(3):1500-1508.

[7] Wu C, Zhao J. H_∞ adaptive tracking control for switched systems based on an average dwell-time method. Int J Syst Sci. 2015; 46(14):2547-2559.

[8] Fang Y, Fei J, Ma K. Model reference adaptive sliding mode control us-ing rbf neural network for active power filter. Int J Electr Power Energy Syst. 2015;73:249-258.

[9] Uçak K, Arslantürk BN. Adaptive mimo fuzzy pid controller based on peak observer. Int J Optim Control Theor Appl. 2023; 13(2).

[10] Ahmed S, Wang H, Tian Y. Modification to model reference adaptive control of 5-link exoskeleton with gravity compensation. In 2016 35th Chinese Control Conference (CCC), 2016;6115-6120.

[11] Nguyen N, Summers E. On time delay margin estimation for adaptive control and robust modifi-cation adaptive laws. 2011;6438.

[12] Raja MM, Vijayakumar V, Veluvolu KC. Improved order in hilfer fractional differential systems: Solvability and optimal control problem for hemivariational inequalities. Chaos Solitons Fractals. 2024;188:115558.

[13] Ma Y-K, Raja MM, Nisar KS, Shukla A, Vijayakumar V. Results on controllability for sobolev type fractional differential equations of order 1¡ r¡ 2 with finite delay. AIMS Math. 2022; 7(6):10215-10233.

[14] Raja MM, Vijayakumar V, Veluvolu KC, Shukla A, Nisar KS. Existence and optimal control results for caputo fractional delay clark’s subdifferential inclusions of order order r ∈ (1, 2) with sectorial operators. Optim Control Appl Methods. 2024; 45(4):1832-1850.

[15] Lavretsky E, Kevin W, Howe D. Robust and adaptive control with aerospace applications. England: Springer-Verlag London, 2013.

[16] Lewis FL, Dawson DM, Abdallah CT. Robot manipulator control: Theory and practice. CRC Press, 2003.

[17] Zhou X, Tian Y, Wang H. Neural network state observer-based robust adaptive fault-tolerant quantized iterative learning control for the rigid-flexible coupled robotic systems with unknown time delays. Appl Math Comput. 2022;430:127286.

[18] Zhou X, Wang H, Wu K, Zheng G. Fixed-time neural network trajectory tracking control for the rigid-flexible coupled robotic mechanisms with large beam-deflections. Appl Math Model. 2023;118:665-691.

[19] Ghazi, Farah F., and Luma NM Tawfiq. Design optimal neural network based on new LM training algorithm for solving 3D-PDEs. An International Journal of Optimization and Control: Theories & Applications (IJOCTA). 2024; 14(3):249-260.

[20] Wang Y, Yan F, Chen J, Ju F, Chen B. A new adaptive time-delay control scheme for cable-driven manipulators. IEEE Trans Ind Informat. 2018; 15(6):3469-3481.

[21] Wang Y, Li B, Yan F, Chen B. Practical adaptive fractional-order nonsingular terminal sliding mode control for a cable-driven manipulator. Int. J. Robust Nonlinear Control 2019; 29(5):1396-1417.

[22] Youcef-Toumi K, Wu S-T. Input/output linearization using time delay control. 1992; 114(1):10-19.

[23] Long Y, Liu X, Yao C, Song E. Model-free adaptive full-order sliding mode control with time delay estimation of high-pressure common rail system. J Vib Control. 2024;10775463241256225.

[24] Ahmed S, Azar AT, Ibraheem IK. Model-free scheme using time delay estimation with fixed-time fsmc for the non-linear robot dynamics. AIMS Math. 2024; 9(4):9989-10009.

[25] Yadegari H, Beyramzad J, Khanmirza E. Magnetorquers-based satellite attitude control using interval type-ii fuzzy terminal sliding mode control with time delay estimation. Adv Space Res 2022; 69(8):3204-3225.

[26] Han S, Wang H, Tian Y, Christov N. Time-delay estimation based computed torque control with robust adaptive rbf neural network compensator for a reha-bilitation exoskeleton. ISA Trans. 2020;97:171-181.

[27] Ahmed S, Azar AT. Enhanced tracking control for n-dof robotic manipulators: A fixed-time terminal sliding mode approach with time delay estimation. Results Eng. 2024;24:102904.

[28] Li G, Ma X, Li Y. Adaptive sliding mode control based on time-delay estimation for underactuated 7-dof tower crane. IEEE Trans Syst Man Cybern Syst. 2025.

[29] Van M, Ge SS, Ren H. Finite time fault tolerant control for robot ma-nipulators using time delay estimation and continuous nonsingular fast terminal sliding mode control. IEEE Trans Cybern 2016; 47(7):1681-1693.

[30] Choi J, Kwon W, Lee YS, Han S. Adaptive time-delay estimation error compensation for application to robot manipulators. Control Eng Pract. 2024;151:106029.

[31] Jin M, Kang SH, Chang PH, Lee J. Robust control of robot manipulators using inclusive and enhanced time delay control. IEEE/ASME Trans Mechatronics. 2017; 22(5):2141-2152.

[32] Jin M, Kang SH, Chang PH. Robust compliant motion control of robot with nonlinear friction using time-delay estimation. IEEE Trans Ind Electron. 2008; 55(1):258-269.

[33] Hsia TC, Gao L. Robot manipulator control using decentralized linear time-invariant time-delayed joint controllers. In Proceedings IEEE International Conference on Robotics and Automation, IEEE, 1990;2070-2075.

[34] Yavuz M, Öztürk M, Yaşkıran B. Comparison of fractional order sliding mode controllers on robot manipulator. ICAM’24 2024;188.

[35] Reichhartinger M, Spurgeon S, Forstinger M, Wipfler M. A robust exact differentiator toolbox for matlab®/simulink®. IFAC-PapersOnLine, 2017; 50(1):1711-1716.

[36] Asl SBF, Moosapour SS. Adaptive backstepping fast terminal sliding mode controller design for ducted fan engine of thrust-vectored aircraft. 2017;71:521-529.

[37] Ahmed S, Azar AT, Tounsi M. Adaptive fault tolerant non-singular sliding mode control for robotic manipulators based on fixed-time control law. Actuators. 2022; 11(12):353.

[38] Jasim Mohamed, Mohamed, et al. Hybrid controller with neural network PID/FOPID operations for two-link rigid robot manipulator based on the zebra optimization algorithm. Frontiers in Robotics and AI. 2024;11:1386968.