Bilinear Control

  • Ming Rao
  • Qijun Xia
  • Yiqun Ying
Part of the Advances in Industrial Control book series (AIC)


In this chapter, the bilinear control strategy for paper machines is discussed based on the characteristics of paper-making process. The bilinear decoupling control, bilinear observer and bilinear optimal control as the typical techniques are discussed. Their applications to the headbox section and drying section of a paper machine, axe presented. Digital simulation and on-site implementation results show that the performance of the bilinear control system is satisfactory.


Optimal Control Problem State Feedback Bilinear System Paper Machine Suboptimal Control 
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  1. Banks S.P. and Yew M.K. On the optimal control of bilinear systems and its relation to Lie algebras. Int. J. Control 1986; 43(:891–900CrossRefGoogle Scholar
  2. Bruni C., Dipillo G. and Koch G. Bilinear systems: an appealing class of “nearly linear” systems in theory and applications. IEEE Tans. Autom. Contr. 1974; AC-19:334–348CrossRefGoogle Scholar
  3. Derese I. and Noldus E. Optimization of bilinear control systems. Int. J. Systems Sci. 1982; 13: 237–246CrossRefGoogle Scholar
  4. Derese I., Stevens P. and Noldus E. Observers for bilinear systems with bounded input. Int. J. Systems Science 1979; 10 (6): 649–668CrossRefGoogle Scholar
  5. Freund E. The structure of decoupled nonlinear system. Int. J. Control 1975; 21: 443–450CrossRefGoogle Scholar
  6. Freund E. Decoupling and pole assignment in nonlinear systems. Electronics Letters 1973; 9: 373–375CrossRefGoogle Scholar
  7. Funahashi Y. A class of state observers for bilinear systems. Int. J. Systems Sci. 1978; 9: 1199–1205CrossRefGoogle Scholar
  8. Hara S. and Furuta K. Minimal order state observers for bilinear systems. Int. J. Control 1976; 24: 705–718CrossRefGoogle Scholar
  9. Hsu C.S. and Karanam V.R. Observer design of bilinear systems. J. of Dyn. Syst. Meas. and Contr. 1983; 105: 206–208CrossRefGoogle Scholar
  10. Isidori A. Nonlinear Control Systems: An Introduction. Springer-Verlag, New York, 1985CrossRefGoogle Scholar
  11. Isidor A., Krener A.J., Gori Giorgi C. and Monaco S. Nonlinear decoupling via feedback: A differential geometric approach. IEEE Trans. Autom. Contr. 1981; AC-26:331–345Google Scholar
  12. Jacobson D.H. Extension of linear-quadratic control optimization and matrix theory. Academic Press, San Francisco, 1977Google Scholar
  13. Li C.W. and Feng Y.K. Decoupling theory of general multivariable analytic non-linear systems. Int. J. Control 1987; 45: 1147–1160CrossRefGoogle Scholar
  14. Maghsoodi Y. Design and computation of near-optimal stable observers for bilinear systems. IEEE Proceedings 1989; 136: 127–132Google Scholar
  15. Mohler R.R. Bilinear Control Processes. Academic Press New York and London, 1973Google Scholar
  16. Mohler R.R. and Kolodziej W.J. An overview of bilinear system theory and applications. IEEE Trans. Syst. Man and Cyb. 1980; 10: 683–689CrossRefGoogle Scholar
  17. Mohler R.R. Nonlinear system - Applications to bilinear control. Prentice Hall, Englewood Cliffs, 1991Google Scholar
  18. Nazar S. and Rekasius Z.V. Decoupling of a class of nonlinear system. IEEE Trans. Autom. Contr. 1971; AC-16:257–260Google Scholar
  19. Nijmeijer H. and Van der Schaft A.J. Nonlinear dynamical control systems. Springer-Verlag, New York, 1990Google Scholar
  20. Rao R., Ying Y. and Corbin J. Intelligent engineering approach to pulp and paper process control. Proceeding of CPPA, Montreal, Canada, 1991, pp A195–A199Google Scholar
  21. Ryan E.P. Optimal feedback control of bilinear systems. J. of Optimization Theory and Applications 1984; 44: 333–362CrossRefGoogle Scholar
  22. Sinha P.K. State feedback decoupling of nonlinear system. IEEE Trans. Autom. Contr. 1977; AC-22:487–489Google Scholar
  23. Sinha P.K. Multivariable control - An introduction. Marcel Dekker Inc., New York and Basel, 1984Google Scholar
  24. Tzafestas S.G., Angnostou K.E. and Pimenides T.G. Stabilizing optimal control of bilinear system with a generalized cost. Optimal Control Appl. and Methods 1984; 5: 111–117CrossRefGoogle Scholar
  25. Ying Y., Rao M. and Sun Y. State-disturbance composite observer for bilinear systems. Proc. of American Control Conference, San Diego, CA, 1990, pp 1917–20Google Scholar
  26. Ying Y., Rao M. and Sun Y. Bilinear control strategy for paper-making process. Chemical Engineering Communications 1992; VIII: 13–28CrossRefGoogle Scholar
  27. Ying Y., Rao M. and Sun Y. Bilinear state-disturbance composite observer and its application. Int. J. Systems Sci. 1991; 22: 2489–2498CrossRefGoogle Scholar
  28. Ying Y., Rao M. and Sun Y. A new design method for bilinear suboptimal systems. Proc of American Control Conference, Boston, Massachusetts, 1991, pp 1820–1822Google Scholar

Copyright information

© Springer-Verlag London Limited 1994

Authors and Affiliations

  • Ming Rao
    • 1
  • Qijun Xia
    • 1
  • Yiqun Ying
    • 1
  1. 1.Department of Chemical EngineeringUniversity of AlbertaEdmontonCanada

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