A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Advanced Search
Volume 2 Issue 4
Oct.  2015

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 15.3, Top 1 (SCI Q1)
    CiteScore: 23.5, Top 2% (Q1)
    Google Scholar h5-index: 77， TOP 5
Turn off MathJax
Article Contents
Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2015  >  2(4): 358-365
Naizhou Wang, Hailong Pei and Yong Tang, "Anti-windup-based Dynamic Controller Synthesis for Lipschitz Systems under Actuator Saturation," IEEE/CAA J. of Autom. Sinica, vol. 2, no. 4, pp. 358-365, 2015.
Citation: Naizhou Wang, Hailong Pei and Yong Tang, "Anti-windup-based Dynamic Controller Synthesis for Lipschitz Systems under Actuator Saturation," IEEE/CAA J. of Autom. Sinica, vol. 2, no. 4, pp. 358-365, 2015.
shu

Anti-windup-based Dynamic Controller Synthesis for Lipschitz Systems under Actuator Saturation

  • 1. the Key Laboratory of Autonomous Systems and Networked Control, Ministry of Education, South China University of Technology, Guangzhou 510640, China, and Key Laboratory of Surface Functional Structure Manufacturing of Guangdong Higher Education Institutes, School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510640, China;

  • 2. the Key Laboratory of Autonomous Systems and Networked Control, Ministry of Education, South China University of Technology, Guangzhou 510640, China;

  • 3. the Key Laboratory of Surface Functional Structure Manufacturing of Guangdong Higher Education Institutes, School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510640, China

Funds:

This work was supported by National Natural Science Foundation of China (61174053), National Key Basic Research Program of China (2014CB845301/2/3), Fundamental Research Funds for the Central Universities (2014ZP0021), Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China (708069), partially by Key Laboratory of Autonomous Systems and Networked Control, Ministry of Education, and Key Laboratory of Surface Functional Structure Manufacturing of Guangdong Higher Education Institutes.

    Abstract
  • This paper presents a new method for simultaneous synthesis of dynamic controller and static anti-windup compensator for saturated Lipschitz systems. Thanks to the reformulated Lipschitz property, the Lipschitz systems can be transformed into LPV (linear parameter-varying) systems whose system matrices are affine in a parameter matrix. Based on the modified sector condition dealing with saturation nonlinearity, the design of a nonlinear anti-windup-based controller leads to the solvability of a set of bilinear matrix inequalities (BMI) on the vertices of a bounded convex set which can be solved by the so-called iterative linear matrix inequality (ILMI) algorithm. A numerical example is presented to illustrate the effectiveness of the proposed method.

     

    • FullText(HTML)
  • loading
    • References(32)
  • [1]
    Tarbouriech S, Turner M C. Anti-windup design: an overview of some recent advances and open problems. IET Control Theory and Applications, 2009, 3(1): 1-19
    [2]
    Teel A R, Kapoor N. The L2 anti-windup problem: its definition and solution. In: Proceedings of the 1997 European Control Conference. Brussels, Belgium: IEEE, 1997. 1897-1902
    [3]
    Grimm G, Hatfield J, Postlethwaite I, Teel A R, Turner M C, Zaccarian L. Antiwindup for stable linear systems with input saturation: an LMIbased synthesis. IEEE Transactions on Automatic Control, 2003, 48(9): 1509-1525
    [4]
    Gomes da Silva Jr J M, Tarbouriech S. Antiwindup design with guaranteed regions of stability: an LMI-based approach. IEEE Transactions on Automatic Control, 2005, 50(1): 106-111
    [5]
    Wu F, Soto M. Extended anti-windup control schemes for LTI and LFT systems with actuator saturations. International Journal of Robust and Nonlinear Control, 2004, 14(15): 1255-1281
    [6]
    Turner M C, Herrmann G, Postlethwaite I. Incorporating robustness requirements into antiwindup design. IEEE Transactions on Automatic Control, 2007, 52(10): 1842-1855
    [7]
    Hu T S, Teel A R, Zaccarian L. Stability and performance for saturated systems via quadratic and nonquadratic Lyapunov functions. IEEE Transactions on Automatic Control, 2006, 51(11): 1770-1786
    [8]
    Dai D, Hu T S, Teel A R, Zaccarian L. Output feedback design for saturated linear plants using deadzone loops. Automatica, 2009, 45(12): 2917-2924
    [9]
    Mulder E F, Tiwari P Y, Kothare M V. Simultaneous linear and antiwindup controller synthesis using multiobjective convex optimization. Automatica, 2009, 45(3): 805-811
    [10]
    Wu F, Grigoriadis K M, Packard A. Anti-windup controller design using linear parameter-varying control methods. International Journal of Control, 2000, 73(12): 1104-1114
    [11]
    Prempain E, Turner M C, Postlethwaite I. Coprime factor based antiwindup synthesis for parameter-dependent systems. Systems and Control Letters, 2009, 58(12): 810-817
    [12]
    Kahveci N E, Ioanou P A, Mirmirani M D. A robust adaptive control design for gliders subject to actuator saturation nonlinearities. In: Proceedings of the 2007 American Control Conference. New York: IEEE, 2007. 492-497
    [13]
    Gomes da Silva Jr J M, Oliveira M Z, Coutinho D, Tarbouriech S. Static anti-windup design for a class of nonlinear systems. International Journal of Robust and Nonlinear Control, 2014, 24(5): 793-810
    [14]
    Wang N Z, Pei H L, Wang J, Zhang Q. Anti-windup design for rational systems by linear-fractional representation. IET Control Theory and Applications, 2014, 8(5): 355-366
    [15]
    Teel A R, Kapoor N. Uniting local and global controllers. In: Proceedings of the 4th European Control Conference. Brussels, Belgium, 1997.
    [16]
    Morabito F, Teel A R, Zaccarian L. Nonlinear antiwindup applied to Euler-Lagrange systems. IEEE Transactions on Robotics and Automation, 2004, 20(3): 526-537
    [17]
    Rehan M, Hong K S. Decoupled-architecture-based nonlinear antiwindup design for a class of nonlinear systems. Nonlinear Dynamics, 2013, 73(3): 1955-1967
    [18]
    Herrmann G, Menon P P, Turner M C, Bates D G, Postlethwaite I. Anti-windup synthesis for nonlinear dynamic inversion control schemes. International Journal of Robust and Nonlinear Control, 2010, 20(13): 1465-1482
    [19]
    Zames G, Falb P L. Stability conditions for systems with monotone and slope restricted nonlinearities. SIAM Journal on Control, 1968, 6(1): 89 -108
    [20]
    Khalil H K. Nonlinear Systems (2nd edition). U. K.: Prentice Hall, 1996.
    [21]
    Gao J F, Su H Y, Ji X F, Chu J. Stability analysis for a class of neutral systems with mixed delays and sector-bounded nonlinearity. Nonlinear Analysis: Real World Applications, 2008, 9(5): 2350-2360
    [22]
    Phanomchoeng G, Rajamani R, Piyabongkarn D. Nonlinear observer for bounded Jacobian systems, with applications to automotive slip angle estimation. IEEE Transactions on Automatic Control, 2011, 56(5): 1163 -1170
    [23]
    Turner M C, Kerr L M. L2 gain bounds for systems with sector bounded and slope-restricted nonlinearities. International Journal of Robust and Nonlinear Control, 2012, 22(13): 1505-1521
    [24]
    Zemouche A, Boutayeb M. On LMI conditions to design observers for Lipschitz nonlinear systems. Automatica, 2013, 49(2): 585-591
    [25]
    Gomes da Silva Jr J M, Castelan E B, Corso J, Eckhard D. Dynamic output feedback stabilization for systems with sector-bounded nonlinearities and saturating actuators. Journal of the Franklin Institute, 2013, 350(3): 464-484
    [26]
    Rehan M, Khan A Q, Abid M, Iqbal N, Hussain B. Anti-windupbased dynamic controller synthesis for nonlinear systems under input saturation. Applied Mathematics and Computation, 2013, 220: 382-393
    [27]
    Peaucelle D, Arzelier D. An efficient numerical solution for H2 static output feedback synthesis. In: Proceedings of the 2001 European Control Conference. Porto Portugal: IEEE, 2001. 3800-3805
    [28]
    Castelan E B, Tarbouriech S, Queinnec I. Stability and stabilization of a class of nonlinear systems with saturating actuators. In: Proceedings of the 16th IFAC World Congress. Check Republic: IFAC, 2005. 776-782
    [29]
    Bender F A, Gomes da Silva Jr J M, Tarbouriech S. Convex framework for the design of dynamic anti-windup for state-delayed systems. IET Control Theory and Applications, 2011, 5(12): 1388-1396
    [30]
    Scherer G, Gahinet P, Chilali M. Multiobjective output-feedback control via LMI optimization. IEEE Transactions on Automatic Control, 1997, 42(7): 896-911
    [31]
    Boyd S, El Ghaoui L, Feron E, Balakrishnan V. Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.
    [32]
    Chilali M, Gahinet P. H∞ design with pole placement constraints: an LMI approach. IEEE Transactions on Automatic Control, 1996, 41(3): 358-367
    • Related Articles
    • Supplements(0)

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
    Get Citation
    PDF
    XML

    Article Metrics

    Article views (1107) PDF downloads(14) Cited by()

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return