Pre-compensator selection for H loop shaping control

  • Sourav Patra
  • Sidhhartha Sen
  • Goshaidas RayEmail author
Regular Papers Control Applications


In this paper, an attempt has been made to address on the design of pre-compensator to obtain the solution of H loop-shaping control problem. Two different design techniques have been proposed where the first one is based on singular value decomposition (SVD) technique along with the matrix perturbation approach; the other one is focused in linear matrix inequality (LMI) framework leading to minimize the condition number of the pre-compensator that, in turn, reduces loop deterioration. A numerical example has been considered to illustrate the effectiveness of the proposed method.


Condition number H loop shaping control linear matrix inequality pre-compensator singular value decomposition 


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  1. [1]
    D. McFarlane and K. Glover, “A loop shaping design procedure using H synthesis,” IEEE Trans. on Automatic Control, vol. 37, no. 6, pp. 759–769, 1992.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    S. Skogestad and I. Postlethwaith, Multivariable Feedback Control: Analysis and Design, Second edition, John Wiley and Sons, Ltd, 2005.Google Scholar
  3. [3]
    K. H. Bang and H. B. Park, Analysis of Robust Performance Improvement Using Loop Shaping and Structured Singular Value, SICE, Tottori, pp. 1269–1274, July 1996.Google Scholar
  4. [4]
    R. A. Hyde, The Application of Robust Control to VSTOL Aircraft, Ph.D. Thesis, Girton College, Cambridge, 1991.Google Scholar
  5. [5]
    A. Lanzon, “Weight optimization in H loop shaping,” Automatica, vol. 41, pp. 1201–1208, 2005.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    K. L. Lo and L. Khan, “Hierarchical micro-genetic algorithm paradigm for automatic weight selection in H loop shaping robust flexible AC transmission system damping control design,” IEE Proceedings Generation, Transmission and Distribution, vol. 151, no. 1, pp. 109–118, 2004.CrossRefGoogle Scholar
  7. [7]
    G. Papegeorgiou and K. Glover, “A systematic procedure for designing non-diagonal weights to facilitate H loop shaping,” Proc. of the 36th conference on Decision and Control, pp. 2127–2132, December 1997.Google Scholar
  8. [8]
    J. F. Whidbrone, I. Postlethwaith, and D. W. Gu, “Robust controller design using H loop shaping and method of inequalities,” IEEE Trans. on Control System Technology, vol. 2, no. 4, pp. 455–461, 1994.CrossRefGoogle Scholar
  9. [9]
    A. Nobakhti and N. Munro, “A new method for singular value loop shaping in design of Multiplechannel controllers,” IEEE Trans. on Automatic Control, vol. 49, no. 2, pp. 249–253, 2004.CrossRefMathSciNetGoogle Scholar
  10. [10]
    W. Reinelt, “Robust control of a two-mass-spring system subject to its input constraints,” Proc. of the American Control Conference, pp. 1817–1921, June 2000.Google Scholar
  11. [11]
    O. Agamemnoni, J. L. Figueroa, A. C. Desages, A. Palazoglu, and J. A. Romagnoli, “A loop shaping technique for feedback control design,” Computers and Chemical Engineering, vol. 20, no. 1, pp. 27–37, 1996.CrossRefGoogle Scholar
  12. [12]
    H. C. Choi, D. Chwa, and S. K. Hong, “An LMI approach to robust reduced-order H filter design for polytopic uncertain systems,” Int. Journal of Control, Automation, and Systems, vol. 7, no. 3, pp. 487–494, 2009.CrossRefGoogle Scholar
  13. [13]
    S. Boyd, E. Feron, L. E. Ghaoui, and V. Balakrishnan, Linear Matrix Inequalities In System And Control Theory, SIAM Frontier Series, 1994.Google Scholar
  14. [14]
    R. Braatz and M. Morari, “Minimizing the Euclidean condition number,” SIAM J. Control and Optimization, vol. 32, no. 6, pp. 1763–1768, 1994.zbMATHCrossRefMathSciNetGoogle Scholar
  15. [15]
    M. Morari and E. Zafiriou, Robust Process Control, Prentice Hall, Englewood Cliffs, NJ, 1989.Google Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of AvionicsIndian Institute of Space Science and TechnologyTrivandrumIndia
  2. 2.Department of Electrical EngineeringIndian Institute of TechnologyKharagpurIndia

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