Robust Sliding Mode Control of Robot Manipulators Using the Fourier Series Expansion in the Presence of Uncertainty

Subject Areas : Control Engineering

Abdullah  Hadipoor ¹ (Department of Electrical Engineering, Bushehr Branch, Islamic Azad University, Bushehr, Iran)
Siamak  Azargoshasb ² (Department of Electrical Engineering, Bushehr Branch, Islamic Azad University, Bushehr, Iran)
Abdolrasool  Ghasemi ³ (Department of Electrical Engineering, Bushehr Branch, Islamic Azad University, Bushehr, Iran)

Received: 2022-06-12 Accepted : 2022-08-08 Published : 2022-12-22

Keywords: robot manipulators, Uncertainty, Voltage Control Strategy, sliding mode control, Fourier series expansion,

Abstract :

In this paper, a robust dynamic slip mode controller for an electrical robot manipulator is presented. The control law calculates the motor voltage based on the voltage control strategy. Uncertainties are estimated using the Fourier series expansion and the cutting error is compensated. Fourier coefficients are adjusted based on stability analysis. Also in this paper is the design of a robust controller using a new adaptive Fourier series extension. Compared to previous related works based on the Fourier series expansion, the advantage of this paper is that it provides a matching law for the main frequency of the Fourier series expansion and thus eliminates the need for trial and error in its regulation. A case study of a Scara robot powered by DC magnet electric motors. The effect of uncertainty estimation based on the Fourier series expansion is studied instead of using the sign function. The proposed method is also compared with Legendre polynomials. The simulation results confirm the robust and satisfactory performance of the proposed controller.

References:

[1]        M. W. Spong, S. Hutchinson and M. Vidyasagar, "Robot Modelling and Control", Wiley, Hoboken, 2006.

[2]        M.  M. Fateh, "On the voltage-based control of robot manipulators", Int. J. Control. Autom. Syst., vol. 6, no. 5, pp.702–712, 2008, doi:10.1007/s12555-017-0035-0.

[3]        F. Wang, Z. Liu, C. L. Chen and Y. Zhang, "Robust adaptive visual tracking control for uncertain robotic systems with unknown dead-zone inputs", Journal of the Franklin Institute, vol. 356, no. 12, pp. 6255-6279, 2019, doi:10.1016/j.jfranklin.2019.05.040.

[4]        L. Kong, S. Zhang and X. Yu, "Approximate optimal control for an uncertain robot based on adaptive dynamic programming", Neurocomputing, vol.423, no. 29, pp.308-317, 2021, doi:10.1016/j.neucom.2020.10.012.

[5]        M.  M. Fateh, "Proper uncertainty bound parameter to robust control of electrical manipulators using nominal model", Nonlinear Dynamics, vol. 61, pp. 655-666, 2012, doi:10.1007/s11071-010-9677-7.

[6]        R. Shahnazi and M. R. Akbarzadeh, "PI Adaptive fuzzy control with large and fast disturbance rejection for a class of uncertain nonlinear systems", IEEE Trans. Fuzzy Syst., vol. 16, no. 1, pp. 187-197, 2008, doi: 10.1109/TFUZZ.2007.903320.

[7]        B. M. Yilmaz, E. Tatlicioglu, A. Savran and M. Alci, “Adaptive fuzzy logic with self-tuned membership functions based repetitive learning control of robotic manipulators”, Applied Soft Computing, vol. 104, 2021, doi:10.1016/j.asoc.2021.107183.

[8]      L. Wei, L. Yang and H. Wang, “Indirect fuzzy adaptive control for trajectory tracking of uncertain robots”, Electric Machines and control, vol.5, pp. 393-397, 2006, doi:10.1109/INDIN.2008.4618148.

[9]        W. Hong-rui, C. Zeng-wei, W. Li-xin, T. Xue-jing and L. Xiu-ling, “Direct adaptive fuzzy control for robots in cartesian space”, Proceedings of Sixth International Conference on Machine Learning Cybernetics, vol.1, pp. 482-486, 2007, doi: 10.1109/ICMLC.2007.4370193.

[10]      K. Singhal, V. Kumar, K. P. S. Rana, “Robust trajectory tracking control of non-holonomic wheeled mobile robots using an adaptive fractional order parallel fuzzy PID controller”, Journal of the Franklin Institute, vol. 359, no. 9, pp. 4160-4215, 2022, doi:10.1016/j.jfranklin.2022.03.043.

[11]      M. M. Fateh, S. Shahrabi Frahani and A. Khatamianfar, “Task space control of a welding robot using a fuzzy coordinator”, International Journal of Control, Automation, and Systems, vol. 8, no. 3, pp. 574–582, 2010, doi:10.1007/s12555-010-0310-9.

[12]      D. Zhang, S. Song, “Research on the adaptive fuzzy sliding mode control of 2-DOF robot”, Fifth International Conference on Fuzzy Systems and Knowledge Discovery, vol. 9, pp. 236-240, 2008, doi: 10.1109/FSKD.2008.269.

[13]      D. Cruz-Ortiz, I. Chairez and A. Poznyak, “Non-singular terminal sliding-mode control for a manipulator robot using a barrier Lyapunov function", ISA Transactions, vol121, pp.268-283,Feb. 2022, doi:10.1016/j.isatra.2021.04.001.

[14]      R. Zarin  and  S. Azargoshasb, " Model-Free Discrete Time Control for Scara Robot Manipulators Using   Descending Gradient Algorithm," Journal of Communication Engineering., vol. 11,no.41, pp. 59-76, 2021(in persian).

[15]    M. Zaraei,  M. M. Zirkohi and  N. C. Shirazi, " Designing Optimal Neural Networks Controller to Regulate and Control the Output Voltage of  DC-DC Boost Converters," Journal of Communication Engineering., vol. 11,no.42, pp. 41-54, 2021(in persian).

  [16]      M. M. Fateh and S. Khorashadizadeh, "Robust control of electrically driven robots by adaptive fuzzy estimation of uncertainty", Nonlinear Dyn., vol. 69, pp. 1465–1477, 2012, doi:10.1007/s11071-012-0362-x.

[17]      S. Khorashadizadeh and M. Majidi, " Chaos synchronization using the Fourier series expansion with application to secure communications", AEU – International Journal of Electronics and Communications, vol. 82, pp. 37–44, 2017, doi:10.1016/j.aeue.2017.07.032.

[18]      J. Chen and j. Li, "Distributed consensus control of periodically time-varying multi-agent systems using neural networks and fourier series expansion", Journal of the Franklin Institute, vol. 358, no. 14, pp. 71707186, 2021, doi:10.1016/j.jfranklin.2021.07.002.

[19]      G. Karimi and M. Heidarian, "Facial expression recognition with polynomial Legendre and partial connection MLP", Neurocomputing, vol. 434, no. 28, pp. 33-44, 2021, doi:10.1016/j.neucom.2020.12.070.

[20]      R. Gholipour, A. Khosravi and H. Mojallali, "Multi-objective optimal backstepping controller design for chaos control in a rodtype plasma torch system using Bees Algorithm", Applied Mathematical Modelling, vol. 39, no. 15, pp. 4432–4444, 2015, doi:10.1016/j.apm.2014.12.049.

[21]      R. Gholipour and M. M. Fateh, "Adaptive task-space control of robot manipulators using the Fourier series expansion without task-space velocity measurements", Measurement, vol. 123, pp.285–292, 2018, doi:10.1016/j.measurement.2018.04.003.

[22]      R. Gholipour and M. M. Fateh, "Observer-based robust task-space control of robot manipulators using Legendre polynomial", In: Electrical Engineering (ICEE), IEEE Iranian Conference, Tehran, Iran, 2–4 May 2017, pp. 766–771, 2017, doi: 10.1109/IranianCEE.2017.7985141.

[23]      H. Sira, "On the dynamical sliding mode control of nonlinear systems", International Journal of Control, vol. 57, no. 5, pp. 1039–1061, 1993, doi:10.1016/0167-6911(92)90069-5.

[24]      S. Khorashadizadeh and M. Fateh, "Uncertainty estimation in robust tracking control of robot  manipulators using the Fourier series expansion", Robotica, vol. 35, no. 2, pp. 310–336, 2017, doi: 10.1017/S026357471500051X.

[25]      F. Lin, S. Chen and K. Shyu, "Robust dynamic sliding-mode control using adaptive RENN for magnetic levitation system", IEEE Transaction on Neural Networks, vol. 20, no. 6, pp. 938–951, 2009, doi: 10.1109/TNN.2009.2014228.

[26]      F. Lin, S. Chen and I. Sun, "Intelligent sliding-mode position control using recurrent wavelet fuzzy neural network for electrical power steering system", International Journal of Fuzzy Systems, vol. 19, no. 5, pp. 1344–1361, 2017, doi:10.1007/s40815-017-0342-x.

[27]      J. Slotine and W. Li, "Applied Nonlinear Control", Englewood Cliffs, NJ: Prentice Hall, 1991.

[28]      M.M. Fateh, " Nonlinear control of electrical flexible-joint robots", Nonlinear Dynamics, vol. 67, no. 4, pp.2549–2559, 2012, doi:10.1007/s11071-011-0167-3.

[29]    M. Singla, L.S. Shieh, G. Song, L. Xie and Y. Zhang, " A new optimal sliding mode controller design using scalar sign function", ISA Transactions, vol. 53, no. 2, pp. 267-279, 2015, doi:10.1016/j.isatra.2013.09.007.

[30]      S. Khorashadizadeh and M. M. Fateh, "Robust task-space control of robot manipulators using Legendre polynomials for uncertainty estimation", Nonlinear Dynamics, vol. 79, no. 2, pp. 1151–1161, 2015, doi:10.1007/s11071-014-1730-5.

[31]      K. Y. Chen, Y. H. Lai and R. F. Fung, "A comparison of fitness functions for identifying an LCD Glass-handling robot system", Mechatronics, vol. 46, pp. 126–142, 2017, doi:10.1016/j.mechatronics.2017.08.001.