Antiwindup for Stable Linear Systems with Input Saturation: An LMI-Based Synthesis

IEEE Transactions on Automatic Control

Volumn 48, Issue 9, 2003, Pages 1509-1525

  Grimm, Gene ^a   Hatfield, Jay ^b   Postlethwaite, Ian ^c   Teel, Andrew R ^d   Turner, Matthew C ^c   Zaccarian, Luca ^e  

^a RAYTHEON COMPANY   (United States)

^b General Dynamics Land Systems   (United States)

^c UNIVERSITY OF LEICESTER   (United Kingdom)

^d University of California at Santa Barbara   (United States)

^e UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

Antiwindup analysis; Antiwindup synthesis; Control systems; Cost optimal control; Finite 2 gain; Linear matrix inequalities (LMIs); Linear parameter varying (LPV)

Indexed keywords

LYAPUNOV METHODS; MATRIX ALGEBRA; OPTIMAL CONTROL SYSTEMS; SYSTEM STABILITY;

ANTIWINDUP ANALYSIS;

LINEAR CONTROL SYSTEMS;

EID: 0141862127     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2003.816965     Document Type: Article

References (33)

1. ∞ controllers," IEEE Trans. Automat. Contr., vol. 40, pp. 853-864, May 1995.
2. K. J. Åström and L. Rundqwist, "Integrator windup and how to avoid it," in Proc. Amer. Control Conf., vol. 2, Pittsburgh, PA, June 1989, pp. 1693-1698.
3. G. Becker, A. Packard, D. Philbrick, and G. Balas, "Control of parametrically-dependent linear systems: A single quadratic Lyapunov approach," in Proc. Amer. Control Conf, vol. 3, San Francisco, CA, June 1993, pp. 2795-2799.
4. S. Boyd, L. El. Ghaoui, E. Feron, and V. Balakrishnan", Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.
5. P. J. Campo, M. Morari, and C. N. Nett, "Multivariable antiwindup and bumpless transfer: A general theory," in Proc. Amer. Control Conf., vol. 2, Pittsburgh, PA, June 1989, pp. 1706-1711.
6. 2 performance," in Proc. Conf. Decision Control, vol. 2, Sidney, NSW, Australia, Dec. 2000, pp. 1063-1068.
7. C. Edwards and I. Postlethwaite, "Anti-windup and bumpless transfer schemes," in Proc. Int. Conf. Control, vol. 1, Sept. 1996, pp. 394-399.
8. ∞control," Int. J. Robust Nonlinear Control, vol. 4, no. 4, pp. 421-448, July-Aug. 1994.
9. P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox. Natick, MA: The MathWorks, Inc., 1995.
10. E. G. Gilbert, I. Kolmanovsky, and K. T. Tan, "Discrete-time reference governors and the nonlinear control of systems with state and control constraints," Int. J. Robust Nonlinear Control, vol. 5, no. 5, pp. 487-504, Aug. 1995.
11. R. Hanus, "Antiwindup and bumpless transfer: A survey," in Proc. 12th IMACS World Congr., vol. 2, Paris, France, July 1988, pp. 59-65.
12. ∞ control problem: LMI existence conditions and state space formulas," Automatica, vol. 30, no. 8, pp. 1307-1317, Aug. 1994.
13. P. Kapasouris, M. Athans, and G. Stein, "Design of feedback control systems for stable plants with saturating actuators," in Proc. Conf. Decision Control, vol. 1, Austin, TX, Dec. 1988, pp. 469-479.
14. H. K. Khalil, Nonlinear Systems, 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 1996.
15. M. V. Kothare, P. J. Campo, M. Morari, and C. N. Nett, "A unified frame-work for the study of antiwindup designs," Automatica, vol. 30, no. 12, pp. 1869-1883, Dec. 1994.
16. M. V. Kothare and M. Morari, "Multivariable antiwindup controller synthesis using multi-objective optimization," in Proc. Amer. Control Conf., vol. 5, Albuquerque, NM, June 1997, pp. 3093-3097.
17. _, "Stability analysis of antiwindup control schemes: A review and some generalizations," presented at the Euro. Control Conf., Brussels, Belgium, July 1997.
18. J. C. Lozier, "A steady-state approach to the theory of saturable servo systems," IRE Trans. Automat. Contr., pp. 19-39, May 1956.
19. V. R. Marcopoli and S. M. Phillips, "Analysis and synthesis tools for a class of actuator-limited multivariable control systems: A linear matrix inequality approach," Int. J. Robust Nonlinear Control, vol. 6, no. 9-10, pp. 1045-1063, 1996.
20. S. Miyamoto and G. Vinnicombe, "Robust control of plants with saturation nonlinearity based on coprime factor representations," in Proc. 35th Conf. Decision Control, vol. 4, Kobe, Japan, Dec. 1996, pp. 2838-2840.
21. E. F. Mulder and M. V. Kothare, "Synthesis of stabilizing antiwindup controllers using piecewise quadratic Lyapunov functions," in Proc. Amer. Control Conf., vol. 5, Chicago, IL, June 2000, pp. 3239-3243.
22. E. F. Mulder, M. V. Kothare, and M. Morari, "Multivariable antiwindup controller synthesis using linear matrix inequalities," Automatica, vol. 37, no. 9, pp. 1407-1416, Sept. 2001.
23. A. Packard, "Gain scheduling via linear fractional transformations," Syst. Control Lett., vol. 22, no. 2, pp. 79-92, Feb. 1994.
24. Y. Peng, D. Vrančić, R. Hanus, and S. S. R. Weller, "Anti-windup designs for multivariable controllers," Automatica, vol. 34, no. 12, pp. 1559-1565, Dec. 1998.
25. ∞-optimal control," Ph.D. dissertation, Univ. Wurzburg, Wurzburg, Germany, 1990.
26. G. Scorletti and L. El. Ghaoui, "Improved LMI conditions for gain scheduling and related control problems," Int. J. Robust Nonlinear Control, vol. 8, no. 10, pp. 845-877, Aug. 1998.
27. J. S. Shamma, "Anti-windup via constrained regulation with observers," Syst. Control Lett., vol. 40, no. 4, pp. 1869-1883, July 2000.
28. G. Strang, Linear Algebra and Its Applications, 3rd ed. New York: Harcourt Brace, 1988.
29. 2 antiwindup problem: Its definition and solution," presented at the Euro. Control Conf., 1997.
30. P. F. Weston and I. Postlethwaite, "Analysis and design of linear conditioning schemes for systems with nonlinear actuators," Dept. of Engineering, Leicester Univ., Leicester, U.K., vol. 98-6, Internal Report, 1998.
31. K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control. Upper Saddle River, NJ: Prentice-Hall, 1995.
32. F. Wu, K. M. Grigoriadis, and A. Packard, "Anti-windup controller design using linear parameter-varying control methods," Int. J. Control, vol. 73, no. 12, pp. 1104-1114, Aug. 2000.
33. L. Zaccarian and A. R. Teel, "A common framework for antiwindup, bumpless transfer and reliable designs," Automatica, vol. 38, no. 10, 2002.