On the Subsystem Level Gain Scheduled Controller Design for MIMO Systems

  • Vojtech Veselý
Regular Paper Control Theory and Applications


This paper presents a unique approach to design in the frequency domain a gain scheduled controller (GSC) to nonlinear Lipschitz MIMO system model. The proposed design procedure is based on the Method of Equivalent subsystems and Integral Quadratic Constraints-Small Gain Theory. The feasible design procedures provide a subsystem equivalent frequency characteristic and frequency design method to obtain design procedure for GSC design. The obtained design results and their properties are illustrated in the simultaneously design of controllers for nonlinear turbogenerator model (6-order). The results of the obtained design procedure are a PI automatic gain scheduled voltage regulator (AVR) for synchronous generator, and a PI governor gain scheduled controller.


Frequency domain gain scheduled controller integral quadratic constraints method of equivalent subsystems small gain theorem 


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  1. [1]
    A. Kozakova, V. Vesely, and J. Osusky, “A new Nyquist based technique for tuning robust decentralized controllers,” Kybernetika, vol. 45, no. 1, pp. 63–83, 2009.MathSciNetzbMATHGoogle Scholar
  2. [2]
    T. Lahdhiri and A. T. Alouani, “Nonlinear excitation control of a synchronous generator with implicit terminal voltage regulation,” Electric Power System Research, vol. 36, 101–112, 1996.CrossRefGoogle Scholar
  3. [3]
    S. A. Pavlushko, “Automatic excitation control of synchronous generators as an effective means to ensure the reliable parallel operation of generation equipment and the united power system as a whole,” Power Technology and Engineering, vol. 46, no. 5, pp. 399–406, 2013.CrossRefGoogle Scholar
  4. [4]
    J. Alveraz-Ramirez, I. Cervantes, R. Escarela-Perez, and G. Espriasa-Perez, “A two-loop excitation control system for synchronnous generators,” Electrical Power and Energy Systems, vol. 27, pp. 556–566, 2005. [click]CrossRefGoogle Scholar
  5. [5]
    V. Veselý and A. Kozáková, Robust PSS Design for a Multivariable Power System, Power Tech Russia, 2004.zbMATHGoogle Scholar
  6. [6]
    P. Zhao, W. Yao, J. Wen, L. Jiang, S. Wang, and S. Cheng, “Improved synergetic excitation control for transient stability enhancement and voltage regulation of power systems,” Electrical Power and Energy Systems, vol. 68, pp. 44–51, 2015.CrossRefGoogle Scholar
  7. [7]
    V. A. Venikov, a. Transient Electromechanical Processes in Electric Power Systems, Vyssaja Skola, Moscow (in Russian), 1985. b.) Transient Processes In Electrical Power Systems, Mir, Moscow, 1978.Google Scholar
  8. [8]
    P. Kundur, Power System Stability and Control, McGraw-Hill Inc., New York, 1994.Google Scholar
  9. [9]
    J. Machovski, J.W. Bialek, and J. R. Bumby, Power System Dynamic. Stability and Control, JohnWiley and Sons, Ltd, 2008.Google Scholar
  10. [10]
    C.-C. Ku and G.-W. Chen, “Gain-scheduled controller design for discrete-time linear parameter varying systems with multiplicative noises,” Inter. Journal of Control, Automation, and Systems, vol. 13, no. 6, pp. 1382–1390, 2016. [click]CrossRefGoogle Scholar
  11. [11]
    M. Sato and D. Peaucelle, “Gain-scheduled outputfeedback controllers using inexact scheduling parameters for continuous-time LPV systems,” Automatica, vol. 49, no. 4, pp. 1019–1025, April 2013. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    C. W. Scherer, “Gain scheduling control with dynamic multipliers by convex optimization,” SIAM Journal on Control and Optimization, vol. 53, no. 3, pp. 1224–1249, 2015. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    V. Veselý and A. Ilka, “Gain-scheduled PID controller design,” Journal of Process Control, vol. 23, no. 8, pp. 1141–1148, September 2013.CrossRefGoogle Scholar
  14. [14]
    V. F. Montagner and P. L. D. Peres, “State feedback gain scheduling for linear systems with time-varying parameters,” Proceedings of the American Control Conference, vol. 3, pp. 2004–2009, 2004.Google Scholar
  15. [15]
    M. Benbrahim, M. Nabil Kabbaj, and K. Benjelloun, “Robust control under constraints of linear systems with Markovian jumps,” Inter. Journal of Control, Automation and Systems, vol. 14, no. 6, pp. 1447–1454, 2016. [click]CrossRefGoogle Scholar
  16. [16]
    K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control, Prentice Hall, New Jersey, 1996.zbMATHGoogle Scholar
  17. [17]
    V. Vesely and A. Ilka, “Design of robust gain-scheduled PIcontrollers,” Journal of Franklin Institute, vol. 352, pp. 1476–1494, 2015.MathSciNetCrossRefGoogle Scholar
  18. [18]
    V. Vesely and A. Ilka, “Novel approach to switched controller design for linear continuous-time systems,” Asian Journal of Control, vol. 18, no. 4, pp. 1365–1375, 2016. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    A. White, G. Zhu, and J. Choi, “Optimal LPV control with hard constraints,” Inter. J. of Control, Aut. and Systems, vol. 14, no. 1, pp. 148–162, 2016. [click]CrossRefGoogle Scholar
  20. [20]
    V. Vesely and J. Osusky, “Robust gain scheduled control design in frequency domain,” IREACO, vol. 7, no. 5, pp. 476–481, 2014.CrossRefGoogle Scholar
  21. [21]
    P. Apkarian, P. Gahinet, and G. Becker, “Self-scheduled H control of linear parameter-varying systems: a design example,” Automatica, vol. 31, no. 9, pp. 1251–1261, 1995.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    A. M. Howlader, H. Matayoshi, and T. Senjyu, “A robust Hinf controller based gain-scheduled approach for the power smoothing of wind turbine generator with a battery energy storage system,” Electric Power Components and Systems, vol. 43, no. 19, pp. 1–12, 2015.CrossRefGoogle Scholar
  23. [23]
    V. Vesely, J. Osusky, and I. Sekaj, “Gain scheduled controller design for thermo-optical plant,” Archives of Control Science, vol. 24, no. 3, pp. 333–349, 2014. [click]zbMATHGoogle Scholar
  24. [24]
    W. J. Rugh and J. S. Shamma, “Survey research on gain scheduling,” Automatica, vol. 36, no. 10, pp. 1401–1425, Oct. 2000. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    G. Wei, Z. Wang, W. Li, and L. Ma, “A survey on gain-scheduled control and filtering for parameter-varying systems,” Discrete Dynamics in Nature and Society, ID105815, Hindawi Publishing Corporation, 2014.Google Scholar
  26. [26]
    D. J. Leith and W. E. Leithead, “Survey of gainscheduling analysis and design,” International Journal of Control, vol. 73, no. 11, pp. 1001–1025, 2000. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    Q. Zhou, D. Yao, J. Wang, and C. Wui, “Robust control of uncertain semi-Markovian jump systems using sliding mode control method,” Applied Mathematics and Computation, vol. 286, pp. 72–87, 2016. [click]MathSciNetCrossRefGoogle Scholar
  28. [28]
    A. A. Megretski and A. Rantzer, “System analysis via integral quadratic constraints,” IEEE Trans. on Automatic Control, vol. 42, no. 6, pp. 819–830, 1997.MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    S. Skogestad and I. Postletwaite, Multivariable Feedback Control Analysis and Design, John Wiley and Sons, 1996.Google Scholar
  30. [30]
    U. Jonsson, Lecture Notes on Integral Quadratic Constraints. Optimization and Systems Theory, Department of Mathematics Royal Institite of Technology, SE-10044 Stockholm, Sweden, ISSN 1401-2294, 2001.Google Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Slovak University of TechnologyFaculty of El. Eng. and Info. Tech. Institute of Robotics and Cybernetics BratislavaBratislavaSlovakia

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