A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 9 Issue 1
Jan.  2022

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 6.171, Top 11% (SCI Q1)
    CiteScore: 11.2, Top 5% (Q1)
    Google Scholar h5-index: 51, TOP 8
Turn off MathJax
Article Contents
Xujun Lyu and Zongli Lin, "PID Control of Planar Nonlinear Uncertain Systems in the Presence of Actuator Saturation," IEEE/CAA J. Autom. Sinica, vol. 9, no. 1, pp. 90-98, Jan. 2022. doi: 10.1109/JAS.2021.1004281
Citation: Xujun Lyu and Zongli Lin, "PID Control of Planar Nonlinear Uncertain Systems in the Presence of Actuator Saturation," IEEE/CAA J. Autom. Sinica, vol. 9, no. 1, pp. 90-98, Jan. 2022. doi: 10.1109/JAS.2021.1004281

PID Control of Planar Nonlinear Uncertain Systems in the Presence of Actuator Saturation

doi: 10.1109/JAS.2021.1004281
Funds:  This work was supported in part by the Fundamental Research Funds for the Central Universities, China (2662018QD031) and the National Natural Science Foundation of China (51905205)
More Information
  • This paper investigates PID control design for a class of planar nonlinear uncertain systems in the presence of actuator saturation. Based on the bounds on the growth rates of the nonlinear uncertain function in the system model, the system is placed in a linear differential inclusion. Each vertex system of the linear differential inclusion is a linear system subject to actuator saturation. By placing the saturated PID control into a convex hull formed by the PID controller and an auxiliary linear feedback law, we establish conditions under which an ellipsoid is contractively invariant and hence is an estimate of the domain of attraction of the equilibrium point of the closed-loop system. The equilibrium point corresponds to the desired set point for the system output. Thus, the location of the equilibrium point and the size of the domain of attraction determine, respectively, the set point that the output can achieve and the range of initial conditions from which this set point can be reached. Based on these conditions, the feasible set points can be determined and the design of the PID control law that stabilizes the nonlinear uncertain system at a feasible set point with a large domain of attraction can then be formulated and solved as a constrained optimization problem with constraints in the form of linear matrix inequalities (LMIs). Application of the proposed design to a magnetic suspension system illustrates the design process and the performance of the resulting PID control law.

     

  • loading
  • [1]
    K. J. Åström and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers. Princeton, NJ: Princeton University Press, 2008.
    [2]
    K. J. Åström and T. Hägglund, “The future of PID control,” Control Eng. Pract., vol. 9, no. 11, pp. 1163–1175, Nov. 2001. doi: 10.1016/S0967-0661(01)00062-4
    [3]
    A. Behera, T. K. Panigrahi, P. K. Ray, and A. K. Sahoo, “A novel cascaded PID controller for automatic generation control analysis with renewable sources,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 6, pp. 1438–1451, Nov. 2019. doi: 10.1109/JAS.2019.1911666
    [4]
    H. B. Gu, P. Liu, J. H. Lu, and Z. L. Lin, “PID control for synchronization of complex dynamical networks with directed topologies,” IEEE Trans. Cybern., vol. 51, no. 3, pp. 1334–1346, Mar. 2021. doi: 10.1109/TCYB.2019.2902810
    [5]
    H. Y. Jin, J. C. Song, W. Y. Lan, and Z. Q. Gao, “On the characteristics of ADRC: A PID interpretation,” Sci. China Inf. Sci., vol. 63, no. 10, pp. 209201:1–209201:3, Apr. 2020. doi: 10.1007/s11432-018-9647-6
    [6]
    A. H. Khan, Z. L. Shao, S. Li, Q. X. Wang, and N. Guan, “Which is the best PID variant for pneumatic soft robots? An experimental study” IEEE/CAA J. Autom. Sinica, vol. 7, no. 2, pp. 451–460, Mar. 2020. doi: 10.1109/JAS.2020.1003045
    [7]
    S. K. Pradhan and B. Subudhi, “Position control of a flexible manipulator using a new nonlinear self-tuning PID controller,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 136–149, Jan. 2020.
    [8]
    J. J. Wang and T. Kumbasar, “Optimal PID control of spatial inverted pendulum with big bang-big crunch optimization,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 3, pp. 822–832, May 2020. doi: 10.1109/JAS.2018.7511267
    [9]
    X. Y. Yu, F. Yang, C. Zou, and L. L. Ou, “Stabilization parametric region of distributed PID controllers for general first-order multi-agent systems with time delay,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 6, pp. 1555–1564, Nov. 2020. doi: 10.1109/JAS.2019.1911627
    [10]
    S. Zhong, Y. Huang, and L. Guo, “A parameter formula connecting PID and ADRC,” Sci. China Inf. Sci., vol. 63, no. 9, pp. 192203:1–192203:3, Jul. 2020. doi: 10.1007/s11432-019-2712-7
    [11]
    C. Zhao and L. Guo, “PID controller design for second order nonlinear uncertain systems,” Sci. China Inf. Sci., vol. 60, no. 2, pp. 022201:1–022201:13, Jan. 2017. doi: 10.1007/s11432-016-0879-3
    [12]
    S. Yuan, C. Zhao, and L. Guo, “Uncoupled PID control of coupled multi-agent nonlinear uncertain systems,” J. Syst. Sci. Complex., vol. 31, no. 1, pp. 4–21, Feb. 2018. doi: 10.1007/s11424-018-7335-1
    [13]
    J. K. Zhang and L. Guo, “Theory and design of PID controller for nonlinear uncertain systems,” IEEE Control Syst. Lett., vol. 3, no. 3, pp. 643–648, Jul. 2019. doi: 10.1109/LCSYS.2019.2915306
    [14]
    C. Zhao and L. Guo, “Control of nonlinear uncertain systems by extended PID,” IEEE Trans. Autom. Control, vol. 66, no. 8, pp. 3840–3847, 2021.
    [15]
    L. Guo, “Feedback and uncertainty: Some basic problems and theorems,” in Proc. 58th IEEE Conf. Decision and Control, Nice, France, 2019.
    [16]
    D. S. Bernstein and A. N. Michel, “A chronological bibliography on saturating actuators,” Int. J. Robust Nonlinear Control, vol. 5, no. 5, pp. 375–380, Aug. 1995. doi: 10.1002/rnc.4590050502
    [17]
    T. S. Hu and Z. L. Lin, Control Systems With Actuator Saturation: Analysis and Design. Boston, MA: Birkhauser, 2001.
    [18]
    Z. L. Lin, “Control design in the presence of actuator saturation: From individual systems to multi-agent systems,” Sci. China Inf. Sci., vol. 62, no. 2, pp. 26201:1–26201:3, Feb. 2019. doi: 10.1007/s11432-018-9698-x
    [19]
    M. C. Obaiah and B. Subudhi, “A delay-dependent anti-windup compensator for wide-area power systems with time-varying delays and actuator saturation,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 106–117, Jan. 2020.
    [20]
    Z. L. Lin, M. Glauser, T. S. Hu, and P. E. Allaire, “Magnetically suspended balance beam with disturbances: A test rig for nonlinear output regulation,” in Proc. 43rd IEEE Conf. Decision and Control, Nassau, Bahamas, 2004, pp. 4577–4582.
    [21]
    J. Huang, Nonlinear Output Regulation: Theory and Applications. Philadelphia: SIAM, 2004.
    [22]
    S. Y. Yoon, P. Anantachaisilp, and Z. L. Lin, “An LMI approach to the control of exponentially unstable systems with input time delay,” in Proc. 52nd IEEE Conf. Decision and Control, Florence, Italy, 2013, pp. 312–317.

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(15)

    Article Metrics

    Article views (602) PDF downloads(72) Cited by()

    Highlights

    • PID control design for planar nonlinear uncertain systems with input saturation
    • Robustness with respect to uncertain nonlinearities
    • Maximization of the domain of attraction and output tracking capacity
    • LMI based design algorithm
    • Application to a test rig for magnetic suspension systems

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return