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Volume 11 Issue 5
May  2024

IEEE/CAA Journal of Automatica Sinica

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Article Contents
Q. Yang, F. Zhang, and  C. Wang,  “Deterministic learning-based neural PID control for nonlinear robotic systems,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 5, pp. 1227–1238, May 2024. doi: 10.1109/JAS.2024.124224
Citation: Q. Yang, F. Zhang, and  C. Wang,  “Deterministic learning-based neural PID control for nonlinear robotic systems,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 5, pp. 1227–1238, May 2024. doi: 10.1109/JAS.2024.124224

Deterministic Learning-Based Neural PID Control for Nonlinear Robotic Systems

doi: 10.1109/JAS.2024.124224
Funds:  This work was supported by the National Natural Science Foundation of China (62203262, 62350083); Natural Science Foundation of Shandong Province (ZR2020ZD40, ZR2022QF124)
More Information
  • Traditional proportional-integral-derivative (PID) controllers have achieved widespread success in industrial applications. However, the nonlinearity and uncertainty of practical systems cannot be ignored, even though most of the existing research on PID controllers is focused on linear systems. Therefore, developing a PID controller with learning ability is of great significance for complex nonlinear systems. This article proposes a deterministic learning-based advanced PID controller for robot manipulator systems with uncertainties. The introduction of neural networks (NNs) overcomes the upper limit of the traditional PID feedback mechanism’s capability. The proposed control scheme not only guarantees system stability and tracking error convergence but also provides a simple way to choose the three parameters of PID by setting the proportional coefficients. Under the partial persistent excitation (PE) condition, the closed-loop system unknown dynamics of robot manipulator systems are accurately approximated by NNs. Based on the acquired knowledge from the stable control process, a learning PID controller is developed to further improve overall control performance, while overcoming the problem of repeated online weight updates. Simulation studies and physical experiments demonstrate the validity and practicality of the proposed strategy discussed in this article.


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  • [1]
    Y. Zhang and S. Li, “Kinematic control of serial manipulators under false data injection attack,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 4, pp. 1009–1019, Apr. 2023. doi: 10.1109/JAS.2023.123132
    L. Wang and B. Meng, “Distributed force/position consensus tracking of networked robotic manipulators,” IEEE/CAA J. Autom. Sinica, vol. 1, no. 2, pp. 180–186, Apr. 2014. doi: 10.1109/JAS.2014.7004548
    M. Bagheri, I. Karafyllis, P. Naseradinmousavi, and M. Krstić, “Adaptive control of a two-link robot using batch least-square identifier,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 1, pp. 86–93, Jan. 2021. doi: 10.1109/JAS.2020.1003459
    A. Visioli and G. Legnani, “On the trajectory tracking control of industrial scara robot manipulators,” IEEE Trans. Ind. Electron., vol. 49, no. 1, pp. 224–232, Feb. 2002. doi: 10.1109/41.982266
    R. Lozano and B. Brogliato, “Adaptive control of robot manipulators with flexible joints,” IEEE Trans. Autom. Control, vol. 37, no. 2, pp. 174–181, Feb. 1992. doi: 10.1109/9.121619
    W. E. Dixon, I. D. Walker, D. M. Dawson, and J. P. Hartranft, “Fault detection for robot manipulators with parametric uncertainty: A prediction-error-based approach,” IEEE Trans. Robot. Autom., vol. 16, no. 6, pp. 689–699, Dec. 2000. doi: 10.1109/70.897780
    K. S. Narendra and K. Parthasarathy, “Identification and control of dynamical systems using neural networks,” IEEE Trans. Neural Netw., vol. 1, no. 1, pp. 4–27, Mar. 1990. doi: 10.1109/72.80202
    R. M. Sanner and J.-J. E. Slotine, “Gaussian networks for direct adaptive control,” IEEE Trans. Neural Netw., vol. 3, no. 6, pp. 837–863, Nov. 1992. doi: 10.1109/72.165588
    S. Zhang, Y. Dong, Y. Ouyang, Z. Yin, and K. Peng, “Adaptive neural control for robotic manipulators with output constraints and uncertainties,” IEEE Trans. Neural Netw. Learn. Syst., vol. 29, no. 11, pp. 5554–5564, Nov. 2018. doi: 10.1109/TNNLS.2018.2803827
    Z.-L. Tang, S. S. Ge, K. P. Tee, and W. He, “Adaptive neural control for an uncertain robotic manipulator with joint space constraints,” Int. J. Control, vol. 89, no. 7, pp. 1428–1446, 2016. doi: 10.1080/00207179.2015.1135351
    Z. Chen, Z. Li, and C. L. P. Chen, “Adaptive neural control of uncertain MIMO nonlinear systems with state and input constraints,” IEEE Trans. Neural Netw. Learn. Syst., vol. 28, no. 6, pp. 1318–1330, Jun. 2018.
    Y. Yang, J. Han, Z. Liu, Z. Zhao, and K.-S. Hong, “Modeling and adaptive neural network control for a soft robotic arm with prescribed motion constraints,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 2, pp. 501–511, Feb. 2023. doi: 10.1109/JAS.2023.123213
    Y. Ren and W. Sun, “Robust adaptive control for robotic systems with input time-varying delay using Hamiltonian method,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 4, pp. 852–859, Jul. 2018. doi: 10.1109/JAS.2016.7510055
    Y. Ouyang, L. Dong, L. Xue, and C. Sun, “Adaptive control based on neural networks for an uncertain 2-DOF helicopter system with input deadzone and output constraints,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 3, pp. 807–815, May 2019. doi: 10.1109/JAS.2019.1911495
    Z. Zhao, J. Zhang, S. Chen, W. He, and K.-S. Hong, “Neural-network-based adaptive finite-time control for a two-degree-of-freedom helicopter system with an event-triggering mechanism,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 8, pp. 1754–1765, Aug. 2023. doi: 10.1109/JAS.2023.123453
    C. Knospe, “PID control,” IEEE Control Syst. Mag., vol. 26, no. 1, pp. 30–31, Feb. 2006. doi: 10.1109/MCS.2006.1580151
    M.-T. Ho and C.-Y. Lin, “PID controller design for robust performance,” IEEE Trans. Autom. Control, vol. 48, no. 8, pp. 1404–1409, Aug. 2003. doi: 10.1109/TAC.2003.815028
    L. H. Keel and S. P. Bhattacharyya, “Controller synthesis free of analytical models: Three term controllers,” IEEE Trans. Autom. Control, vol. 53, no. 6, pp. 1353–1369, Jul. 2008. doi: 10.1109/TAC.2008.925810
    M. T. Söylemez, N. Munro, and H. Baki, “Fast calculation of stabilizing PID controllers,” Automatica, vol. 39, no. 1, pp. 121–126, Jan. 2003. doi: 10.1016/S0005-1098(02)00180-2
    J. Kang, W. Meng, A. Abraham, and H. Liu, “An adaptive PID neural network for complex nonlinear system control,” Neurocomputing, vol. 135, pp. 79–85, Jul. 2014. doi: 10.1016/j.neucom.2013.03.065
    D. Ma, M. Song, P. Yu, and J. Li, “Research of RBF-PID control in maglev system,” Symmetry, vol. 12, no. 11, p. 1780, Oct. 2020. doi: 10.3390/sym12111780
    Z. Wang, Y. Zhu, H. Xue, and H. Liang, “Neural networks-based adaptive event-triggered consensus control for a class of multi-agent systems with communication faults,” Neurocomputing, vol. 470, pp. 99–108, Jan. 2022. doi: 10.1016/j.neucom.2021.10.059
    K. S. Tang, K. F. Man, G. Chen, and S. Kwong, “An optimal fuzzy PID controller,” IEEE Trans. Ind. Electron., vol. 48, no. 4, pp. 757–765, Aug. 2001. doi: 10.1109/41.937407
    J. Carvajal, G. Chen, and H. Ogmen, “Fuzzy PID controller: Design, performance evaluation, and stability analysis,” Inf. Sci., vol. 123, no. 3–4, pp. 249–270, Apr. 2000. doi: 10.1016/S0020-0255(99)00127-9
    I. Cervantes and J. Alvarez-Ramirez, “On the PID tracking control of robot manipulators,” Syst. Control Lett., vol. 42, no. 1, pp. 37–46, Jan. 2001. doi: 10.1016/S0167-6911(00)00077-3
    S.-Z. He, S. Tan, F.-L. Xu, and P.-Z. Wang, “Fuzzy self-tuning of PID controllers,” Fuzzy Sets Syst., vol. 56, no. 1, pp. 37–46, May 1993. doi: 10.1016/0165-0114(93)90183-I
    T. Y. Kuc and W.-G. Han, “An adaptive PID learning control of robot manipulators,” Automatica, vol. 36, no. 5, pp. 717–725, May 2000. doi: 10.1016/S0005-1098(99)00198-3
    C. Zhao and L. Guo, “PID controller design for second order nonlinear uncertain systems,” Sci. China Inf. Sci., vol. 60, no. 2, p. 022201, Feb. 2017. doi: 10.1007/s11432-016-0879-3
    C. Wang and D. J. Hill, “Learning from neural control,” IEEE Trans. Neural Netw., vol. 17, no. 1, pp. 130–146, Jan. 2006. doi: 10.1109/TNN.2005.860843
    T. Liu, C. Wang, and D. J. Hill, “Learning from neural control of nonlinear systems in normal form,” Syst. Control Lett., vol. 58, no. 9, pp. 633–638, Sept. 2009. doi: 10.1016/j.sysconle.2009.04.001
    M. Wang and C. Wang, “Learning from adaptive neural dynamic surface control of strict-feedback systems,” IEEE Trans. Neural Netw. Learn. Syst., vol. 26, no. 6, pp. 1247–1259, Jun. 2015. doi: 10.1109/TNNLS.2014.2335749
    F. Zhang and C. Wang, “Deterministic learning from neural control for uncertain nonlinear pure-feedback systems by output feedback,” Int. J. Robust Nonlinear Control, vol. 30, no. 7, pp. 2701–2718, May 2020. doi: 10.1002/rnc.4902
    M. Wang and A. Yang, “Dynamic learning from adaptive neural control of robot manipulators with prescribed performance,” IEEE Trans. Syst. Man Cybern. Syst., vol. 47, no. 8, pp. 2244–2255, Aug. 2017. doi: 10.1109/TSMC.2016.2645942
    F. Zhang, W. Wu, J. Hu, and C. Wang, “Deterministic learning from neural control for a class of sampled-data nonlinear systems,” Inf. Sci., vol. 595, pp. 159–178, May 2022. doi: 10.1016/j.ins.2022.02.034
    A. J. Kurdila, F. J. Narcowich, and J. D. Ward, “Persistency of excitation in identification using radial basis function approximants,” SIAM J. Control Optim., vol. 33, no. 2, pp. 625–642, Mar. 1995. doi: 10.1137/S0363012992232555
    J. Park and I. W. Sandberg, “Universal approximation using radial-basis-function networks,” Neural Comput., vol. 3, no. 2, pp. 246–257, Jun. 1991. doi: 10.1162/neco.1991.3.2.246
    C. Wang and D. J. Hill, Deterministic Learning Theory for Identification, Recognition, and Control. Boca Raton, USA: CRC Press, 2009.
    S. S. Ge, C. C. Hang, and T. Zhang, “Adaptive neural network control of nonlinear systems by state and output feedback,” IEEE Trans. Syst. Man Cybern. Part B Cybern., vol. 29, no. 6, pp. 818–828, Dec. 1999. doi: 10.1109/3477.809035
    S.-L. Dai, C. Wang, and M. Wang, “Dynamic learning from adaptive neural network control of a class of nonaffine nonlinear systems,” IEEE Trans. Neural Netw. Learn. Syst., vol. 25, no. 1, pp. 111–123, Jan. 2014. doi: 10.1109/TNNLS.2013.2257843
    J. N. Franklin, Matrix Theory. Mineola, New York: Courier Corporation, 2012.
    J. P. Hespanha, Linear Systems Theory. 2nd ed. Princeton, New Jersey: Princeton University Press, 2018.
    K. S. Narendra and A. M. Annaswamy. Stable Adaptive Systems. New Jersey, USA: Prentice-Hall, 1989.
    H. K. Khalil, Nonlinear Systems. 3rd ed. New Jersey, USA: Prentice-Hall, 2002.
    W. He, Y. Chen, and Z. Yin, “Adaptive neural network control of an uncertain robot with full-state constraints,” IEEE Trans. Cybern., vol. 46, no. 3, pp. 620–629, Mar. 2016. doi: 10.1109/TCYB.2015.2411285


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    • A novel learning-based intelligent PID control scheme is proposed
    • The uncertainties are accurately learned in neural PID closed-loop control
    • The learned knowledge can be reused to further improve control performance
    • The complexity of traditional PID parameters selection is weakened to some extent
    • Simulation and physical experiments verified the validity of the proposed method


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