Coprime Factor Reduction of Parameter Varying Controller

  • Saragih, Roberd (Industrial and Financial Mathematics Group, Faculty of Mathematics and Natural Science, Institut Teknologi Bandung) ;
  • Widowati, Widowati (Department of Mathematics, Diponegoro University)
  • Published : 2008.12.31


This paper presents an approach to order reduction of linear parameter varying controller for polytopic model. Feasible solutions which satisfy relevant linear matrix inequalities for constructing full-order parameter varying controller evaluated at each polytopic vertices are first found. Next, sufficient conditions are derived for the existence of a right coprime factorization of parameter varying controller. Furthermore, a singular perturbation approximation for time invariant systems is generalized to reduce full-order parameter varying controller via parameter varying right coprime factorization. This generalization is based on solutions of the parameter varying Lyapunov inequalities. The closed loop performance caused by using the reduced order controller is developed. To examine the performance of the reduced-order parameter varying controller, the proposed method is applied to reduce vibration of flexible structures having the transverse-torsional coupled vibration modes.


  1. P. Apkarian and R. J. Adam,"Advanced gain scheduling techniques for uncertain system," Proc. of the American Control Conference, Vol. 5,pp. 3331-3335,1997
  2. P. Apkarian and J. M. Biannie, "Self-scheduled $H\infty$ control of missile via linear matrix inequality," Journal of Guidance, Control and inequality," Journal of Guidance, Control and Dynamic, vol. 18, no. 3, pp. 532-538, 1995
  3. P. Apkarian, P. Gahinet and G. Becker, "Self-scheduled $H\infty$ control of linear parameter varying systems: A design example," Automatica, vol. 31, no. 9, pp. 1251-1261, 1995
  4. R. Bambang "Self-scheduled $H\infty$ control design for N250 aircraft dynamics based on polytopic LPV model," Proc. of the LASTED International Conference Control and Applications, Banff, Canada, pp. 52-57, 1999
  5. G. S. Becker, Quadratic Stability and Performance of Linear Parameter Varying Systems, Ph.D. Dissertation, University of California at Berkeley, 1993
  6. D. C. Oh, K. H. Bang and H. B. Park, "Controller order reduction using singular perturbation approximation," Automatica, vol. 33, no. 6, pp. 1203-1207, 1997
  7. H. M. H. El-Zobaidi and I. Jaimoukha, "Robust control and model and controller reduction of linear parameter varying systems," Proc. of the 37th IEEE Conference on Decision and Control, Tampa, Florida, USA, vol. 3, pp. 3015-3020, 1998
  8. R. Ravi, A. M. Pascoal and P. P. Khargonekar, "Normalized coprime factorizations for linear time varying systems," Systems and Control Letters, vol. 18, pp. 455-465, 1992
  9. R. Saragih and K. Yoshida, "Reduced-order controller of transverse-torsional coupled vibration based on linear matrix inequalities," Journal of Vibration and Control, vol. 5, pp. 907-923, 1999
  10. Widowati, R. Bambang, R. Saragih, and S. M. Nababan, "Model reduction for unstable LPV systems based on coprime factorizations and singular perturbation," Proc. of the 5th Asian Control Conference, Melbourne, Australia, pp. 692-699, 2004
  11. G. D. Wood, P. J. Goddard, and K. Glover, "Approximation of linear parameter-varying systems," Proc. of 35th IEEE Conference on Decision and Control, Kobe, vol. 4, pp. 406-411, 1996
  12. K. Zhou and J. Chen, "Performance bounds for coprime factor controller reductions," System and Control Letter, vol. 26, pp. 119-127, 1995
  13. K. Zhou, C. D'Souza, and J. R. Cloutier, "Structurally balanced controller order reduction with guaranteed closed loop performance," System and Control Letters, vol. 24, pp. 235-242, 1995