On distributed delay in linear control laws - Part II: Rational implementations inspired from the δ-operator

IEEE Transactions on Automatic Control

Volumn 50, Issue 5, 2005, Pages 729-734

  Zhong, Qing Chang ^a  

^a UNIVERSITY OF GLAMORGAN   (United Kingdom)

Author keywords

operator; Dead time compensator; Distributed delay; Finite spectrum assignment; Implementation error; Modified Smith predictor; Rational implementation

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; DELAY CONTROL SYSTEMS; DISTRIBUTED PARAMETER CONTROL SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; LOW PASS FILTERS; OPTIMAL CONTROL SYSTEMS; SYSTEM STABILITY; TRANSFER FUNCTIONS;

DEAD TIME COMPENSATOR; DISTRIBUTED DELAY; FINITE SPECTRUM ASSIGNMENT; IMPLEMENTATION ERROR; MODIFIED SMITH PREDICTOR; RATIONAL IMPLEMENTATION;

LINEAR CONTROL SYSTEMS;

EID: 20344408528     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2005.847043     Document Type: Article

References (30)

1. A. Manitius and A. Olbrot, "Finite spectrum assignment problem for systems with delays," IEEE Trans. Autom. Control, vol. AC-24, no. 4, pp. 541-553, Apr. 1979.
2. K. Watanabe, "Finite spectrum assignment and observer for multivariable systems with commensurate delays," IEEE Trans. Autom. Control, vol. AC-31, no. 6, pp. 543-550, Jun. 1986.
3. Q. Wang, T. Lee, and K. Tan, Finite Spectrum Assignment for Time-Delay Systems. London, U.K.: Springer-Verlag, 1999.
4. K. Watanabe and M. Ito, "A process-model control for linear systems with delay," IEEE Trans. Autom. Control, vol. AC-26, no. 6, pp. 1261-1269, Jun. 1981.
5. Z. Palmor, "Time-delay compensation - Smith predictor and its modifications," in The Control Handbook, S. Levine, Ed. Boca Raton, FL: CRC, 1996, pp. 224-237.
6. Q.-C. Zhong, "Robust control of systems with delays," Ph.D. dissertation, Imperial College London, London, U.K., 2003.
7. ∞ control for dead-time systems," IEEE Trans. Autom. Control, vol. 45, no. 2, pp. 272-285, Feb. 2000.
8. ∞ control of dead-time systems based on a transformation," Automatica, vol. 39, no. 2, pp. 361-366, 2003.
9. L. Mirkin, "On the extraction of dead-time controllers and estimators from delay-free parametrizations," IEEE Trans. Autom. Control, vol. 48, no. 4, pp. 543-553, Apr. 2003.
10. ∞ control of processes with a single delay," IEEE Trans. Autom. Control, vol. 48, no. 6, pp. 1097-1103, Jun. 2003.
11. Q.-C. Zhong, "Control of integral processes with dead-time Part 3: Deadbeat disturbance response," IEEE Trans. Autom. Control, vol. 48, no. l, pp. 153-159, Jan. 2003.
12. P. Tam and J. Moore, "Stable realization of fixed-lag smoothing equations for continuous-time signals," IEEE Trans. Autom. Control, vol. AC-19, no. 1, pp. 84-87, Jan. 1974.
13. S. Mondié, R. Lozano, and J. Collado, "Resetting process-model control for unstable systems with delay," in Proc. 40th IEEE Conf. Decision and Control, vol. 3, Orlando, FL, 2001, pp. 2247-2252.
14. V. Van Assche, M. Dambrine, J. Lafay, and J. Richard, "Some problems arising in the implementation of distributed-delay control laws," in Proc. 38th IEEE Conf. Decision and Control, Phoenix, AZ, 1999, pp. 4668-4672.
15. O. Santos and S. Mondié, "Control laws involving distributed time delays: Robustness of the implementation," in Proc. 2000 Amer. Control Conf., vol. 4, 2000, pp. 2479-2480.
16. S. Mondié and O. Santos, "Approximations of control laws with distributed delays: A necessary condition for stability," presented at the 1st IFAC Symp. System Structure and Control, Prague, Czech Republic, Aug. 2001.
17. V. Van Assche, M. Dambrine, J. Lafay, and J. Richard, "Implementation of a distributed control law for a class of systems with delay," in Proc. 3rd IFAC Workshop on Time-Delay Systems, 2001, pp. 266-271.
18. K. Engelborghs, M. Dambrine, and D. Roose, "Limitations of a class of stabilization methods for delay systems," IEEE Trans. Autom. Control, vol. 46, no. 2, pp. 336-339, Feb. 2001.
19. L. Mirkin, "Are distributed-delay control laws intrinsically unapproximable?," presented at the 4th IFAC Workshop on Time-Delay Systems (TDS'03), Rocquencourt, France, Sep. 2003.
20. W. Michiels, S. Mondié, and D. Roose, "Necessary and sufficient conditions for a safe implementation of distributed delay control," in Proc. CNRS-NSF Workshop: Advances in Time-Delay Systems, Paris, France, Jan. 2003, pp. 85-92.
21. A. Fattouh, O. Sename, and J.-M. Dion, "Pulse controller design for linear time-delay systems," presented at the 1st IFAC Symp. System Structure and Control, Prague, Czech Republic, 2001.
22. S. Mondié and W. Michiels, "Finite spectrum assignment of unstable time-delay systems with a safe implementation," IEEE Trans. Automat. Control, vol. 48, no. 12, pp. 2207-2212, 2003.
23. J.-P. Richard, "Time-delay systems: An overview of some recent advances and open problems," Automatica, vol. 39, no. 10, pp. 1667-1694, 2003.
24. Q.-C. Zhong, "On distributed delay in linear control laws Part I: Discrete-delay implementations," IEEE Trans. Autom. Control, vol. 49, no. 11, pp. 2074-2080, Nov. 2004.
25. R. Middleton and G. Goodwin, "Improved finite word-length characteristics in digital control using delta operators," IEEE Trans. Autom. Control, vol. AC-31, no. 11, pp. 1015-1021, Nov. 1986.
26. R. Middleton and G. Goodwin, Digital Control and Estimation: A Unified Approach. Upper Saddle River, NJ: Prentice-Hall, 1990.
27. Y. Kannai and G. Weiss, "Approximating signals by fast impulse sampling," Math. Control. Signals, Syst., vol. 6, pp. 166-179, 1993.
28. C. N. Dorny, A Vector Space Approach to Models and Optimization. New York: Wiley, 1975, ch. 1-5.
29. Q.-C. Zhong, "Rational implementation of distributed delay using extended bilinear transformations," presented at the 16th IFAC World Congr., Prague, Czech Republic, Jul. 2005.
30. Q.-C. Zhong, Robust Control of Time-Delay Systems. London, U.K.: Springer-Verlag, 2006, to be published.