International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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Adaptive Predictive Control using Multiple Models, Switching and Tuning

  • Giovanini Leonardo (Industrial Control Centre, University of Strathclyde) ;
  • Ordys Andrzej W. (Kingston University) ;
  • Grimble Michael J. (Industrial Control Centre, University of Strathclyde)
  • Published : 2006.12.30
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Abstract

In this work, a new method of design adaptive controllers for SISO systems based on multiple models and switching is presented. The controller selects the model from a given set, according to a switching rule based on output prediction errors. The goal is to design, at each sample instant, a predictive control law that ensures the robust stability of the closed-loop system and achieves the best performance for the current operating point. At each sample the proposed control scheme identifies a set of linear models that best characterizes the dynamics of the current operating region. Then, it carries out an automatic reconfiguration of the controller to achieve the best possible performance whilst providing a guarantee of robust closed-loop stability. The results are illustrated by simulations a nonlinear continuous and stirred tank reactor.

Keywords

References

  1. M. Morari and J. Lee, 'Model predictive control: Past, present and future,' Computers and Chemical Engineering, vol. 23, no. 9, pp. 667-682, 1999 https://doi.org/10.1016/S0098-1354(98)00301-9
  2. J. Lee and Z. Yu, 'Worst-case formulation of model predictive control for system with bounded parameters,' Automatica, vol. 33, no. 5, pp. 763-781, 1997 https://doi.org/10.1016/S0005-1098(96)00255-5
  3. D. Wang and J. Romagnoli, 'Robust model predictive control design using a generalized objective functions,' Computers and Chemical Engineering, vol. 27, no. 10, pp. 965-982, 2003 https://doi.org/10.1016/S0098-1354(03)00007-3
  4. T. Badgwell, 'Robust model predictive control of stable linear systems,' International Journal of Control, vol. 68, pp. 797-818, 1997 https://doi.org/10.1080/002071797223343
  5. L. Giovanini and M Grimble, 'Robust predictive feedback control for constrained systems,' International Journal of Control and Systems, vol. 2, no. 4, pp. 407-422, 2004
  6. H. Su and T. Me Avoy, 'Artificial neural networks for nonlinear process identification and control,' in M. Henson and D Seborg (Eds.), Nonlinear Process Control (chapter 7), pp. 371428, Prentice-Hall, Englewood Cliffs, 1997
  7. J. Roubos, S. Mollov, R. Babuska, and H. Verbruggen, 'Fuzzy model-based predictive control using Takagi-Sugeno models,' International Journal of Approximate Reasoning, vol. 22, no. 1, pp. 3-30, 1999 https://doi.org/10.1016/S0888-613X(99)00020-1
  8. K. Fruzzetti, A. Palazoglu, and K. Mac Donald, 'Nonlinear model predictive control using Hammerstein models,' Journal of Process Control, vol. 7, no. 1, pp. 31-41, 1997 https://doi.org/10.1016/S0959-1524(97)80001-B
  9. A. Lusson Cervantes, O. Agamennoni, and J. Figueroa, 'A nonlinear model predictive control system based on Weiner piecewise linear models,' Journal of Process Control, vol. 13, no. 5,pp.655-666,2003 https://doi.org/10.1016/S0959-1524(02)00121-X
  10. J. Norquay, A. Palazoglu, and J. Romagnoli, 'Model predictive control based on Weiner models,' Chemical Engineering Science, vol. 53, pp. 75-84, 1998 https://doi.org/10.1016/S0009-2509(97)00195-4
  11. H. Genceli and M. Nikolaou, 'Design of robust constrained model predictive controllers with Volterra series,' AIChE J, vol. 41, no. 10, pp. 2098-2107, 1995 https://doi.org/10.1002/aic.690410909
  12. N. de Oliveira and L. Biegler, 'An extension of Newton type algorithms for nonlinear process control,' Automatica, vol. 31, no. 2, pp. 281-286, 1995 https://doi.org/10.1016/0005-1098(94)00086-X
  13. J. Momingred, B. Paden, D. Seborg, and D. Mellichamp, 'An adaptive nonlinear predictive controller,' Chem. Eng. Sci., vol. 47, no. 4, pp. 755-765, 1992 https://doi.org/10.1016/0009-2509(92)80266-F
  14. B. Aufderheide and B. Bequette, 'Extension of dynamic matrix control to multiple models,' Computers and Chemical Engineering, vol. 27, no. 11, pp. 1079-1096, 2003 https://doi.org/10.1016/S0098-1354(03)00038-3
  15. K. Narendra and J Balakrishnan, 'Improvement transient response of adaptive control systems using multiple models and switching,' IEEE Trans. on Automatic Control, vol. 39, no. 9, pp. 1861-1866, 1994 https://doi.org/10.1109/9.317113
  16. B. Anderson, T. Brinsmead, F. de Bruyne, J. Hespanha, D. Liberzon, and S. Morse, 'Multiple model adaptive control I: Finite controller coverings,' International Journal of Robust and Nonlinear Control, vol. 10, no. 9, pp. 909-929, 2000 https://doi.org/10.1002/1099-1239(200009/10)10:11/12<909::AID-RNC532>3.0.CO;2-Z
  17. S. Morse, 'Supervisory control of families of linear set-point controllers-Part 1: Exact matching,' IEEE Trans. on Automatic Control, vol. 41, no. 8, pp. 1413-1431,1996 https://doi.org/10.1109/9.539424
  18. K. Narendra and J Balakrishnan, 'Adaptive control using multiple models,' IEEE Trans. on Automatic Control, vol. 42, no. 2, pp. 171-187, 1997 https://doi.org/10.1109/9.554398
  19. L. Giovanini, 'Predictive feedback control,' ISA Transaction Journal, vol. 42, no. 2, pp. 207-226, 2003 https://doi.org/10.1016/S0019-0578(07)60127-X
  20. K. Dabke, 'A simple criterion for stability of linear discrete systems,' International Journal of Control, vol. 37, pp. 657-659, 1983 https://doi.org/10.1080/00207178308933000
  21. C. Desoer and M. Vidyasagar, Feedback System: Input-Output Properties, Academic Press, 1975
  22. B. Polyak and M. Halpern, 'Optimal design for discrete-time linear systems via new performance index,' Adaptive Control and Signal Processing, vol. 15, no. 2, pp. 153-168, 2001 https://doi.org/10.1002/acs.648
  23. F. Bianchini and M. Snaizer, 'A convex optimization approach for fixed-order controller design for disturbance rejection in SISO systems,' IEEE Trans. on Automatic Control, vol. 45, pp. 784-789,2000 https://doi.org/10.1109/9.847123
  24. B. Polyak and P. Scherbakov, 'Superstable Linear Control Systems I: Analysis,' Autom. and Remote Control, vol. 63, no. 8, pp. 1-16,2002 https://doi.org/10.1023/A:1013700816650
  25. J. Adamy and A. Flemming, 'Soft variablestructure controls: A survey,' Automatica, vol. 40, no. 11, pp. 1821-1844, 2004 https://doi.org/10.1016/j.automatica.2004.05.017
  26. V. Utkin, Sliding Modes in Control and Optimization, Springer-Verlag, 1992
  27. E. Gilbert, and I. Kolmanovsky, 'Maximal output admissible sets for discrete-time systems with disturbance inputs,' Proc. of the American Contr. Conf, pp. 2000-2005, 1995
  28. G. Angelis, System Analysis, Modelling and Control with Poly topic Linear Models, Ph.D. Thesis, University of Eindhoven, 2001
  29. M. Campi, J. Hespanha, and M. Prandini, 'Cautious hierarchical switching control of stochastic linear systems,' International Journal of Adaptive Control and Signal Processing, vol. 18, no. 4,pp. 319-333,2004 https://doi.org/10.1002/acs.797
  30. W. Zhuang, 'RLS algorithm with variable forgetting factor for decision feedback equalizer over time-variant fading channels,' Wireless Personal Communications, vol. 8, no. 1, pp. 1529, 1998
  31. A. Rantzer and M. Johansson, 'Piecewise linear quadratic optimal control,' IEEE Trans. on Automatic Control, vol. 45, no. 4, pp. 629-637, 2000 https://doi.org/10.1109/9.847100
  32. M. Johanson and A. Rantzer, 'Computation of piecewise quadratic Lyapunov function for hybrid system,' IEEE Trans. on Automatic Control, vol. 43, no. 4, pp. 555-559, 1998 https://doi.org/10.1109/9.664157